arguments for a new early vision model of lightness perception

A B S T R A C T

Lightness is the perceived relectance of a surface. Human observers are ca-pable of accurately judging the lightness of surfaces in diferent illuminationconditions, despite the fact that the retinal input to the visual system difersmarkedly for two identical surfaces seen under diferent illumination. heield of lightness perception is concerned with the question how the visualsystem achieves this feat, and how lightness is computed based on the spatio-temporal stimulation pattern on the retina. he ield is currently divided be-tween researchers who claim that most lightness phenomena are best under-stood as results of complex processes, requiring e.g. an estimation of the il-lumination ield, and those who maintain that many phenomena can alreadybe explained as results of early visual processing of simple stimulus features.he most prominent low-level account of lightness perception are spatial il-tering models with contrast normalization. heir popularity can be ascribedto two reasons: they correctly predict how human observers perceive a varietyof lightness illusions, and the processing steps involved in the models bear anapparent resemblance with known physiological mechanisms at early stages ofvisual processing. Here, I present two independent experimental approachesthat demonstrate the mechanistic inadequacy of current spatial iltering mod-els. he irst approach is based on globally masking stimuli with narrowbandnoise, the second on locally masking luminance edges with contour adapta-tion. he conclusion that current spatial iltering models are inadequate is sup-ported by computer simulations of four diferent models, all of which fail toaccount for the experimental data. he tested models are the ODOG model byBlakeslee and McCourt, the model by Dakin and Bex, the FLODOG modelby Robinson, Hammon and de Sa, and the BIWaM by Otazu, Vanrell andPárraga. he experimental part focuses on one particular stimulus, White’sillusion. his stimulus presents a challenge to classical low-level accounts of

lightness perception, which where based on luminance ratios across the edgesof a surface. Spatial iltering models on the surface appear to explain White’sillusion, which was part of their allure. However, the results presented hereshow that the mechanisms producing White’s illusion in these models arelikely not the same mechanisms responsible for the illusion in the human vi-sual system. he experimental results are generally compatible with a diferentlow-level approach, based on the explicit treatment of luminance ratios acrossedges, if an additional orientation normalization step is included. I review thehistorical development of edge-ratio based theories, and present a sketch of amodel that could integrate the present indings with these ideas.

Z U S A MM E N FA S S U N G

Die wahrgenommene Helligkeit einer Oberläche hängt von ihrer Relektanzab, d.h. von dem Anteil des eintrefenden Lichtes, der von der Oberlächerelektiert wird. Beobachter sind unter natürlichen Bedingungen in der Lage,die Helligkeit von Oberlächen relativ akkurat zu beurteilen. Dies ist inso-fern beachtlich, als die retinale Stimulation, und somit das Eingangssignalfür die Verarbeitung im visuellen System, sich für die selbe Oberläche in un-terschiedlichen Beleuchtungssituationen stark unterscheiden kann. Ein Zielder Forschung im Bereich der Helligkeitswahrnehmung ist es zu verstehen,wie das visuelle System dieses Problem löst, d.h. wie die wahrgenommeneHelligkeit aus dem Erregungsmuster auf der Netzhaut errechnet wird. EineKontroverse im Feld betrift die Frage, inwiefern die beobachteten Phänome-ne sich durch frühe kortikale Verarbeitungsschritte erklären lassen. Währendeinige Forscher der Meinung sind, dass die für Helligkeitswahrnehmung re-levanten Prozesse komplexe Verarbeitungsschritte wie z.B. die Interpretati-on der Beleuchtungssituation erfordern, gehen andere davon aus, dass vieleBeobachtungen bereits durch frühe kortikale Prozesse zu erklären sind. Dermomentan verbreitetste Ansatz in diesem Bereich sind Modelle, die auf räum-licher Filterung des Bildes in verschiedenen Raumskalen und anschließender

Kontrastnormalisierung beruhen. Die weite Verbreitung und Akzeptanz die-ses Ansatzes kann auf zwei Ursachen zurückgeführt werden: erstens stimmendie Modellvorhersagen für eine große Zahl von Helligkeitsillusionen quali-tativ mit der menschlichen Wahrnehmung überein, und zweitens ähneln dieVerarbeitungsschritte der Modelle bestimmten aus neurophysiologischen Un-tersuchungen bekannten neuronalen Prozessen im visuellen System. In dervorliegenden Doktorarbeit wird durch zwei voneinander unabhängige experi-mentelle Ansätze - einerseits globale Maskierung der Stimuli durch schmal-bandiges Rauschen, andererseits lokale Maskierung bestimmter Kanten durchFlickeradaptation - gezeigt, dass die aktuellen Modelle keine mechanistischadäquate Beschreibung der frühen Verarbeitungsschritte von Helligkeitswahr-nehmung darstellen. Diese Interpretation wird durch Computersimulationenvon vier verschiedenen aktuellen Modellen unterstützt, von denen keines dieexperimentellen Daten korrekt beschreibt. Die getesteten Modelle sind dasODOG Modell von Blakeslee und McCourt, das Modell von Dakin undBex, das FLODOG Modell von Robinson, Hammon und de Sa, und dasBIWaM von Otazu, Vanrell und Párraga. Der experimentelle Teil der Arbeitbeschäftigt sich mit einem bestimmten Stimulus: Whites Illusion. Dieser Sti-mulus war ein Problem für klassische Ansätze, die Helligkeitswahrnehmungdurch frühe Verarbeitungsschritte, insbesondere Luminanzkontraste an Kan-ten, zu erklären versuchten. Die auf räumlicher Filterung basierenden Model-le schienen diesen Stimulus erklären zu können, was einen Teil ihres Reizesausmachte. Die Resultate der vorliegenden Arbeit zeigen jedoch, dass die Me-chanismen, die im visuellen System für Whites Illusion verantwortlich sind,wahrscheinlich nicht die selben sind wie die, die den Efekt in den Modellenerzeugen. Stattdessen sind die experimentellen Resultate mit der klassischenAnnahme kompatibel, dass wahrgenommene Helligkeit von Luminanzkon-trasten an Kanten abhängt. Die historische Entwicklung von auf dieser An-nahme basierenden heorien wird beschrieben, und der Entwurf eines Mo-dells, das diese Ideen mit den aktuellen Ergebnissen verbinden könnte, wirdvorgestellt und diskutiert.

v

C O N T E N T S

I Ba 11 Introduction 32 History of edge-based accounts of lightness perception 73 White’s efect: a challenge to edge based accounts 17

II N a 474 Introduction 495 Multi-scale iltering models 536 Efects of noise on perceived lightness 597 Psychophysical experiment 638 Modeling results 719 Discussion 81

III C a a a 9110 Introduction 9311 Methods 9912 Results 10513 Computational modeling 11114 Discussion 119

IV C 12715 General discussion 12916 Outlook 149

R 153

Part I

B A C K G R O U N D

1I N T R O D U C T I O N

he paper on which you are reading this sentence is white. he letters formingthe sentence are black. Perceiving this presents no diiculty to a human ob-server, and you probably did not even have to pause to think about these twostatements. If you do pause to think about it, it is far from simple to explainhow we diferentiate between black and white. If you happen to be readingthis text outside on a beautiful sunny day, the black letters may relect morelight into your eyes than the white paper will in the more likely scenario thatyou are sitting at a desk in a dimly lit room. Nevertheless, in both scenarios,the paper will appear white and the letters black. Since the light relected intothe eyes determines the responses of the rods and cones that transmit informa-tion about the visual input to the brain, the above example presents a problem.Apparently, we are able to perceive the physical property relectance of surfaces,represented perceptually as colors such as black, white or gray, even thoughthe intensity of the light that these surfaces relect onto the retina does notuniquely determine any speciic relectance value. In fact, there is no uniquemathematical solution to the problem, since any retinal stimulation could arisefrom an unbounded number of diferent combinations of relectances and il-luminations (although not all of these combinations are equally plausible inthe real world). And still the visual system solves the problem every momentof our waking life. he goal of lightness research is to understand how thisis done, and in particular which properties of the spatio-temporal stimulationpattern on the retina determine perceived lightness. he present thesis focuseson one such property: the luminance ratios across the edges of a surface, i.e.the ratio between the luminance values on both sides of an edge.

he idea that luminance ratios at edges are an important factor in lightnessperception is by no means new, and there is extensive experimental evidence

4 B A C K G R O U N D

in its favor (see Chapter 2). However, we are lacking a comprehensive theorythat is based primarily on luminance ratios at edges and which explains per-ceived lightness in complex stimulus conigurations. Furthermore, the focus ofresearch in the ield has moved to either higher-level phenomena that cannoteasily be explained by local image properties (Knill & Kersten, 1991; Adelson,1993; Gilchrist et al., 1999), or sought low level explanations in terms of spa-tial iltering operations instead of edge ratios (Blakeslee & McCourt, 1999;Dakin & Bex, 2003; Robinson, Hammon, & de Sa, 2007; Otazu, Vanrell, &Párraga, 2008). his dissertation is an attempt to improve our understandingof the low-level processes that must constitute the irst steps in a completeaccount of lightness perception. he main body of the work critically evalu-ates the spatial iltering approach, which is arguably the most popular mech-anistic low-level account of lightness perception (Kingdom, 2011). I provideevidence against spatial iltering models and in favor of explicit processing ofluminance ratios at edges, both through model simulations and psychophys-ical experiments. he irst part of this thesis reviews some earlier work em-phasizing the importance of luminance ratios at edges. his is followed by areview of previous work on White’s illusion (White, 1979), which I use as atest stimulus throughout much of this thesis, and which provides a challengefor simple edge-based accounts. Part II introduces the main spatial ilteringmodels, and contains the results of a study comparing the efects of narrow-band noise masking on human lightness perception with the predictions ofthese models. he results suggest that spatial iltering models are unlikely tobe a correct explanation of lightness perception. Part III explicitly tests the roleof luminance ratios at edges with a contour adaptation paradigm and showsthat, at least in White’s illusion, surface lightness is determined at the edges.It also presents a sketch of a lightness model that is based on edge processing,and uses iso-orientation surround suppression to solve the problem of howdiferent edge-ratios are integrated. Like many scientiic investigations, theresults of this dissertation raise more new questions than they have answered.In part IV, I discuss some open questions, connect them to the literature, andpresent some ideas of how these questions may be tackled in future research.

I N T R O D U C T I O N 5

Since some central terms in the ield of lightness perception have histori-cally been used diferently by diferent authors, it will be useful to begin bydeining some important terminology used in this thesis. I use non-technicaldeinitions for most terms, because in the simple world of lat, matte surfacesand difuse illumination that is the domain of this thesis, these deinitions aresuicient. My usage will closely follow that of Gilchrist (2006).

L a : Luminance is the physical amount of light relected from asurface, or more accurately the luminous intensity per unit area. he SI unitof luminance is cd/m2.

R a : Relectance is the fraction of incoming light that a surfacerelects. It is unitless and in the range [0, 1].

L : Lightness is here used for perceived relectance. It is the achro-matic color of a surface, and ranges from black via gray to white. In somework, the term brightness is used to refer to perceived relectance, which ispotentially confusing because brightness can also refer to perceived luminance.Further complication is added by the fact that perceived relectance and per-ceived luminance cannot be cleanly separated in lat computer-generated stim-uli that have no separate illumination and relectance components. hus, inthese stimuli, lightness and brightness might be used interchangeably, but forconsistency, I will use the term lightness.

B : Brightness here refers only to the perceived luminance of animage region.

L a : An abrupt local change in the luminance proile of animage. Sometimes, the term luminance border is used instead in the literature.

C a : he term contrast can refer to a number of diferent concepts.First, it can describe the relation of the luminances of two diferent image


regions. his is the meaning usually implied in this thesis, and the deinitionused is Michelson contrast, which is computed as L1−L2

L1+L2, where L1 and L2

are the luminances of the two regions. his concept is closely related to thatof a luminance ratio between two regions, which would simply be L1

L2. Second,

contrast is often used to describe a perceptual efect where an image regionappears darker when its surround is light, and lighter when its surround isdark. his efect will here always be referred to as simultaneous lightness contrast(SLC), or simultaneous contrast for short. he term simultaneous brightness con-trast (SBC) is common in the literature, but is not used here in order to avoidthe confusion between lightness and brightness.

A a : Assimilation is here only used as a descriptive term, to in-dicate a lightness efect that is opposite in direction to that of simultaneouscontrast. I. e., image regions that look lighter when their surround becomeslighter are said to undergo assimilation. he term here does not imply anyspeciic process, nor does it imply that all assimilation efects have the samemechanistic cause.

2H I S T O RY O F E D G E - B A S E D A C C O U N T S O F L I G H T N E S S P E R C E P T I O N

he perceived lightness of a surface is inluenced by its surround. his basic fact

Illustration ofsimultaneouslightness contrast.

is easily demonstrated by the stimulus coniguration known as simultaneouslightness contrast (SLC, see illustration). In this stimulus, two equiluminantgray squares appear diferent in lightness, depending on the luminance of thebackground they are embedded in. he square on the dark background lookslighter than the square on the light background. Hering (1920) discussed theSLC efect in detail, and argued that it provides clear evidence for the depen-dence of perceived lightness on surround luminance. He also suggested thatthe mechanisms underlying this surround efect may be an important steptowards lightness constancy under diferent illuminations.

Wallach (1948) quantiied the relationship between the perceived lightnessof a test region and the luminance in its surrounds. He showed that in simpledisc-annulus displays, the lightness of the central disk is determined by theratio between the disk’s luminance and the annulus’s luminance, a result thatbecame famous as Wallach’s ratio principle.

Illustration of adisc-annulusstimulus used byWallach (1948).

Whittle and Challands (1969) also measured the inluence of backgroundluminance on target lightness (or brightness, which are inseparable in theirstimuli). heir data support Wallach’s ratio principle. One important aspectof their data is that targets that were increments relative to their surround al-ways appeared brighter than decrements, regardless of the absolute luminanceof the two targets. Further evidence for the importance of luminance ratiosacross edges came from a stimulus discussed independently by O’Brien (1958);Craik (1966); Cornsweet (1970), henceforth called the COBC stimulus. Inthis display, two equiluminant areas are connected by a step edge that grad-ually decreases or increases to the luminance of the homogenous surfaces onboth sides of the edge (see Figure 1). If the gradual change is subtle enough to


not be perceived, the stimulus appears to consist of two homogenous surfacesthat difer in lightness. he surface on the dark side of the edge looks darkerthan the surface on the light side of the edge. It appears as if the luminancediference at the edge is extrapolated to the entire surfaces.

Figure 1: Illustration of the Craik-O’Brien-Cornsweet (COBC) stimulus. Left: acommon version with two equiluminant rectangles joint by two ramps. heline at the bottom indicates the luminance proile of the stimulus above.Right: he illusion is enhanced in a circular version. he center of the discis equiluminant with the outer region of the ring, but appears lighter. heline at the bottom is the luminance proile through the vertical center of thestimulus.

he study of images stabilized on the retina also lent support to the ideathat only the luminance ratios at the edges are relevant for surface lightnessperception. Yarbus (1967) showed that after a few seconds of complete stabi-lization on the retina, all contours disappear from perception, and what Yarbuscalled an empty ield is formed. If only part of the visual ield was stabilizedagainst a moving background that did not disappear, the empty ield tookon the color of the background. Similar results have been reported by manyother researchers (Ditchburn & Ginsborg, 1952; Riggs, Ratlif, Cornsweet,& Cornsweet, 1953; Krauskopf, 1963). Yarbus (1967, p. 82) concluded:

In perception of a uniform surface, the eye extrapolates the appar-ent color from the edges of a surface to its center. he absence ofsignals from a particular area of the retina provides the eye with

H I S T O RY O F E D G E - B A S E D A C C O U N T S O F L I G H T N E S S P E R C E P T I O N 9

information that this area corresponds to a uniform surface, thecolor of which does not change and is equal to the color of itsedges.

In one experiment, he created conditions under which a large circle with oneblack and one white half became invisible against a red background throughstabilization. He then moved a small red circle on top of the large circle, suchthat it became visible due to the movement. If the small circle was in front ofthe white half of the large circle, it appeared very saturated, and darker thanthe background red. In front of the dark half of the large circle, the smallcircle appeared pink, and lighter than the background. hese results seem toindicate that the perceived color of the small circle depends on the color andluminance ratio at its edge. If the circle is seen against a dark background,it appears bright. If it is seen against a bright background, it appears dark.What is interesting is that the perceived color of the small circle seems tobe determined by integrating the edge ratio with the perceived color of thebackground.

Arend (1973) used these and other stabilized image results to argue thatsurface perception depends on a process that integrates the spatio-temporaldiferential signal obtained from retinal receptors. He used a number of dif-ferent stimuli to test how edge information determines perceived lightness(Arend, Buehler, & Lockhead, 1971). In one experiment, two equal incremen-tal patches were embedded on the two isoluminant sides of a COBC stimu-lus. In that coniguration, the patch on the side that appeared lighter lookedlighter than the patch on the perceptually darker side. his inding is inter-esting, because the local edge ratios of the two targets are identical, so if tar-get lightness was only determined by the local edge contrast, the two patchesshould appear identical. hus, the results conirmed the importance of lumi-nance ratios across edges for perceived brightness, but also emphasized thatsome edge integration mechanism that combines information from direct andremote edges is necessary. In this respect, it is analogous to the result of Yarbusdescribed above. Similar efects of remote edges were also obtained with iden-tical incremental patches superimposed on the isoluminant gray targets of a


simultaneous contrast stimulus (Shapley & Reid, 1985). In that stimulus, thepatch embedded in the target on the dark background appeared lighter thanthe patch embedded in the target on the light background, despite identicallocal edge ratios.

Retinex theory (Land & McCann, 1971), which aimed to account for light-ness constancy under shallow illumination gradients, proposed one answer tothe question of how edges are integrated: he theory efectively posits thatall edges are treated the same, regardless of their distance (both spatial andin terms of the number of intermittent edges) from the target surface. he as-sumption behind retinex theory is that the relative lightness of every surface ina complex scene can in principle be determined by comparing its luminanceto the luminance of a white standard. Since a white standard is usually notavailable directly adjacent to the target surface, precluding the possibility ofcomputing a direct luminance ration across an edge, the targets lightness isdetermined by sequentially multiplying the luminance ratios at all edges be-tween areas along a path connecting the target surface to the standard. In

Illustration of thepaths from the

highest luminancereference to the two

test patches in theSLC stimulus.

practice, the surface in the scene with the highest sequential luminance ratioto all other surfaces is taken as the standard. his theory ofers an explanationof lightness constancy in the presence of illumination gradients. Since locallyat both sides of any edge, the illumination is roughly equal, the luminanceratio is only determined by the relectance ratio between the neighboring sur-faces. Integrating relectance ratios will give the correct relectance ratio be-tween the target surface and the white standard, and thus lightness constancy.One problem with this theory is that it predicts veridical lightness perceptionin stimuli where human observers make errors. For example, a retinex-typeintegration would allow an observer to perceive the two test patches in the si-multaneous contrast display as identical. Assume that the dark surround has aluminance of 1cd/m2 and the bright surround has a luminance of 100cd/m2,while the test patches are both 50cd/m2. he relative lightness of the patchon the bright surround can be computed directly as 50cd/m2

100cd/m2 = .5. helightness of the patch on the dark surround is integrated along the path from


the bright surround to the dark surround, and from there to the test patch:1cd/m2

100cd/m2 ∗50cd/m2

1cd/m2 = .5.A further problem of retinex theory is that it only works if relectance edges

are sharp and illumination edges are shallow. Otherwise, some of the inte-grated ratios will not in fact be relectance ratios, while some relectance ratioswill not be integrated. Gilchrist, Delman, and Jacobsen (1983) have shownthat for human observers, it does in fact make a diference whether an edge isinterpreted as resulting from a diference in illumination or from a diferencein relectance. his result implies that a complete model of lightness percep-tion based on luminance ratios at edges needs to address the edge classiicationproblem. Retinex theory thus on the one hand failed to account for more orless veridical human lightness perception under complex stimulus conditions,and on the other hand failed to account for errors in lightness perception insimple stimuli like the simultaneous contrast display. Still, the mood in theield at the time is nicely expressed in a remark by Epstein (1982):

here is universal agreement that luminance ratios count promi-nently in determining perceived lightness.

here seemed to be no doubt that edge contrast determines surface lightness.he only question was how, and given the diiculties of edge integration andedge classiication in complex stimuli, this question proved to be a tough one.

he diiculties of formulating a computationally tractable, image-basedmodel of lightness perception based on edge contrast led to two diferenttrends. Part of the ield focused on the issues of edge classiication, and foundmany examples that showed that a simple low-level feature-based account oflightness perception is insuicient (Adelson, 1993; Knill & Kersten, 1991;Anderson, 1997; Gilchrist et al., 1999). Researchers in this tradition tend toexplain lightness phenomena by making reference to abstract concepts such asframeworks of illumination, intrinsic images, image layers, and the illumina-tion ield, removing the explanations one or several levels from simple imageproperties such as edge contrast. Others, inspired by the success of ilter-basedapproaches in spatial vision, developed image-based, low-level spatial iltering


models that correctly predicted perceived lightness in a number of well-knownillusions, without any explicit treatment of luminance edges (Blakeslee & Mc-Court, 1999; Blakeslee, Pasieka, & McCourt, 2005; Dakin & Bex, 2003;Robinson et al., 2007; Otazu et al., 2008). his second approach will be dealtwith in detail in Part II.

In recent years, some researchers have reemphasized the role of luminanceratios across edges. Rudd has argued for an edge integration approach thatis similar in spirit to the retinex model, but weights edges relative to theirdistance from the target surface (Rudd & Zemach, 2005; Rudd, 2010, 2013,2014). One problem of this approach is that when edges do not all receive thesame weight, the path along which one computes the ratio between the whitestandard and the target surface becomes relevant. Diferent paths can lead todiferent ratios, and so far, there is no mechanism in Rudd’s model that canpick an integration path, essentially limiting the model’s applicability to sim-ple stimuli consisting of central discs and any number of surrounding rings.Vladusich, Lucassen, and Cornelissen (2006) added further support for thiskind of weighted edge integration, again using disc and ring stimuli. Salmelaand Laurinen (2005, 2009) have examined the inluence of narrowband noisemasks on perceived lightness. hey found that noise in a narrow frequencyrange between 1 - 5 cpd can strongly inluence perceived lightness in a num-ber of classical illusions, while noise with higher or lower frequencies has littleefect. hey also reported that noise at these frequencies reduces the detectabil-ity of test patches, and that the most efective noise frequency was relativelyindependent of the spatial dimensions of the test patches. hey concluded thatthe 1 - 5 cpd noise afects the visibility of edges, and thus indirectly changesperceived lightness. In this interpretation, their results support the importantrole of edge contrast for lightness perception. hese experiments form the ba-sis of my critique of spatial iltering models, and are discussed in more detailin Part II.

Kurki, Peromaa, Hyvärinen, and Saarinen (2009) used a classiication imagetechnique to determine the features that are relevant for perceived lightnessin stimuli with a luminance step edge, as well as COCB edges. hey found


that perceived lightness is determined by the information at the edge, and thatthe absolute luminance level at the center of the surface has no inluence onperceived brightness.

Illustration of theefect of abackground gradienton the Chevreulillusion, after Hudakand Geier (2011).

Geier and Hudák (2011) showed that the perceived brightness gradients inthe Chevreul illusion can be greatly altered by introducing a gradient in thebackground of the luminance staircase that comprises the classical Chevreulstimulus. Despite the fact that the introduction of the gradient did not changeany of the luminances within the staircase, it dramatically changed the per-ceived luminance gradients on the individual steps of the staircase. he stan-dard illusion of induced gradients on the individual steps (top panel in mar-gin) is enhanced by a background gradient that has the same direction as thestaircase (middle panel), and reduced by a gradient of the opposite direction(bottom panel). he authors concluded that the luminance relationships acrossthe side edges of the staircase have a great inluence on perceived lightness.

he efect of luminance edges can be examined more directly in adaptationparadigms. Anstis (2013) tested the efect of adapting to lickering outlinesof shapes on the perceived contrast of solid shapes. He found that this contouradaptation could render entire low-contrast shapes invisible after licker adap-tation, even though no adaptation had taken place in the center of the stimuli.Perceptually, the stimuli were illed in with the gray value of the background(see also Anstis & Greenlee, 2014). One particularly interesting example stim-ulus with regard to the importance of luminance ratios for lightness perceptionis presented schematically in Figure 2.

In this stimulus, two light gray rings are shown next to each other on aslightly darker, mean gray background. One adaptor is lickered at the outeredge of the one ring, another one at the inner edge of the other ring. hepercept after adaptation at the inner edge is that of a large incremental discon the mean gray background. If the adaptor is lickered at the outer edge ofthe ring, observers perceive a small dark disc. Interestingly, this disc appearsdarker than the background, even though the region where it is perceived hasthe same luminance as the background. his percept can be explained if oneassumes that the adapted edges are not processed by the visual system, while


Figure 2: Schematic of the efect of contour adaptation on an incremental ring. Fromleft to right: actual stimulus; adaptor; approximate perceptual impressionafter adaptation. See text for details.

the unadapted ones are integrated. In that case, after adaptation to a largecircle, only the decremental inner edge of the ring is perceived, so the regioninside of that edge has to appear darker than the surround. After adaptation toa small circle, the inner edge is not processed, so the region inside of that edgeappears equal in luminance to the surrounding ring, which in turn is brighterthan the background. What remains unexplained in this account is why thesmall disc looks darker than it is, rather than the background becoming lighteraround it, which might be expected if the luminance of the ring bleeds intothe background through the adapted outer edge.

Adaptation experiments that support the crucial role of luminance edgesfor lightness perception were also reported by Robinson and de Sa (2012,2013), although these authors emphasize other issues in their presentationof the results and discussion. In these studies, the efect of solid adaptors ondetectability was tested. It was found that the detectability of test stimuli de-creased only when the edges of the adaptors where aligned with the edges of


the test stimulus. hese results can be interpreted to show that the processingof the edge ratios is critical for detecting a stimulus on a background, and inturn for perceiving it to difer in lightness from that background.

In summary, the importance of luminance ratios at edges has long been rec-ognized as one of the main factors determining perceived lightness. In simpledisc-annulus displays, lightness is determined entirely by the luminance ratioat the disc’s edge. In the COBC illusion, a local luminance step edge has anefect on the perceived lightness of large regions. And interfering with theperception of luminance edges in one of numerous ways greatly afects theperceived lightness of entire surfaces. hese insights have however not beenin the focus of the ield for some time. he present thesis adds to the body ofrecent evidence that is beginning to reemphasize the role of edges in lightnessperception, and provides strong arguments against one of the main competingapproaches, namely spatial iltering models.

3WH I T E ’ S E F F E C T: A C H A L L E N G E T O E D G E B A S E D A C C O U N T S

In 1979, White presented a stimulus that caused a problem for edge-contrastbased accounts of lightness perception (White, 1979). He showed that whengray patches were embedded in a black-and-white grating, those patches thatwere placed on the black bars of the grating looked lighter than the patchesthat were placed on the white bars (Fig. 3). Assuming a simple edge inte-gration scheme that weights the inluence of an edge’s luminance ratio efectby the length of the edge, a lightness computation based on luminance ra-tios would predict the opposite efect. Test patches placed on black bars sharemore border with white bars, and hence should appear darker than patchesplaced on white bars. Since the original publication, numerous attempts havebeen made to explain this illusion, and to integrate it with existing theoriesof lightness perception. However, to this day there seems to be no consensusabout how White’s illusion can be explained. Many of the accounts that havebeen put forward can successfully deal with one version of the stimulus, butfail to explain other variants, and unfortunately, often simply do not addressthem.

Due to the fact that it contradicts the predictions of a simple luminanceratio based account of lightness perception, White’s illusion has been usedas a critical test case for spatial iltering models. his is also the reason whythe stimulus was selected as the target of investigation in this thesis. On thesurface, it appears simple enough that a low level, early vision account of light-ness perception might suice to explain it. hus, I explore in parts II and IIIwhether spatial iltering models actually capture the critical features of hu-man lightness perception regarding White’s stimulus, and test the role of lu-minance ratios across borders for the perceived lightness of the test patches.In this chapter, I review previous research on the stimulus. I irst provide an


overview of the stimulus parameters that have been claimed to inluence theperceptual efect, and should therefore be accounted for by any successful ex-planation. I then review existing explanations and relate them to the relevantempirical efects in order to identify their respective successes and shortcom-ings. Finally, I highlight open questions, empirical and theoretical, that I feelneed to be addressed before a successful account of this efect can be given, anefect which has puzzled lightness researchers for over 30 years.

3.1 R E L E VA N T S T I M U L U S P R O P E R T I E S

In his original publication on the stimulus, White (1979) noted that the strengthof the efect is rather independent of the length of the gray test patches, whichwould indicate that the relative amount of shared border with the bars of thecarrier grating is not important. He also observed, by looking at his demosfrom diferent distances, that the efect was stronger at higher spatial frequen-cies of the grating (i.e. when the stimulus was viewed from further away). Fi-nally, he claimed that the efect was weakened if fewer test patches were pre-sented. Over time, a number of additional stimulus properties have been re-ported to afect the strength, or sometimes even the occurrence, of the illusion.hese include the presence and extent of the carrier grating (White, 1981;Moulden & Kingdom, 1989), the orientation and phase of the test patcheswithin the grating (White, 1981), the relative luminance relations betweenthe light and dark bars of the grating and the test patches (Spehar, Gilchrist,& Arend, 1995; Ripamonti & Gerbino, 2001), the depth of the test patchesrelative to the bars (Taya, Ehrenstein, & Cavonius, 1995), and the percep-tion of the test patches as transparent. Many of these stimulus properties havebeen manipulated in a number of diferent studies yielding diferent results.Below, I will review the available data for each of the above mentioned stim-ulus parameters, and comment on the experimental conditions under whichthey were obtained.

WH I T E ’ S E F F E C T: A C H A L L E N G E T O E D G E B A S E D A C C O U N T S 19

Figure 3: Original demonstration of White’s efect, recreated from White (1979).he stimulus is reproduced here in full size in order to keep the spatialfrequency of the grating comparable to the original presentation.


3.1.1 T E S T PAT C H A S P E C T R AT I O

White (1979) was the irst to point out that the strength of the illusion wasrather unafected by the height of the test patches (compare Fig. 4 to Fig. 3).his property has been taken as one of the deining features of the stimulus(e.g., Blakeslee & McCourt, 1999). It was later conirmed empirically, whenWhite and White (1985) showed that two versions of the stimulus with as-pect ratios of 5:1 and 1:1 resulted in similar lightness diferences. Kingdomand Moulden (1991, Exp. 2) on the other hand reported a reduction in theperceived lightness diference when taller test patches were tested (aspect ra-tios tested were 3:1 and 1:1). However, the experiments are hard to comparebecause White and White (1985) tested naive observers (n=15), with a gratingthat contained 12 bars in total (spatial frequency of 3 cpd) and four patchesfor the test, whereas Kingdom and Moulden (1991) tested the two authors,with a grating consisting of only three bars (spatial frequencies of 2.5, 1.25and 0.63 cpd) and a single test strip. Spehar, Cliford, and Agostini (2002)tested two diferent aspect ratios (5:1 and 1:5) and found a small reduction inthe lightness diference for the smaller aspect ratio, i.e. the wider test patches.However, the aspect ratio manipulation co-occurred with a spatial frequencychange, so it is diicult to say which of the two properties actually causedthe change in efect size. Blakeslee and McCourt (2004) tested four observers(two naive) with four diferent aspect ratios (1:1, 1:2, 1° height, 3° height)at diferent spatial frequencies. hey found that aspect ratio had a small in-luence on illusion strength at the highest spatial frequency, where the ixedheight test patches had aspect ratios of 8:1 and 24:1. For one observer, smalleraspect ratios led to a larger efect, while for the other three, larger aspect ra-tios led to larger efects. Only one observer showed an efect of aspect ratioat lower spatial frequencies. In conclusion, the idea that the illusion is rela-tively independent of test patch aspect ratio is widespread (e.g. White, 1979;Blakeslee & McCourt, 1999; Howe, 2005). he empirical data largely supportthis claim, but complex interactions with the efect of spatial frequency showthat the independence is not absolute.


Figure 4: Version of White’s stimulus with diferent test patch aspect ratio comparedto Figure 3, recreated from White (1979).


3.1.2 S PAT I A L F R E Q U E N C Y O F T H E C A R R I E R G R AT I N G

Like test patch height, spatial frequency was one of the parameters discussedin White’s original publication of the stimulus. he irst data on this camefrom Kingdom and Moulden (1991), who found that increasing the width ofthe inducing bars without changing test patch height (i.e. letting test patch as-pect ratio vary) increased the perceived lightness diference. his is opposite toWhite’s (1979) observation of an increase in lightness diference with higherspatial frequencies, because an increase in bar width corresponds to a decreasein spatial frequency. When the aspect ratio was kept constant, however, in-creasing spatial frequency (or rather 2D spatial scale) resulted in a larger light-ness diference (Kingdom & Moulden, 1991, Exp. 1). Taya et al. (1995) pre-sented stimuli at four diferent spatial frequencies (1.1 to 8.7 cpd) and withconstant height, and found an increase in efect size with increasing spatialfrequencies. It should be noted that their aspect ratios were all at least 2:1, notswitching between portrait and landscape, while in Kingdom and Moulden(1991, Exp. 1), aspect ratios varied from 4:1 to 1:4. Furthermore, spatial fre-quency in Taya et al.’s experiment was confounded with the number of testpatches present, because the width of the area covered by test patches waskept constant. Blakeslee and McCourt (1999) reported data on stimuli withtwo diferent spatial frequencies (.25 and .5 cpd) and constant aspect ratios.Although they did not directly compare the data, the error bars on their resultigure indicate that there was no signiicant diference in efect size betweenthe aspect ratios for the two subjects tested. Spehar et al. (2002) collected dataon two diferent spatial frequencies, but they also covaried with aspect ratios,and the efect sizes were not compared statistically. Blakeslee and McCourt(2004) examined the efect of spatial frequency (0.25 to 4 cpd in six steps)with four diferent test patches, two of them with ixed height, two with ixedaspect ratio (1:1 and 1:2). hey found an increase in efect size with increas-ing spatial frequency for all four observers (two naive). he increase began ata spatial frequency of about 1 cpd, and was observed at all test patch heightsfor three out of the four subjects. Finally, (Anstis, 2005) reported data from


two naive subjects, showing an increase in efect size over a spatial frequencyrange from 0.63 to 7.5 cpd (aspect ratios were constant). To summarize, themajority of the evidence now seems to indicate an increase in White’s illusionwith increased frequency, but specifying the exact interaction with the efectof changing aspect ratios may require additional data.

3.1.3 N U M B E R O F T E S T PAT C H E S

White (1979) claimed that reducing the number of test patches reduces thestrength of the illusion without destroying it (compare Fig. 5 and Fig. 3). Insubsequent studies, both versions of the stimulus with single and multipletest patches have been used, but the inluence of the number of test patcheson the strength of the illusion has not been examined systematically. Com-paring efect sizes between studies seems to support White’s notion, but thisis not authoritative, because other factors varied between these studies, too.he number of test patches may exert an indirect efect on illusion strength,because it might inluence whether the patches are perceived as one surfacethat is occluding or being occluded by the grating bars. his will be furtherdiscussed in Section 3.1.7.

3.1.4 E X T E N T O F T H E C A R R I E R G R AT I N G

In an attempt to reduce White’s stimulus to its essential components, someauthors (e.g. Moulden & Kingdom, 1989; Zaidi, 1990; Kingdom & Moulden,1991) have used very restricted stimulus conigurations that contained, for ex-ample, only one black and two white bars (or vice versa), with the test patchplaced on the central bar. his approach was based on the assumption that theextended stimulus was of less importance to the efect. However, such an as-sumption may be premature, because at least some of the theoretical accountsattribute a role to the larger context (see Section 3.3). To date, the inluenceof the larger context on the illusion has not been systematically examined. A


Figure 5: Version of White’s stimulus with only one test patch on each grating phase,recreated from White (1979).


related stimulus aspect is the length of the bars that constitute the grating.Moulden and Kingdom (1989) examined this by separately manipulating thelength of the bar on which the test patch was placed, and the lengths of thetwo adjacent bars (their grating consisted of only three bars). hey found thatwhen grating height matched test patch height, White’s efect was reversed(for one of two observers) as in simultaneous lightness contrast, and hence atest patch between white bars looked darker than a test patch between darkbars. As soon as there was a minimal diference between lanking bars and teststrip height (⩾ 0.1° visual angle) White’s illusion was preserved, and almostimmediately achieved its full magnitude. he same was true for the height ofthe bar on which the test patch was placed: increasing the height of the barbeyond that of the test patch increased the lightness efect. In an extendedgrating with multiple cycles, the extent of the two types of bars cannot be sep-arated so easily. he efect of extending the entire grating above and below thetest strip has not been examined. Surprisingly, it is not even certain whetherthe grating has to extend above and below the test patch at all.

3.1.5 T E S T PAT C H O R I E N TAT I O N A N D P H A S E

In the classical White’s illusion, the test patches are perfectly aligned withthe inducing grating. White (1981) examined the efect of rotating the testpatches and the immediately surrounding grating by 90°. For patches placedon black bars this reduced the induced lightening of the test patch by aboutone Munsell step. For patches placed on white bars it had no signiicant efect.he inluence of parametrically varying test patch orientation has not beenexamined.

White and White (1985) shifted the phase of the test patch with respect tothe inducing grating and found a gradual efect. he patch appeared lightestwhen it was in phase with the dark bars, and darkest when it was in phasewith the white bars. his is the classical illusion. Intermediate phases led tointermediate perceived lightness levels, the more the patch was shifted fromblack to white, the darker it appeared. Blakeslee and McCourt (1999) have


repeated this experiment, and report that the test patches appeared inhomo-geneous in lightness at intermediate positions. Observers perceived the sideof the test patch superimposed on the dark grating bar as lighter, and the sideon the light bar as darker. his efect has not been noted by White and White(1985), which may be due to the fact that very thin test patches had been used.However, Ripamonti and Gerbino (2001) used test patches shifted by 90°, i.e.exactly in between black and white bars, and reported that robservers adaptedto the procedure without any apparent efort.s (Ripamonti & Gerbino, 2001,p. 479). his may indicate that there was no striking inhomogeneity.

3.1.6 R E L AT I V E L U M I N A N C E R E L AT I O N S

Spehar et al. (1995) were the irst to point out the importance of the relativeluminance relations between the test patches and the inducing grating. heyshowed that White’s illusion is only observed when the test patch luminance isin between the minimum and maximum luminance of the grating. In Speharet al.’s (1995) data, there was no signiicant diference in perceived lightnessbetween test patches that were lighter than both dark and light grating bars(double increments). For test patches that were darker than the grating bars(double decrements), results were somewhat inconsistent across the three ob-servers, but the efect was either absent, or in the opposite direction of White’sefect. he patch on the darker bar appeared darker than the patch on thelighter bar. Ripamonti and Gerbino (2001) measured the perceived lightnessof test patches in a matching paradigm and found that the efect on doubledecrements and double increments was in the opposite direction to the classi-cal White’s illusion, and considerably smaller.

3.1.7 D E P T H A N D T R A N S PA R E N C Y

Taya et al. (1995, p. 687) noticed rthat the test grey bars may be perceivednot as separate bars but as a rectangle located in front of or behind the grid.s


hey investigated whether this percept inluenced the strength of the illusionby stereoscopically presenting the test patches in three diferent depth planes:in front of the grating, coplanar with the grating (standard White’s stimulus),and behind the grating. hey found that White’s efect was strongest whenthe to-be-compared test patches were presented in front of the grating. In thatcondition the patches appeared to constitute a transparent rectangle. he efectwas weaker, but still enhanced compared to the standard coplanar condition,when the test patches were presented behind the grating. In this condition,the grating was perceptually divided in depth, because the bars that containedthe test patches were perceived as a uniform background, the test patches werealso perceived as a continuous surface, but occluded by the bars of the othercolor which appeared to be in front.

Reproduction ofAnderson’s (1997)demonstration thattest patch alignmentis not critical.

A role for perceived transparency in White’s efect has been pointed out byAnderson (1997). He also presented a demo suggesting that the perceptualcompletion of the test patches into a continuous surface is not relevant forthe transparency impression. In that stimulus, the illusion does not appear tochange much when the vertical position of individual test patches was jittered.Ripamonti and Gerbino (2001) tested which combinations of grating and teststrip luminances led to percepts of transparency, and found that White’s illu-sion occurred for stimulus conditions where there was no conscious perceptof transparency.

Zaidi, Spehar, and Shy (1997) examined the efect of perceived depth onWhite’s illusion with perspective instead of stereoscopic cues to depth. heyreported that the perceived 3D structure of their stimuli was irrelevant, andthat the local 2D layout, which was similar across diferent 3D conigurations,was suicient to explain the observed efects. However, according to Gilchrist(2006, p. 171), this lack of 3D efect may have been due to the limited lumi-nance range in the study by Zaidi et al. (1997).


3.1.8 R E L AT I V E E F F E C T S I Z E C O M PA R E D T O O T H E R L I G H T N E S S I L L U S I O N S

Another aspect of the illusion that could constrain potential explanatory at-tempts is the relative efect size compared to other lightness illusions, in par-ticular with respect to simultaneous lightness contrast. White (1981) reportedthat the illusion was three times larger than simultaneous contrast. his claimhas been repeated by Anderson (1997, p. 8): robservers uniformly report thatthe Munker-White illusion is stronger than either of these patterns.s, wherethe patterns in question were two forms of simultaneous contrast. he claimis also found in Gilchrist (2006, p. 281) without an explicit reference to aparticular experiment. On the other hand, it has been reported that White’sefect is smaller than simultaneous lightness contrast (Blakeslee & McCourt,1999). hese authors reported efect sizes for White’s illusion similar to thosereported by Zaidi et al. (1997), but measured contrast efects that were 1.5 -3 times larger, depending on the size of the test patch in the contrast display.It may be worth noting that the subjects in that study were identical to thetwo authors, and that the inding of a larger contrast efect agrees with theirmodel prediction. White (1981) on the other hand tested 104 naive observers.In general, it seems diicult to make universal comparisons between efectssizes in White’s illusion and simultaneous contrast, because the strength ofboth efects can be greatly inluenced by a number of diferent stimulus pa-rameters. What is needed is empirical data from naive observers when thetwo types of stimuli are presented under comparable conditions, ideally over arange of spatial frequencies and test patch sizes. Since the question of what arecomparable conditions cannot be answered independently of a theory aboutwhich factors inluence the two illusions, this problem cannot be solved aseasily as it might appear.

3.1.9 ( A ) S Y MM E T RY B E TW E E N L I G H T E N I N G A N D D A R K E N I N G E F F E C T S

A general problem in the quantiication of lightness efects is whether a per-ceived lightness diference between two equiluminant targets results from a


selective lightening of one of the targets, a darkening of the other, or from acombination of the two efects (see e.g. the debate between Blakeslee, Reetz,& McCourt, 2009; Economou, Zdravković, & Gilchrist, 2007). Establish-ing a symmetry or asymmetry between lightening and darkening can be im-portant for deciding between competing explanations of an efect, but it isalso diicult, because one needs to identify a neutral point of rveridicals light-ness perception. his can be illustrated with the original measurements byWhite (1981). In his experiment, the test patches were made of mid-gray pa-per (Munsell 5), and the task was to match the paper within the grating to acomparison paper on a complete achromatic Munsell scale. he test patcheson black bars received an average rating of 7.3, the test patches on white barswere rated 4.6. his could suggest that the efect was mostly due to a light-ening of the patches on black bars. However, the matching palette itself waspresented on a white background, and that could have caused a perceptualdarkening of the matching papers. In such a setup, it is hardly possible to se-lectively attribute the observed efect to either a lightening or darkening ofthe two types of test patches.

Moulden and Kingdom (1989) reported that test patches ranging in lumi-nance from 16-24 cd/m2 appeared darker in both grating positions than theywould if presented against a homogeneous (neutral) background of 20 cd/m2.his would indicate that White’s illusion is exclusively an efect of darkeningof the test patch embedded on the white bar, and that the illusion is actu-ally weakened by the fact that the test patch on the dark bar is also darkened,but to a lesser degree. However, whether a 20 cd/m2 uniform background,which was the spatial average of their grating luminance, constitutes a neutralbackground is an open question.

he data of Taya et al. (1995) could also be interpreted as showing an asym-metry between darkening and lightening. While the lightening of the testpatches on the black bar was weak and present only at the highest spatial fre-quency of 8.7 cpd, the darkening of the test patch on the light bar was strongerand present at all spatial frequencies. Participants in this experiment had tomatch the test patches to Munsell chips which they held in their hands, and


the neutral value was determined prior to the main experiment by matchinguniform gray screens of diferent luminances to the Munsell chips. Whetherthis really established neutral values is questionable and may depend on un-known factors such as the color of the monitor encasing. An interesting aspectof Taya et al.’s data is that the asymmetry seemed to disappear in the condi-tions where the test patches were presented in a diferent depth plane than thegrating. One caveat to these results is that the two types of test patches werenot equiluminant. he Munsell value that corresponded to the luminance oftest patches on dark bars in the full screen calibration version was 6.55, andthat of test patches on light bars was 5.85.

Spehar et al. (1995) measured lightness and darkness induction as a functionof the inducing grating luminance. heir matches were made with adjustablegray patches presented on a black-and-white checkerboard pattern, the min-imal and maximal luminance of which were the minimal and maximal lumi-nances of the gratings that were used in any of their experiments. hey found astronger efect of lightening in conditions where both grating bars were muchdarker than the white checks in the matching display. hey found a strongerdarkening efect in the other conditions, sometimes with both test patches ap-pearing darkened. In a later study using a similar matching paradigm, Speharet al. (2002) found mostly lightening when the grating was dark comparedto the checkerboard, but found a relatively symmetric efect (on the Munsellscale) for a brighter grating.

Blakeslee and McCourt (1999) pointed out that there were some asymme-tries in their matching data, without discussing them further in that article,or providing statistics. From inspecting the results igure, it seems that theirasymmetry is also in the direction of more darkening than lightening. hebackground for their matching stimuli was a homogenous ield set to the meanluminance of the grating. In a later study with the same matching task, theyfound that increasing the spatial frequency of the grating caused the patch onthe dark bar to appear lighter and the patch on the light bar to appear darker(Blakeslee & McCourt, 2004). his would suggest that White’s illusion de-pends on a combination of lightening and darkening.


Ripamonti and Gerbino (2001) tested for symmetry efects in White’s stim-ulus with reference patches that were embedded in the test grating, but 90°

phase-shifted compared to the test patches, and hence located half-way ondark and light bars. hey observed comparable efect sizes for test patches sit-ting on dark and light bars and interpreted this to argue against any asymmetry.his is problematic, because if we alternatively assume that only the patcheson dark bars undergo a lightening efect while the patches on light bars remainrneutrals, then it is possible that the reference bars, sitting to 50% on top ofa dark bar, might undergo partial lightening, and hence their lightness wouldbe exactly in between that of the test patches.

Anstis (2005) reported that at low spatial frequencies (0.63 cpd) both typesof test patches appeared darker than their actual luminances. When the spa-tial frequency was increased the patches on light bars became darker, and thepatches on dark bars became lighter. At 7.53 cpd the efect was approximatelysymmetrical. Unfortunately in that study no details were given on the back-ground of the matching patch. Still, plotting the matching data as a functionof spatial frequency seems to provide an opportunity to test for symmetry,because it removes the requirement of establishing a neutral value.

A question that complicates matters is that of the right scale to assess sym-metry. It is known that luminance does not linearly translate into lightness.he Munsell neutral value scale tries to address this problem by providing graypapers that are supposed to be equidistant in perceptual space. he transfor-mation used is a cubic root (Pauli, 1976). Another common approach is to uselog-luminance values (e.g. Gilchrist, 2006). If we take an example where a testpatch has a luminance of 100 cd/m2 and is matched to a 90 cd/m2 referencein one condition and to a 110 cd/m2 reference in another, then this is sym-metrical on a linear scale. On a log scale, however, the darkening would be0.046, while the lightening would only be 0.041. It should be noted that thisreasoning cannot be invoked to explain the conlicting results reported above,because White (1981) and Taya et al. (1995) both measured lightness in Mun-sell units. Furthermore, data that already show a stronger efect of darkeningon a linear scale will of course still do so on a logarithmic or Munsell scale.


he extent to which White’s efect can be attributed to darkening of oneof the test patches or lightening of the other remains an issue of debate.Notonly are the empirical data inconclusive, but it is unclear how to best designan experiment that would properly address this question. he most promisingapproach seems to be an indirect one of measuring whether manipulationsthat change the strength of the illusion do so for test patches on both types ofbars.

3.2 S T I M U L U S VA R I A N T S

he circular White’sillusion, recreated

from Howe (2005).

In addition to parametrically manipulating certain stimulus parameters andobserving the efect on the lightness illusion, there have also been attemptsto derive new variants of the stimulus in order to identify those parts thatare essential for the lightness illusion. he three most relevant variations withrespect to the proposed mechanisms discussed below are the textured White’sillusion (Anderson, 2003), the circular White’s illusion (Howe, 2005), and theradial White’s illusion (Robinson et al., 2007; based on an online presentationby Anstis).

In the textured White’s illusion, the gray test patches are replaced by a black-and-white noise pattern. Although the same pattern is placed on the black andand on the white bars, Anderson reports that subjects perceive the pattern asvery diferent depending on which bars it is placed on. In a control conditionwhere the pattern is placed on a uniform black or white background insteadof the grating, the perceptual diference is much reduced. He also describesthat when the pattern is placed on black bars, it is seen as a white occlusivescreen with holes through which the black background can be perceived, andvice versa for the pattern placed on white bars. his claim, however, is notsystematically assessed in his experiment, perhaps because the impression onegets when looking at the demonstration is so striking that it was deemed un-necessary to verify.

In the circular White’s illusion (Howe, 2005) the grating of parallel bars isreplaced by concentric circles, and instead of gray patches some of the black or


white rings are replaced by gray ones. As in the classical White’s illusion, graycircles placed between black ones appear darker than those placed betweenwhite ones. Howe also included a control condition where the concentric ringsare replaced by a uniform black or white background. In this case, the efectalmost disappeared, and the gray rings looked similar on both backgrounds.his excluded the possibility that the circular White’s illusion is merely anefect of assimilation between the gray rings and their immediate surround,because such an assimilation efect should be at least as strong in the controlcondition.

he radial White’sillusion, recreatedfrom Robinson et al.(2007).

he radial White’s illusion (Robinson et al., 2007) consists of circular sectorsalternating between black and white. Parts of these sectors are replaced by graytest patches. he efect seems to be similar to the classical White’s illusionbut no data have been published with this stimulus. he importance of thisstimulus comes from the fact that it contains almost identical energy at allorientations. hus, it is a critical test case for explanatory accounts that relyon orientation-speciic mechanisms

3.3 P R O P O S E D M E C H A N I S M S

As mentioned in the opening paragraph of this chapter, a simple account basedon luminance ratios across edges cannot explain White’s illusion, because itwould predict the opposite to the observed lightness efect: test patches thatshare more border with white bars should appear darker, and patches thatshare more border with black bars should appear lighter. he assumption thatan edge’s inluence depends on its length, which underlies the rejection ofedge-ratio based explanations of White’s illusion, is seldom made explicit. hismay be a result of the fact that historically, the mechanism underlying the lu-minance ratio computation was thought to be lateral inhibition in the retina orlateral geniculate nucleus. If one interprets the statement rperceived lightnessdepends on luminance ratios across edgess as rperceived lightness dependson the iring of neurons responsive to a surface after lateral inhibition fromneurons responsive to neighboring surfacess, then this explanation is indeed


challenged by White’s illusion. hus, if the illusion is to be explained in termsof luminance ratios across edges, an additional mechanism is required thatcauses the edges between the test patch and the bar on which it is placed to beweighted more strongly than the edges between the test patch and the lankingbars.

It has also long been known that contrast, in the sense of a perceptual en-hancement of the diference between two regions, is not the only possibleefect of the context on a target region. Under certain conditions the per-ceived lightness of a retinal image region can shift towards the lightness ofthe surround, a phenomenon called assimilation (Helson, 1963). While someauthors use the term assimilation to indicate a mechanism by which spatialsmoothing over large receptive ields causes the lightness efect (e.g. Jameson& Hurvich, 1975), others use the term simply to describe any efect that isopposite in direction to contrast (e.g. Ripamonti & Gerbino, 2001; Spehar etal., 2002). Given the direction of the efect, White’s illusion can be regardedas an instance of assimilation of the test patch to the lanking bars of the grat-ing. However, the mechanistic interpretation of the term indicating spatialsmoothing cannot be taken as an explanation of all instances of the illusion,because the spatial frequencies at which White’s efect has been reported tooccur are much lower than those found for assimilation (Helson, 1963). Usingthe term assimilation simply to describe the direction of the efect adds little interms of theoretical understanding. In the following section, mechanisms willbe summarized that have been proposed to account for White’s efect. Someauthors actually invoked a combination of diferent mechanisms, such as con-trast from the carrier bar and assimilation to the lanking bars. While there isno a priori reason to assume that all the perceptual efects that have been re-ported under the label White’s illusion are caused by a single mechanism, and itis indeed possible that multiple causes interact to evoke the reported percept,the diferent mechanisms will be kept separate here for the sake of clarity. Allmechanisms discussed here, together with an evaluation of which stimulusproperties they can and cannot explain, are summarized in Table 1.


3.3.1 PAT T E R N - S P E C I F I C I N H I B I T I O N

White (1981) proposed that regular patterns are self-inhibitory, potentiallythrough a gain control mechanism. According to this explanation, the inhibi-tion leads to decreased contrast of the grating, making the dark phase lighterand the light phase darker. his efect carries over onto the test patches andcauses them to appear lighter when placed on the dark bars and vice versa. InWhite’s view, there may still be a contrast efect from the lanking bars thatworks in the opposite direction to the pattern-speciic inhibition, but the latterefect is stronger, and thus determines the direction of the perceptual efect.

Pattern-speciic inhibition can potentially be used to explain an increasein efect size with increasing spatial frequency, since the inhibition could befrequency dependent. he relative weight of the assimilation efect comparedto the contrast efect could then increase with increasing grating frequency.Similarly, small changes in efect size caused by changing test patch heightcould be explained through a changed contrast-assimilation balance. However,it is not clear how the efects of depth and perceived transparency should beintegrated into this theory. Also, the existence of the circular White’s illusionwould require that not only parallel gratings, but also circular ones are self-inhibitory.

he pattern-speciic inhibition account is in conlict with the results re-ported for stimuli with test patch luminances that were lower or higher thanthe grating range (see Section 3.1.6). However, it could be argued that the re-duction in grating contrast that is necessary to produce these stimuli leads to areduction in pattern-speciic inhibition. If one assumes that the perception ofWhite’s stimulus depends on a combination of pattern-speciic inhibition andcontrast from the lanking bars (as White did), it could be that in these stimu-lus conigurations, contrast is simply the stronger of the two competing mech-anisms. While interesting on a descriptive level, the idea of pattern-speciicinhibition was not developed quantitatively, so it is diicult to evaluate whatits predictions would be in detail.


As formulated by White, pattern-speciic inhibition is not an edge basedexplanation, but assumes that the perceived lightness of the bars is signaledby neurons that are tuned to the spatial frequency of the grating. Still, theidea that the grating is self-inhibitory, and that this inhibition leads to a re-duction in perceived contrast between the test patches and their lanking barscan also be incorporated into an edge based account (see Section 14.1 andSection 15.1).

3.3.2 C O R N E R R E S P O N S E A F T E R S PAT I A L F I LT E R I N G

Another proposed explanation contends that center-surround iltering of theinput leads to a particularly strong response on the bar that carries the testpatch just outside of the corners of the test patch (Moulden & Kingdom,1989; Kingdom & Moulden, 1991). he authors suggested that a secondary,unspeciied mechanism operating on the output of this center-surround stagecould use the corner signal to disproportionately weight the carrier bar in asubsequent contrast computation determining the perceived lightness. Sincethe center-surround stage already instantiates a contrast computation, it is un-clear what this second stage is supposed to be doing in general. Apparently,at least one of the original authors meanwhile endorses a diferent model (seeSection 3.3.6) that does not require the secondary stage (Kingdom, 2011).

3.3.3 C O N T R A S T M E D I AT E D B Y T- J U N C T I O N S

A number of authors have proposed that White’s illusion is mediated by thejunctions formed at the intersections of test patches, lanking bars and car-rier bars (Anderson, 1997; Todorović, 1997; Zaidi et al., 1997). Zaidi et al.claimed that T-junctions cause the test patches to be grouped with their car-rier bars and separated from the lanking bars. A contrast computation thatweights the carrier bar stronger then (or even completely ignores) the lank-ing bars would cause a lightness illusion in the direction of White’s efect.


his contrast computation could be based on the luminance ratios across thetest patches’ edges. Anderson (1997) pointed out that such an explanationwould limit the maximal efect size of White’s illusion to that of simultaneouscontrast, and because he observed White’s illusion to be stronger than simul-taneous contrast, he argued against this explanation. However, as discussed inSection 3.1.8, the premise of this argument is not universally agreed upon. heT-junction account is also called into question as a complete explanation ofthe efect by two stimulus manipulations discussed by Howe (2000, 2005). hecircular White’s illusion does not contain any T-junctions, an yet it retains theillusion (Howe, 2005). he stimulus presented by Howe (2000) achieves theopposite: it largely abolishes the illusion without changing the local junctionstructure of the test patches. Furthermore, the T-junction contrast accounthas no immediate explanation for the inluence of global stimulus propertieson efect size, such as the spatial frequency or the extent of the grating.

3.3.4 A N C H O R I N G T H E O RY

According to anchoring theory (Gilchrist et al., 1999), visual scenes are seg-regated into diferent frameworks of illumination, within which luminanceratios are computed. he highest luminance within each framework is ran-choreds to white, and other surfaces within the framework are assigned grayvalues according to their luminance ratio with the white surface. An impor-tant feature of the theory is that a scene is composed of multiple frameworks,a global framework that encompasses the entire image, and one or more localframeworks that might overlap. he lightness value of any scene location is aweighted average of the values that it is being assigned within each framework.he weights depend on how strongly a framework is insulated by diferentGestalt grouping cues. In White’s illusion, the test patches are grouped withthe bars on which they are placed, and the grouping cues are the T-junctions.hus, within the local framework, test patches on black bars have the highestluminance and get anchored to white, while test patches on white bars areassigned an intermediate gray value. In the global framework, the highest lu-


minance is that of the white bars, and hence the test patches on black andon white bars are both mid-gray. he inal lightness value of patches on blackbars is a weighted average of white and mid-gray, whereas that of patches onwhite bars is an average of mid-gray in both frameworks. Accordingly, theequiluminant patches look lighter when placed on black bars.

Anchoring theory allows for the possibility that White’s illusion is strongerthan simultaneous lightness contrast. If the insulation of the local frameworkis stronger in White’s stimulus than in a simultaneous contrast display, White’sillusion should be stronger. he theory can also be used for explaining vari-ants of the stimulus without T-junctions, by invoking other grouping factors,such as the Gestalt law of Prägnanz. It is possible that all changes in White’sillusion that are afected via a change in some stimulus parameter, e.g. spa-tial frequency, could be accommodated in a similar manner by claiming thatthis stimulus parameter afects grouping strength. As has been pointed out byHowe (2005):

It seems that the anchoring theory of lightness perception is ableto explain many aspects of White’s efect. However, it does thisby invoking grouping mechanisms that might be thought to lackrigor and concreteness, even by the authors’ own admission [...].Indeed it is not hard to think of situations where diferent Gestaltgrouping laws predict diferent outcomes, making it unclear as towhich outcome should occur.

hus, the theory may be too vague, lacking in real predictive, and ultimatelyexplanatory, power. On the other hand, this criticism might be slightly unfair.We may not yet understand grouping principles well which have (often de-scriptively) been invoked by Gestalt psychology. But anchoring theory insiststhat such factors could play an important role in determining frameworks of il-lumination and lightness computations, highlighting the importance of betterunderstanding them.

A concrete prediction derived from anchoring theory is that the illusionshould be due to a lightening of the test patch that is embedded on a dark


bar, whereas the test patch on the white bar should be perceived veridically.Ripamonti and Gerbino (2001) reported that both patches underwent an al-most equal change in lightness, and that this was incompatible with anchoringtheory. Although the design of their task makes a deinite conclusion aboutthis point diicult, later results (Blakeslee & McCourt, 2004; Anstis, 2005)seem to support their argument.

Anchoring theory does not explain perceived lightness based on luminanceratios across edges. However, the theory is not formalized on an implementa-tion level, so it remains unspeciied e.g. how the relative relectance between atarget and the surface of highest luminance within its framework is computed,and edge ratios may have a role in these computations.

3.3.5 P E R C E P T U A L S C I S S I O N

Anderson (1997) proposed a theory according to which White’s illusion isdue to perceived transparency. He argued that the test patches could be inter-preted as a transparent layer through which the grating is seen. In that case,the luminance that reaches the retina from a test patch region would be thesum of the luminance relected from the transparent patch and the luminancepassing through the transparent patch from behind. In order to determine thelightness of the test patch, the visual system has to attribute some of that lumi-nance to the occluded layer. Anderson called this mechanism by which an im-age region is perceptually separated into two layers scission. According to thisaccount, White’s illusion is explained as follows: when the test patch is seen infront of a white bar, much of the luminance coming from the patch region isattributed to the white bars that are in the back but seen through the transpar-ent patch, and this attribution causes the patch to appear darker. When thetest patch is seen in front of a black bar, all of the luminance is attributed to thepatch itself, making it appear lighter. Anderson pointed out that the scissionprocess is cued by the luminance relations along the T-junctions in the stim-ulus. However, the causal mechanism for the lightness efect in this accountis perceptual scission. hus, even in stimulus variations without T-junctions,


the theory applies as long as other cues can be identiied which might triggerthe scission into two layers.

Ripamonti and Gerbino (2001) have shown that White’s illusion occurs alsoin stimuli for which the speciic luminance relations do not cause a consciouspercept of transparency. hey pointed out that it is possible that a transparencymechanism afects lightness perception even if transparency is not perceivedexplicitly. However, they did not support such an interpretation, and arguedthat whether or not transparency is perceived should at least inluence thestrength of the illusion to some degree, which they did not ind.

While this argument may have intuitive appeal, there is in principle no rea-son why this would have to be the case. Whether or not one quantity has to beexplicitly perceived in order to inluence the computation of another quantityis an interesting question for which no convincing experimental test has yetbeen proposed, and hence it remains a matter of opinion.

Anderson expanded his scission account in a later publication, where he pre-sented a new variant of the stimulus, the textured White’s illusion (Anderson,2003, see Section 3.2). In this stimulus, a black-and-white noise pattern wasused instead of homogeneous test patches, and either the black spots or thewhite spots are perceived as a perforated layer overlaying the background grat-ing. his separation of the noise pattern into two layers is somewhat similarto the scission mechanism proposed for the regular White’s illusion.

However, now the location on the grating (embedded in a black or whitestripe) informs a igure-ground separation of the noise pattern, not a split intotwo continuous layers one of which is translucent. Anderson (2003) claimsthat his new stimulus is modulated by the same properties as the traditionalstimulus, and that this speaks in favor of them having the same underlyingmechanism. here exist so far no empirical data to test this claim, perhapsbecause it is not entirely clear how the efect size is to be quantiied on thetextured White’s illusion, where the igure-ground separation seems to be anall-or-none efect.

A problem for the scission account in its present form that Anderson (2003)pointed out himself is that it is a local mechanism. hus, it cannot explain why


changes in the stimulus that are remote to the test patches, such as extendingthe grating, should inluence the illusion. However, since the explicitly localingredients in the theory are really just the cues causing the scission, the ac-count can easily be modiied to allow for global factors to inluence the layerseparation.

Similarly to anchoring theory, the scission account does not mention lu-minance ratios across edges as a factor determining perceived lightness. It isunclear if and how edge ratios may be involved in computing the lightness ofthe individual layers after scission.

3.3.6 S PAT I A L F I LT E R I N G M O D E L S

Blakeslee and McCourt (1999) introduced a model that conceives of perceivedlightness as the result of a spatial iltering operation on the input. More specif-ically, the model output is a weighted sum of the responses of oriented difer-ence of Gaussians (ODOG) ilters at seven spatial frequencies and six orienta-tions. While the spatial frequency weights are ixed according to a psychophys-ically determined contrast-sensitivity function, the weights of the individualorientations are obtained by normalizing each orientation response to unitstandard deviation. his has the efect of boosting the signal in orientationsin which little is happening. While this model correctly predicts the classicalWhite’s efect, it fails on a number of other variations. Generally, the modelfails to correctly predict stimuli that have equal energy at all orientations, e.g.circular White’s illusion or radial White’s illusion (Robinson et al., 2007). Inmy own tests, the model also made incorrect predictions for stimuli in whichthe test patch luminance lies outside of the grating’s luminance range (doubleincrements or decrements, Spehar et al., 1995; Ripamonti & Gerbino, 2001).Furthermore, the model predicts White’s illusion to be weaker than simultane-ous lightness contrast (by a factor between two and six depending on stimulusparameters). he available empirical data are still ambiguous to this point (seeSection 3.1.8).


Robinson et al. (2007) proposed a new version of the model in which theweights of the individual orientation responses are not computed globally forthe entire stimulus, but over a local range of 2 - 8° of visual angle. Whilethis modiication made correct predictions for some of the radial versions ofWhite’s illusion, it failed for the circular ones. hey additionally proposed amodel in which the weights of individual spatial frequencies were adjusteddynamically, and succeeded in predicting the correct direction of the efect inall variants described so far. However, the authors conceded that there is aversion of the stimulus by Anderson (2001) on which even their best modelfailed. Furthermore, these models predicted White’s illusion to be weaker thansimultaneous contrast.

Dakin and Bex (2003) proposed another spatial iltering model of lightnessperception that aimed mainly at explaining the Craik-O’Brien-Cornsweet ef-fect, but it also correctly predicted White’s efect. he model modiies thespatial frequency spectrum of input images to make it conform to the averagespectrum of natural images. It thus boosts frequencies that are underrepre-sented in an image, and attenuates those that are too strong. According tothis account, White’s illusion is driven by the fact that the addition of the testpatches to the grating introduces a low spatial frequency peak to the spectrumthat is otherwise dominated by the higher frequency of the grating. he modelboosts this peak because natural images have higher power at low frequenciesthan the stimulus, and this increase, according to the authors, causes White’sillusion. hey supported their claim by showing a version of White’s stimulusin which low spatial frequency content had been removed, and the illusionwas claimed to be absent. However, the test patches were also no longer equi-luminant in the so-modiied stimulus, and it is thus problematic to attributethe absence of the efect solely to the removal of low spatial frequencies. Spa-tial iltering models are discussed in more detail, and ultimately rejected asadequate explanations of White’s illusion, in Part II and Part III.


PSI Cor T-jun Anch Scis Sp fil

aspect ratios ++ − + + ++ −

spatial freq. + 0 0 0 0 ++

# test patches × × × × × ×

grating extent × × × × × ×

patch orientation × × × × × ×

patch phase ++ − − − − ++

luminance relations − − 0 + ++ −

depth − − − + + −

transparency − − − 0 − 0

White’s > SLC 0 − −− 0 ++ −−

White’s < SLC 0 + ++ 0 − ++

lightening darkening × × × × × ×

textured 0 0 0 0 ++ 0

circular − −− −− 0 − +

radial − + + 0 − +

Table 1: Summary of proposed explanations of White’s illusion and reported phe-nomena related to the illusion. ++ indicates that the mechanism explicitlypredicts the phenomenon, + indicates that it is easily accommodated withinan approach, 0 indicates that the phenomenon is not informative about theapproach, − that it speaks against, −− that it speaks strongly against theapproach. Phenomena with an unclear empirical status have been markedwith × for all explanations. For the relative efect size of White’s illusion vs.simultaneous lightness contrast, both possible outcomes have been included,since both have been reported. he explanations are: PSI: Pattern-speciicinhibition; Cor: Corner response after spatial iltering; T-jun: Contrast me-diated by T-junctions; Anch: anchoring theory; Scis: Perceptual scission; Spil: Spatial iltering models.


3.4 C O N C L U S I O N

Despite over 30 years of ongoing research, with more than 150 articles citingWhite’s original presentation of the illusion, the questions of why observersperceive the stimulus the way they do, and what this tell us about the un-derlying mechanisms of lightness perception, are still debated. One diicultycomes from the fact that White’s efect may depend on a number of diferentmechanisms that dominate in diferent stimulus conigurations, and thus itmay be misleading to speak of White’s illusion as a single phenomenon. For ex-ample, the increase in efect size at high spatial frequencies may indicate thatpart of the illusion is due to a form of assimilation that depends on spatialsmoothing. Some authors have dismissed spatial smoothing as an explanationof White’s efect because there are stimulus conigurations that cannot be ex-plained through such a mechanism. Still, this dismissal misses the point thatspatial smoothing is likely to be a contributing factor in some variants of thestimulus. It thus seems unlikely that a single explanation will be able to explainall phenomena that have been discussed under the label White’s illusion.

If the investigation of White’s illusion is not seen as an end in itself but asa means to understand general principles of lightness perception, diferent is-sues may appear most relevant depending on the investigators’ investment in aparticular theory. For example, anchoring theory (Gilchrist et al., 1999) makesthe prediction that White’s illusion is exclusively due to a lightening of the testpatch on the dark grating bar. hus, the empirical question whether the illu-sion depends on lightening of one test patch, darkening of the other, or both,is very relevant in the light of anchoring theory, while researchers favoring dif-ferent explanatory approaches tend to spend little time on it. Similarly, spatialiltering models make speciic predictions about the efect of the grating fre-quency on the strength of the illusion, so accurate quantitative data on thisefect seem especially relevant for evaluating these models. More high-levelapproaches like Anderson’s scission theory, on the other hand, may attributethe increased efect size at high spatial frequencies to an increase in spatialsmoothing, which acts independently and on top of the mechanisms that they


propose to explain the, in their view, critical aspects of the illusion. hus, whilethe exact quantitative contributions of grating frequency, test patch height,number of grating cycles, and number and spatial arrangement of test patches(potentially aiding perceptual grouping to a transparent object) all remain aspotential targets of future research, it is impossible to assign priority to anyparticular experiment without a commitment to a particular explanatory ap-proach.

In what follows, I adopt the working hypothesis that lightness perceptioncan be understood as the result of integrating luminance ratios across edges.he goal of the present thesis is to test how far this approach can take ustowards an understanding of White’s illusion, a stimulus that was originallybelieved to be a counter example to edge ratio based explanations.

Part II

N O I S E M A S K I N G

his part has been published as:Betz T, Shapley R, Wichmann F A, Maertens M (2015). Noisemasking of White’s illusion exposes the weakness of current spa-tial iltering models of lightness perception. Journal of Vision15(14): 1, 1-17


It has been known for a long time that the luminance ratio, or contrast, atedges (i.e. steps in luminance) is of crucial importance for the perception oflightness¹ (e.g. Wallach, 1948; Cornsweet, 1970; Whittle, 1994; Gilchrist,2006, for a historical overview) . At the same time, mid- to high-level fac-tors appear also to be important for lightness perception (e.g. Mach, 1886;Gilchrist, 1980; Knill & Kersten, 1991; Bloj & Hurlbert, 2002; Radonjić,Todorović, & Gilchrist, 2010; Maertens, Wichmann, & Shapley, 2015). Itis therefore unlikely that early visual processes alone will provide a completeaccount of lightness perception, but it remains an open question to what ex-tent low-level vs. high-level visual mechanisms contribute to diferent light-ness phenomena. We think that understanding their relative contributions tothe computation of lightness is crucial, because low-level visual mechanismsprovide the input to mid- and high-level vision.

One popular class of low-level models of lightness perception are multi-scale spatial iltering models (Blakeslee & McCourt, 1999; Dakin & Bex,2003; Robinson et al., 2007; Otazu et al., 2008). hey attempt to explainlightness phenomena as the result of a spatial iltering operation where themodel output is a weighted sum of spatial frequency (and sometimes orienta-tion) tuned ilter responses. he weights are determined through contrast or

1 Lightness is the perceived relectance of a surface, while brightness is its perceived luminance.In the stimuli considered here, the two are not separable, since there is no information aboutillumination, or surfaces for that matter. We opt to use the term lightness throughout becausewe believe that relectance (i.e. achromatic color black, white, gray) is a more accessible percep-tual category than luminance, and thus should be the ultimate target of lightness/brightnessmodels. When citing the work of others, we use the term brightness if that term is used intheir work.

50 N O I S E M A S K I N G

response energy normalization mechanisms, the details of which difer frommodel to model.

As Kingdom (2011) pointed out, rhowever appealing is the idea that con-trast normalization is responsible for many brightness errors, there is at presentlittle actual evidence for it. Experiments that manipulate the amount of con-trast normalization, perhaps via adaptation or masking, in order to test whetherthe predicted changes in the magnitude and direction of brightness errors oc-cur, would be welcomes.

Salmela and Laurinen (2009) took an important step in the direction sug-gested by Kingdom (2011). hey generated versions of simultaneous bright-ness contrast, White’s illusion (White, 1979, see Figure 6) and the Benarycross (Benary, 1924), and masked them with narrowband noise. hen theymeasured the efect of the noise’s spatial frequency and orientation on per-ceived brightness. hey found that noise with a narrow frequency band (be-tween 1 and 5 cpd) had a strong masking efect on the illusions, meaning thatthe apparent brightness diferences were considerably reduced, whereas noiseat higher or lower frequencies had little efect (see Figure 7). hey concludedthat their results rsuggest that ilters below 1 cpd and above 5 cpd are not usedin the computation of surface brightnesss.

We replicated and extended Salmela and Laurinen’s (2009) results, andtested a number of diferent multi-scale spatial iltering models with respect totheir capability to reproduce the psychophysically observed efects of narrow-band noise on lightness perception. In particular, we implemented the modelsby Blakeslee and McCourt (1999), and Dakin and Bex (2003), and used pub-licly available implementations of the models by Robinson et al. (2007) andOtazu et al. (2008). We used White’s illusion to test the models, because itsphenomenological efect in terms of perceived lightness is popposite’ to that of(simultaneous) contrast, and it is more diicult to account for. Spatial ilteringmodels were shown to account for both efects, White’s illusion and simulta-neous contrast, and we decided to take the more diicult one as the test casein order to probe for the postulated mechanisms. We show that all modelssystematically fail to reproduce the noise-masking efect that was observed


Figure 6: An example of White’s illusion. To most observers, the gray patch on thedark bar looks lighter than the gray patch on the light bar, even though thetwo are equiluminant. he illusion cannot simply be explained in terms ofcontrast, because both test patches share an equal amount of border withdark and light regions.

Figure 7: Illustration of the efect of narrowband noise on White’s illusion. Left: stim-ulus is masked with a noise center frequency of 0.58 cpd, Middle: 3 cpd,Right: 9 cpd (assuming a viewing distance of 40 cm). White’s efect shouldbe reduced or absent in the middle panel.


psychophysically. We discuss the results with regard to the mechanisms thatare implemented in the models and argue that the models, despite an apparentresemblance to known physiological mechanisms, do not capture the mech-anisms that are crucial for lightness perception in human observers. Insteadwe think that our results point to an important role of luminance edges forlightness perception.

5M U LT I - S C A L E F I LT E R I N G M O D E L S

his section introduces the diferent models that we tested and explains howeach of the models accounts for White’s illusion. Our Python implementa-tions of the models by Blakeslee and McCourt and Dakin and Bex are avail-able at https://github.com/TUBvision/lightness_models. he models byRobinson et al. and Otazu et al. can be obtained from the respective authors,and also from https://github.com/TUBvision/betz2015_noise, where wesupply all code required to reproduce the results of the present article.

5.1 T H E O R I E N T E D D I F F E R E N C E O F G A U S S I A N S M O D E L ( O D O G )

In the oriented diference of Gaussians (ODOG) model by Blakeslee andMcCourt (1999), the input image is convolved with ODOG ilters in six ori-entations (0°, 30°, 60°, 90°, 120°, 150°) and seven spatial frequencies (zero-crossing distance 0.13°−8.16° in octave steps, corresponding to peak frequen-cies of 6.5 cpd, 3.25 cpd, 1.63 cpd, 0.81 cpd, 0.41 cpd, 0.2 cpd, 0.1 cpd). heoutputs of ilters within the same orientation are summed, with weights thatare determined by the spatial frequency. Lower frequencies receive smallerweights than higher frequencies, and the weights fall of with an exponent of0.1 (i.e. halving the ilter frequency decreases the ilter weight by a factor of20.1). his yields six multi-frequency orientation responses. hese orientationresponses are normalized by their root-mean-square (RMS) energy which iscomputed across all pixels and summed to yield the model output. In otherwords, the ilter output is multiplied by the inverse of the output’s RMS en-ergy (the normalization factor) prior to summation. As a consequence of theresponse normalization, orientations with little energy in the input image willhave a proportionally larger inluence on the model output.

https://github.com/TUBvision/lightness_models

https://github.com/TUBvision/betz2015_noise


In the ODOG model, two mechanisms contribute to the diference in pre-dicted lightness between the two equiluminant test patches in White’s illusion.he irst critical mechanism is the orientation normalization step (cf. Robin-son et al., 2007). After the ilter responses are summed across spatial frequen-cies, the response of the ilter that is oriented orthogonal to the square wavegrating is positive for the test patch on the dark grating bar, and negative forthe test patch on the light grating bar (fourth row in Figure 8). his happensbecause ilters in this orientation are sensitive to the contrast between the testpatch and the bar on which the patch is placed. Conversely, the response ofthe ilters that are oriented parallel to the grating is positive for the test patchon the light bar and negative for the test patch on the dark bar (irst row in Fig-ure 8). his is because the ilters oriented parallel to the grating are sensitiveto the contrast between the test patch and the adjacent bars. he responses ofthe ilters that are sensitive to all other orientations lie in between these values.For the model to produce White’s illusion, the response of the ilters orthogo-nal to the grating must receive a larger weight, because it is this response thatentails a diference in the correct direction between the two test patches. henormalization by RMS energy does precisely that, because the ilters orientedorthogonal to the grating do not respond to the grating itself, and thus havelower total response energy (see Figure 8).

A second mechanism is at work for stimulus versions in which the gratinghas a relatively high spatial frequency. Here, the response of ilters with lowerspatial frequency will perform a spatial smoothing of the luminance difer-ences between test patches and underlying grating and this will cause the testpatches to perceptually assimilate with the adjacent bars even for ilters thatare oriented parallel to the grating. his explains why the model correctly pre-dicts White’s illusion to increase with increasing grating frequency (Blakeslee& McCourt, 2004).

M U LT I - S C A L E F I LT E R I N G M O D E L S 55

Figure 8: Illustration of the ODOG model. he model consists of ODOG ilterswith seven spatial scales and six diferent orientations. To predict bright-ness, it processes images in four steps: First, an input image is convolvedwith all 42 (6*7) ilters. Second, the ilter outputs of diferent spatial fre-quency at the same orientation are summed, and outputs of higher frequen-cies receive slightly larger weights, indicated by the inset igure above thesummation, where each dot corresponds to the weight of one spatial fre-quency. hird, the diferent orientation responses are normalized by point-wise division through their root-mean-square energy computed over theentire image. Fourth, the normalized responses are summed to yield themodel output.White’s illusion in the model response is mainly caused by a higher weightgiven to the ilter oriented orthogonal to the grating (4th row), because itsresponse has little energy. Since in this ilter response, the test patch on theleft has a higher value than the one on the right, it also receives a highervalue in the inal output.


5.2 F R E Q U E N C Y- S P E C I F I C L O C A L LY N O R M A L I Z E D O D O G ( F L O D O G )

Robinson et al. (2007) have criticized the global nature of the response normal-ization in the ODOG model and proposed an extended model that uses localnormalization. his model computes the RMS energy of the ilter responsesin a spatially more restricted, local, window, and applies the normalization ateach pixel based on the energy in its surround. Robinson et al. (2007) arguedthat the more local model is physiologically more plausible than the origi-nal ODOG model. In addition, the model makes qualitatively correct predic-tions for a number of stimuli for which ODOG failed, such as radial versionsof White’s illusion, while it still accounts for all the stimuli that the originalmodel predicted correctly. Robinson et al. also presented a model in which thenormalization is frequency speciic in addition to being local. his model iscalled the FLODOG model (frequency-speciic locally normalized ODOG).In this model, unlike in the original ODOG model, the responses of the in-dividual spatial frequencies are not added prior to normalization. Instead, thenormalization weight for each ilter response and location is computed as theRMS energy of the responses of ilters with identical orientation and similarspatial frequency in a local surround. his implements a form of surround-inhibition that is orientation- and frequency-speciic. he model adds morestimuli to the list of correctly predicted illusions. he frequency speciic nor-malization makes the model a good candidate for investigation with the noisemasked stimuli, so it was included in our analysis.

he FLODOG model has two free parameters, the size of the orientationnormalization window, n, and the weighting of nearby frequencies, m. Wechose the values n = 4 and m = 0.5 in our simulations, because those are thevalues that Robinson et al. consider to yield the best overall predictions.

5.3 D A K I N A N D B E X

Dakin and Bex’s (2003) model of lightness perception is inspired by the shapeof the (average) amplitude spectrum of natural images. In this model, the av-

M U LT I - S C A L E F I LT E R I N G M O D E L S 57

erage amplitude spectrum of natural images is believed to guide the visualsystem’s attempt to reconstruct the input image based on its internal ilter ac-tivations. heir main focus was the Craik-O’Brien-Cornsweet (COBC) illu-sion (O’Brien, 1958; Craik, 1966; Cornsweet, 1970), but they also used theirmodel to account for White’s illusion. heir model consists of isotropic (i.e.non-oriented) log Gabor ilters. he ilters span the entire range of frequen-cies encountered in an image and they are spaced in half-octave steps (from1 cycle per image up to the Nyquist frequency, corresponding to 0.08 cpd to20.4 cpd with the image parameters we used in our model evaluation).

he normalization, unlike in the ODOG model, is frequency speciic. In-dividual frequencies are weighted so as to make the amplitude spectrum ofthe reconstructed image more similar to the average amplitude spectrum ob-served in natural images (1/f). he model assumes that all input images arecomposed of spatial frequencies following this 1/f distribution. It weights theactual ilter responses such that the energy distribution in the model outputconforms to this assumption. hus, if in the actual input, low frequencies areunderrepresented, they will be boosted, and vice versa.

his model predicts a diference between the two test patches in White’s illu-sion, because ilters tuned to very low frequencies will average the luminancesof the test patches and their surround. A test patch on a dark bar increases thelocal mean luminance by replacing a part of the dark bar with mean gray. Itwill thus have a relatively higher response in those low frequency ilters. A testpatch on a light bar decreases the local mean luminance by replacing a part ofthe light bar with mean gray, and hence leads to a relatively lower response inthose low frequency ilters. Since the amplitude spectrum of White’s stimulushas more power in high frequencies than natural stimuli, the model increasesthe weight given to the low frequencies, and so the efect of local surroundaveraging from the low frequency ilters is seen in the model prediction.


5.4 B I WAM

he last model that we tested is the brightness induction wavelet model (BI-WAM) by Otazu et al. (2008). It is similar to the ODOG and FLODOGmodels as it also decomposes the image into frequency- and orientation-speciicsubbands, but the ilters are not ODOG ilters, the number of orientationbands is lower (three instead of six), and the frequency space is larger rangingfrom 1 cycle per image (cpi) to the Nyquist frequency. he most crucial difer-ence, again, is the normalization scheme. Normalization is performed withineach frequency and orientation subband, so in this aspect, the BIWAM ismost similar to the FLODOG model. However, unlike in FLODOG, thenormalization factor is determined by the relationship between the ilter re-sponse and the average response in the local surround, not simply by the to-tal local response energy. Computationally, the normalization is achieved bycomputing the standard deviation of a ilter response in a square centered ateach location, and dividing it by the standard deviation of a surround areathat is three times as large as the central area and excludes the center square.his yields a normalization factor which, after some non-linear but monotonictransformations, is used to weight the ilter response at the location for whichit was computed. hus, at each location, ilters that have a stronger responsein the center than in the surround will be boosted and ilters with a high sur-round response will be suppressed. By contrast, in the FLODOG model, thesuppression is dependent on the weighted sum of the response energy in thecenter and in the surround, not on the ratio between the two. BIWAM isless well known than the ODOG model, but we included it in our analysisbecause its normalization scheme is more neurophysiologically plausible thanthat of ODOG. At the same time, it makes qualitatively (and in many casesquantitatively) correct predictions for all the stimuli tested by Blakeslee andMcCourt (1999). Furthermore, the fact that the normalization scheme is fre-quency speciic makes the model an interesting candidate for explaining thefrequency-speciic efects of narrowband noise masking.

6E F F E C T S O F N O I S E O N P E R C E I V E D L I G H T N E S S

Salmela and Laurinen (2005) showed that brightness polarity identiication,i.e. the judgment whether a target patch is relatively lighter or darker than itssurround, depends on information represented in a narrow spatial frequencyband. hey found that brightness polarity identiication of an oval test areaon a uniform surround was compromised by narrowband Gaussian noise, andthat the efect of the noise strongly depended on its spatial frequency. Impor-tantly, the most efective noise frequency did not scale proportionally with thesize of the test area. Increasing the stimulus 16-fold shifted the most efectivemasking frequency only about one octave (i.e. 2-fold) towards lower frequen-cies. hey drew two conclusions from these results: irst, brightness perceptiondoes not depend on ilters that are matched in size to the test areas. And sec-ond, the visual system seems to use edge information to determine brightness,but does not exploit the full frequency range that would be informative aboutedges¹. In a later study, Salmela and Laurinen (2009) extended their previousresults by quantitatively assessing brightness (not just brightness polarity) indiferent types of classical lightness illusions. hey found a strong efect ofnoise masking on perceived brightness and the efect again depended on thespatial frequency of the noise. Comparable results have been reported by Pernaand Morrone (2007), who used iltered images instead of noise masking, andalso found that brightness information was mediated by a narrow spatial fre-quency band (in their case, centered at somewhat lower frequencies, around 1cpd).

1 Sharp edges cause a response in a wide range of frequency-selective ilters. he deining featureof an edge is not that it is localized in frequency, but that the phases of all frequency componentsare aligned.


A similar type of noise masking has also been used by Solomon and Pelli(1994) to show that letter identiication is mediated by a single frequency chan-nel. hus in letter identiication the visual system failed to integrate relevantinformation from diferent spatial frequency bands, similar to the results inbrightness perception discussed here. However, the relationship between themost efective noise frequency and the stroke width of the letters was strongerthan for brightness polarity estimation. A ive-fold increase in stimulus sizeled to a 2.8-fold increase in most efective masking frequency (Petkov & West-enberg, 2003). As a side note, although both types of experiments showedsome dependence of the most efective noise frequency on the scale of thestimuli, Salmela and Laurinen emphasized that the scaling was incomplete,whereas Petkov and Westenberg emphasized the presence of scaling. Still, itseems clear that the scaling between stimulus frequency and most efectivenoise frequency is not 1:1. his can be easily demonstrated by looking at Fig-ure 7 from diferent viewing distances. Even though the visibility and thelightness of the test patches change as a function of distance, the relationshipbetween noise frequency and grating frequency is not afected by the change inviewing distance. he same is true for letter stimuli (see Figure 1 in Solomon& Pelli, 1994, and also the cover of that issue).

he efect of narrowband noise on perceived brightness provides an oppor-tunity to test, as Kingdom (2011) suggested, whether contrast normalizationis indeed responsible for the brightness diferences in White’s illusion. hehypothetical processing channels in the visual system that are thought to beafected by narrowband noise are precisely those that the models attempt tocapture. he efects of narrowband noise on the models’ output are thereforea critical test for a model’s adequacy to account for White’s illusion. If themechanism causing the illusion in the visual system is in fact the same mech-anism as the one emulated in the model (or at least one of the models), thenthe model should predict the psychophysically observed efects of noise mask-ing. We repeated the lightness matching experiment of Salmela and Laurinen(2009), and included versions of White’s illusion at three diferent spatial fre-quencies. hus, we could examine the relationship between stimulus size and

E F F E C T S O F N O I S E O N P E R C E I V E D L I G H T N E S S 61

most efective noise frequency not only for polarity matching or detection, butdirectly for lightness matching. We replicated the main indings of Salmelaand Laurinen (2009). herefore a strong test of lightness models is testingtheir predictions of results in the noise masking experiments. Speciically, themodels should predict (A) a reduction in illusion strength for noise frequen-cies between 1 and 5 cpd, and (B) the location of this reduction along the fre-quency axis should not shift proportionally with changes in grating frequency.We tested these predictions by simulating our noise masking experiment withthe four models.

7P S Y C H O P H YS I C A L E X P E R I M E N T

7.1 M E T H O D S

7.1.1 PA R T I C I PA N T S

Eleven observers (authors TB and MM, two experienced and 7 naive ob-servers; four male) participated in the experiment. Observers’ mean age was29 years (min 23, max 35). All observers had normal or corrected to normalvision. Naive observers were inancially compensated for their time. All ob-servers gave written informed consent to their participation in the study.

7.1.2 S T I M U L I A N D A P PA R AT U S

he test stimuli consisted of a horizontal square wave grating in which a sin-gle square test patch was embedded. hree diferent grating frequencies wereused. At the lowest frequency (0.2 cpd), the grating contained four bars, twolight and two dark bars, with a total size of 10.2° × 10.2°. he test patchwas 2.55°× 2.55° wide. At the medium frequency (0.4 cpd), the grating con-tained six bars, total size was 7.66° × 7.66°, and the test patch measured1.28° × 1.28°. his condition corresponded to the stimulus dimensions usedby Salmela and Laurinen (2009) in their matching experiment. he highestfrequency grating (0.8 cpd) consisted of 12 bars, total size was again 7.66° ×

7.66° and the test patch measured 0.64° × 0.64°. While higher frequenciesthan 0.8 cpd are often used in experiments on White’s illusion, in our particu-lar case with square test patches, the test patches would have become so smallat grating frequencies above 0.8 cpd that lightness matching would have been


very diicult. he test patch was alway located on the bar directly below thecenter of the grating, and centered horizontally on the grating. Test stimuliwere embedded in a 16.3°×16.3° noise mask. hese noise masks were slightlylarger than those employed by Salmela and Laurinen (2009) in order to ac-commodate the larger low-frequency grating. he noise was uniform whitenoise, band-pass iltered with a Gaussian ilter with 1 octave spatial frequencybandwidth (full-width at half height). he root mean square contrast of thenoise was 0.2. We used six diferent noise center frequencies ranging in log-arithmic steps from 0.58 to 9, and one control condition without noise. henoise masks were created with Matlab code kindly provided by Dr. Salmela,saved as .mat iles, and then loaded into our own Python scripts.

In all conditions, the dark bars had a luminance of 41.8 cd/m2 and the lightbars of 46.2 cd/m2 corresponding to a Michelson contrast of 0.05. Salmelaand Laurinen (2009) report a contrast of 0.1 for their grating, but presentedthe grating and the noise in alternating frames, which resulted in an efectivegrating contrast over time of 0.05, so we used this value. he backgroundluminance was 44 cd/m2, and the test patch luminance was also 44 cd/m2.he comparison square was always 2.37°× 2.37° in size. Its initial luminancewas randomly set in each trial to a value between 35.2 and 52.8 cd/m2. Itwas presented on top of a random checkered background that consisted of6×6 checks of size 0.8°×0.8° with gray values sampled uniformly from valuesbetween 35 and 53 cd/m2.

he noise mask with the embedded grating was centered on the screen. hecomparison background was placed on the left of the screen (Fig. 9).

Stimuli were presented on a linearized 21s Siemens SMM21106LS moni-tor (400×300 mm, 1024×768 px, 130 Hz) controlled by a DataPixx (VPixxTechnologies Inc. Saint-Bruno, QC, Canada) and custom presentation soft-ware developed in our lab and published at https://github.com/TUBvision/TUBvision/hrl. Observers were seated 70 cm from the screen, and their posi-tion was ixed with a chin-rest. Responses were recorded with a ResponsePixxbutton-box (VPixx Technologies Inc.).

https://github.com/TUBvision/TUBvision/hrl

https://github.com/TUBvision/TUBvision/hrl

P S Y C H O P H YS I C A L E X P E R I M E N T 65

Figure 9: Illustration of the screen during matching. he observer adjusted the com-parison square on the left to match the lightness of the test patch in thegrating. he gray background was actually larger, and has been cropped forthis illustration. he contrast of the grating has been increased for bettervisibility in this illustration.

7.1.3 P R O C E D U R E

Our goal was to measure the efect of noise on the perceived lightness of thetest patches in White’s illusion. On each trial, observers irst saw a low con-trast ixation ring (inner diameter 4 px, outer diameter 10 px, ring luminance26.4 cd/m2), centered on the position where the test patch would later appear.he low contrast of the test patch was chosen to avoid afterimages or adapta-tion that could interfere with perception of the test patch. Upon a button press,the stimulus was shown for 0.5 s, after which the ixation ring reappeared. Ob-servers could then adjust the lightness of the comparison patch so as to matchthe perceived lightness of the target patch that was embedded in the squarewave grating of the White’s stimulus. hey could review the stimulus as oftenas they liked with a button press, but the viewing time on each presentationwas limited to 0.5 s. We chose this procedure in order to reduce the efect ofstrategies by diferent observers (see Section 9.3). Observers indicated when


they were satisied with their setting by a button press and continued to thenext trial.

7.1.4 E X P E R I M E N TA L D E S I G N

he independent variables were the frequency of the noise, which could takeseven values (six diferent frequencies, or no noise), and the frequency of thegrating. Grating frequencies were blocked, such that each observer irst com-pleted all trials at one grating frequency before moving on to the next. heorder in which the diferent grating frequencies were tested was randomizedacross observers. he topmost bar of the grating could either be light or dark,so that the test patch could become an increment or a decrement with respectto the bar on which it was placed.

Overall, the experiment consisted of 420 trials (7 noise types × 3 gratingfrequencies× 2 grating phases× 10 repetitions). Each repetition used a difer-ent random noise mask, but the masks were the same for all observers. Masks6-10 were 180° rotated versions of masks 1-5. Experienced observers onlycompleted 5 repetitions. Since both incremental and decremental test patcheswere presented in the same position, diferences in the luminance levels of thenoise masks should not afect White’s illusion, which was computed as thediference in matched luminance between incremental and decremental testpatches with the same noise mask.

7.2 R E S U LT S

he matching data were analyzed by computing the diference in match lumi-nance between each pair of trials that difered only in whether the test patchwas placed on a dark or a light grating bar, but that had the same noise maskand the same grating frequency. his diference was taken as a measure of thestrength of White’s illusion. For the no-noise control trials, no such pairingscould be made, so the illusion strength at each individual trial was computed


as the diference between the match luminance at that trial and the meanmatch luminance of the trials with a complementary background bar light-ness. Data from a typical observer are shown in Figure 10. It can be seen thatat all grating frequencies, there is a small range of noise frequencies for whichillusion strength is reduced. Results of all individual observers are available assupplemental material.

To quantify the location of this most efective noise frequency range, a logGaussian function was itted to the data with the lmit package in Python. hefunction was deined as

f(x) = b− (b−m) ∗ exp

(

−(log (x) − µ)2

2σ2

)

,

where b determined the upper asymptote of the function, m the minimumvalue at the dip, σ the width of the dip, and µ the location of the dip. heparameter of interest was µ, the location of the dip on the spatial frequencyaxis, i.e. the noise frequency that most strongly reduced White’s illusion. hisvalue was computed for all observers and all grating frequencies, and is plottedin Figure 11. Two observers (supplemental Figures e1 and n2) did not show aclear efect of the noise, and one was extremely variable in her responses (sup-plemental Figure n7), so they were excluded from this analysis . An additionalobserver (supplemental Figure n4) only showed a clear noise efect at the twohigher grating frequencies, so no function was it to her low grating frequencydata. It is clear from these results that all observers for which a clear efect ofthe noise was measurable were most afected by noise in the range between1 and 5 cpd. Furthermore, the most efective noise frequency increased withincreasing grating frequency, but not proportionally. he mean slope acrossobservers in Figure 11 is 0.63 for both line segments. 95% conidence inter-vals (bootstrapped with 10000 trials with replacement) are [0.51, 0.75] for thelower segment and [0.52, 0.76] for the upper segment.


Figure 10: Noise masking results for one typical observer. X-axis indicates the centerspatial frequency of the noise mask. 0.06 cpd would correspond to 1 cycleper image (cpi) in these stimuli. Y-axis indicates illusion strength, mea-sured as the diference in matched lightness between test patches placedon diferent background bars. he grating frequency is indicated by thestar on the x-axis. Large circles are means across trials, small circles areindividual trials. he results in the no-noise control are shown on the veryleft. Light gray circles are trials where the test patch was an incrementwith respect to the bar on which it was placed, dark gray circles are trialswhere the test patch was a decrement. he dotted line indicates the overallmean illusion strength of the no-noise condition. he light gray line is thebest it to the data, and the location of the minimum of the it is indicatedby the light gray text inset.


Figure 11: Summary of the efect of narrowband noise on White’s illusion at diferentgrating frequencies. he x-axis indicates the spatial frequency of the grat-ing, the y-axis the frequency at which the noise had the largest efect onillusion strength. Results from the psychophysical experiment are shownin blue (individual observers in light blue, mean across observers in dark).he results for the two models that also predict noise in a speciic frequencyrange to be most efective are shown in red and green. Both models predictmuch lower noise frequencies to be most efective, and both predict the in-crease in most efective noise frequency with increasing grating frequencyto be steeper than observed psychophysically.

8M O D E L I N G R E S U LT S

Modeling results were obtained by computing the output of each of the mod-els to each of the noise stimuli used in the psychophysical experiment, withthree minor changes. First, to speed up computations, and avoid shifts in meanstimulus luminance caused by the introduction of a test patch on either a lightor a dark grating bar, all stimuli contained two test patches, one on the bar justabove the center of the stimulus, one on the bar just below. he test patcheswere shifted to opposite sides so that there was 2° of space between them. Sec-ond, we included three additional lower noise frequencies, because for someof the models, a frequency speciic efect appeared at lower frequencies thanfor observers, and we wanted to quantify this efect. hese frequencies werenot included in the psychophysical experiment to reduce the number of trials.We had found in pilot experiments that responses at these low frequencies didnot difer from those at the lowest frequency tested in the main experiment.hird, we included 50 diferent noise masks, instead of the 10 used in the psy-chophysical experiment. he relatively small number of 50 samples was chosenbecause it was already suicient to make the standard error in the model pre-diction small in comparison to the mean efect size of the noise frequency. Dueto the random nature of the noise, i.e. random luminance variation across theimage, it was possible that by chance diferent noise values would be added tothe luminances at each of the two test patch positions. To counteract such ran-dom luctuation in test patch luminance, Illusion strength was computed asthe diference between responses to incremental and decremental test patchesthat were placed in the exact same noise environment on consecutive trials.Since the scaling of the output is arbitrary in three out of the four models, il-lusion strengths were normalized such that the illusion strength for a stimuluswith the medium grating frequency in the absence of noise received a value


of 4. his approximately corresponds to the mean illusion strength across ob-servers in this condition. he normalization does not unduly alter the resultsand makes comparing the models easier. Model results can be compared tothe psychophysical data shown in Figure 10.

8.1 O D O G

he ODOG model did not reproduce the psychophysical efects (Figure 13).he illusion was abolished at all but the highest noise frequencies, not just ina narrow range between 1 and 5 cpd. he noise with 9 cpd was least efec-tive, which is plausible given that the highest ilter frequency in the modelhas a center frequency of 6.5 cpd. Increasing the grating frequency had littleefect on the model results, other than generally raising the predicted illusionstrength.

he results show that the ODOG model cannot account for the efect ofnarrowband noise on lightness perception in White’s illusion. To understandthis failure, recall that the model produces White’s efect mainly through ori-entation normalization. Adding isotropic noise to the stimuli adds energy inall orientations, thus reduces the ratio of weights between diferent orienta-tions, and in turn reduces the efect size. As long as the range of noise fre-quencies is within the range picked up by the model, i.e. between 6.5 cpd and0.1 cpd, the frequency of the noise will have no speciic efect, because the en-ergy is computed after summing across all spatial frequencies. herefore, themodel cannot capture this aspect of human lightness perception, that White’sillusion is not afected by adding low or very high frequency noise.

8.2 F L O D O G

he ODOG model failed in accounting for the frequency speciic maskingefect because energy was pooled across all spatial frequencies within an ori-entation channel. he FLODOG model might be better equipped to account

M O D E L I N G R E S U LT S 73

for the efect of noise on White’s illusion, because it uses frequency speciicnormalization. Indeed, as depicted in Figure 14, the frequency of the noisedid have an efect on the predicted illusion strength in the FLODOG model.However, the most efective masking frequency was much lower than the 1 to5 cpd observed to be most efective psychophysically. Furthermore, the mask-ing frequency scaled almost proportionally with the grating frequency, whichcan be seen by comparing the middle and bottom panels in Figure 14. his isalso evident in Figure 11, where the slope of the line connecting the two valuesfor the FLODOG model is 0.82. he it for the low frequency grating shouldbe ignored, since it is not suiciently constraint by data at noise frequenciesbelow the dip frequencies.

he precise location of the dip in the FLODOG model is determined bytwo factors: an orientation-speciic efect and a spatial smoothing related ef-fect. hese are easiest understood by considering which of the 42 individualilter responses contributed most to White’s illusion (see Figure 8 for individ-ual ilter responses to a stimulus without noise). One needs to look at ilterswhich have a higher average response to the region that corresponds to thetest patch on the dark bar than to the region that corresponds to the test patchon the light bar. his is the case in all ilters that are oriented orthogonal tothe grating. However, the diference is most pronounced in the ilters with aspatial frequency that matches that of the grating. In addition, all the low fre-quency ilters have a higher average response to the test patch on the dark bar,regardless of ilter orientation. his latter efect is due to spatial smoothing. Areduction in the normalization weight for any of those ilters that contributeto White’s illusion will lead to a reduction in predicted illusion strength.

Following the above reasoning, adding noise with a spatial frequency whichmatches that of the grating has a pronounced efect. However, an even largerefect is achieved with a noise frequency slightly below the grating frequency,because that noise afects both the orientation speciic and the spatial smooth-ing related contributions to the illusion. hese model predictions are in con-tradiction to the psychophysical results, where the largest masking efect isachieved with noise between 1 and 5 cpd, and the scaling relationship be-


tween the grating frequency and the most efective masking frequency is notconstant. he above analysis also implies that changing the free parameters ofthe FLODOG model, i.e. the size of the local normalization window or theinluence of neighboring spatial frequencies on response normalization, couldnot make the model reproduce the psychophysical results, because no suchchange would make noise between 1 and 5 cpd most efective if the gratingfrequency is below 1 cpd.

8.3 D A K I N A N D B E X

In the model of Dakin and Bex, White’s illusion is not produced by orien-tation normalization, because the model contains only isotropic ilters. heirmodel increases the contribution of low spatial frequency ilters to the outputimage, and the resulting spatial smoothing between the surround grating andthe test patches causes the illusion. As illustrated in Figure 15, the Dakin-Bexapproach failed in the presence of narrowband noise. Adding energy, in theform of noise, to the low frequencies, caused the model to assign less weight tothe ilters with low frequencies. herefore, the model predicted the illusion todisappear or even reverse in the presence of low frequency noise. Conversely,for higher noise frequencies, the model increased the weights given to lowfrequency responses and so the predicted illusion strength rose above baselinelevel, contradicting the data in Figure 10. Since in the model, White’s illu-sion is based on spatial smoothing between the grating and the test patch,the model predictions for a high frequency grating are shifted towards higherspatial frequencies and predictions for a lower frequency grating are shifteddownward by an amount that corresponded almost exactly to the frequencydiference between the two gratings. his shift is also in contradiction to thepsychophysical data.

It should be noted that the most prominent reduction in illusion strengthfor low frequency noise was predicted for frequencies that were not includedin the psychophysical experiments. As mentioned above, the illusion was notmuch afected by noise at these frequencies in pilot experiments. he reader


Figure 12: Illustration of the efect of low frequency noise on White’s illusion. heleftmost stimulus is masked with a noise center frequency of 0.11 cpd,the central stimulus with 0.19 cpd, the rightmost stimulus with 0.33 cpd(assuming a viewing distance of 40 cm). None of these masks appear tocause a large reduction in illusion strength.

can convince her- or himself of this fact by inspecting the example stimuliwith very low frequency noise that are depicted in Figure 12.

8.4 B I WAM

In the BIWAM, White’s illusion is explained through a combination of con-trast and assimilation efects mediated by center-surround interactions of theilter responses. Since BIWAM output is not arbitrarily scaled and can beinterpreted in the same units as the input image, the results show that theillusion strength predicted by BIWAM is much smaller than observed psy-chophysically (dotted lines in Figure 16). hese small efect sizes are a resultof the low contrast of the stimulus. At least for the two lower frequencies, thepredicted efect is so small that it would be impossible to measure. In addi-tion, the BIWAM incorrectly predicted that White’s illusion is reversed forthe low frequency grating (the dotted line is below the zero-line in the top-most panel of Figure 16, implying that even without noise, the test patch onthe dark bar is predicted to be darker than the test patch on the light bar at thelowest spatial frequency). he BIWAM is also very sensitive to random dif-


ferences in the noise masks, which can be seen in the large variability acrossthe individual trials. Finally, the BIWAM predicted noise at approximatelythe frequency of the carrier grating to be most efective in reducing White’sillusion. hus, although the model predicted a frequency speciic efect of nar-rowband noise on White’s illusion, it predicted the wrong frequency to bemost efective. It also incorrectly predicted a stronger coupling between themost efective noise frequency and the frequency of the square wave gratingthan observed psychophysically. he slope of the line connecting the two val-ues for the BIWAM model in Figure 11 is 0.86, which lies outside the 95%conidence interval computed from the psychophysical data.


Figure 13: Noise masking results for the ODOG model, analogous to Figure 10. X-axis indicates the center spatial frequency of the noise mask, Y-axis in-dicates illusion strength, measured as the diference in model output be-tween test patches placed on diferent background bars, but in the samenoise environment. he grating frequency is indicated by the star on the x-axis. Large circles are means across trials, small circles are individual trials.For most models and noise frequencies, the efect of diferent noise masksis so small that individual trial data cluster together and form a line, or arehidden by the mean. he dotted horizontal line indicates the overall meanillusion strength of the no-noise condition. No single trial data are plottedfor the no-noise condition, since the model response does not vary acrosstrials without noise.


Figure 14: Noise masking results for the FLODOG model. Same conventions as inFigure 13. he light gray line is the best it to the data, and the locationof the minimum of the it is indicated by the light gray text inset.


Figure 15: Noise masking results for the model by Dakin and Bex (2003). Same con-ventions as in Figure 13.


Figure 16: Noise masking results for the BIWAM. Same conventions as in Figure 13.he light gray line is the best it to the data, and the location of the mini-mum of the it is indicated by the light gray text inset.

9D I S C U S S I O N

None of the spatial iltering models tested in this study was able to reproducethe efect of narrowband noise on White’s illusion that had been observed psy-chophysically. his failure is critical, because, as we argued above, narrowbandnoise speciically interferes with the mechanisms that are supposedly respon-sible for White’s illusion in these models. herefore if this type of interferencedoes not result in a model response that parallels the observed perceptual ef-fects, something important is wrong. he fact that the models seemed to cap-ture human perception in the simple case without noise appears to have beena coincidence. We have therefore arrived at the conclusion that the models arenot simply incomplete, but qualitatively inadequate.

A common criterion for evaluating models of any kind is their predictivepower. For example, Allred, Radonjić, Gilchrist, and Brainard (2012) writethat r[a] complete model of the perception of surface lightness would allowprediction of the lightness of any image region.s However, in addition to be-ing interested in predicting how observers perceive the lightness of an imageregion, we are also interested in explaining why they perceive it as they do. Weagree with Kaplan and Craver (2011) who argued that rmodels [in systems orcognitive neuroscience], like models in plower-level’ neuroscience, carry ex-planatory force to the extent, and only to the extent, that they reveal (howeverdimly) aspects of the causal structure of a mechanism.s Our criticism of themodels discussed here touches precisely on their mechanistic adequacy. hemodels considered in this article aimed at more than prediction. his is ev-ident from the fact that the authors of each model we considered discussedthe model’s physiological plausibility. And although some parts of the modelswere not expected to be found in visual cortex, the critical mechanisms for theexplanation of lightness efects, such as the response normalization and sur-


round integration, were intended to have physiological equivalents. To sum-marize, we think that the failure of multi-scale spatial iltering models in thepresence of narrowband noise speaks against their adequacy as explanations ofhuman lightness perception Even if a model is designed to carry out computa-tions that bear a resemblance to those happening in cortex, that does not meanthat it is a correct model of a speciic process, such as lightness perception.

9.1 L I G H T N E S S P E R C E P T I O N A N D L U M I N A N C E E D G E S

Given that spatial iltering models cannot explain lightness perception in thepresence of noise, the question is whether there are other low-level mecha-nisms that might be able to account for the observed efects. Salmela andLaurinen (2005) proposed that their results are compatible with the idea thatlightness perception is served by mechanisms that respond to luminance edges.his conclusion requires some explanation, because luminance edges are notnarrowband, but instead would elicit responses in ilters sensitive to a rangeof frequencies. However, the results from letter detection (Solomon & Pelli,1994) already indicated that the visual system does not always exploit the fullrange of spatial frequencies for solving a speciic task. If the edges that de-termine perceived lightness are similarly detected only in a limited frequencyrange, this would explain why noise at these frequencies interferes with light-ness perception. he argument linking the noise masking results to the impor-tance of luminance edges for lightness perception further relies on the indingthat the most efective noise frequency did not scale proportionally with thesize of the stimulus. Luminance edges are an obvious candidate to accountfor that efect, because they remain locally unchanged when the stimulus isscaled. hus, a mechanism that irst detects edges would still be impaired bynoise at the same frequency, even if the surface bounded by the edge becomessmaller or larger. his interpretation also its well with the perceptual impres-sion many observers have in Figure 7: In the central panel, the edges of thetest patch are diicult to see, and this in turn makes the test patches mergewith the bars on which they are embedded.

D I S C U S S I O N 83

One argument against the edge based explanation is that the most efec-tive noise frequency was not fully constant across stimulus scales. here wassome scaling with grating frequency although much less than what would beexpected if White’s efect depended on the response of ilters matched to thescale of the test patches. he partial scaling of the efective noise frequencywith grating frequency could hint at the involvement of more than one mech-anism in the judgment of lightness in the present task. For example, it hasbeen suggested that White’s illusion depends on a perceptual scission of thetest patches and the grating bars into two layers (Anderson, 1997). In addition,separating the test patches and the grating in depth through stereo presenta-tion has also been found to afect the illusion (Taya et al., 1995). If indeedmultiple mechanisms are involved in causing White’s illusion, it might bethat some of these mechanisms are not scale-invariant. A further complicationcould be caused by the fact that the scission mechanism may also be inluencedby noise. A number of observers have informally reported that they perceivethe low frequency noise as a layer of clouds overlaying the grating stimulus.his layer separation does not seem to happen for the high frequency noise.

here are a number of studies that support the importance of luminanceedges in lightness perception, psychophysically (Shapley & Tolhurst, 1973;Kurki et al., 2009; Geier & Hudák, 2011; Anstis, 2013; Robinson & de Sa,2013), as well as physiologically (von der Heydt, Friedman, & Zhou, 2003;Zurawel, Ayzenshtat, Zweig, Shapley, & Slovin, 2014). Rudd (Rudd & Zemach,2005; Rudd, 2013, 2014) proposed a model of lightness perception in whichedge integration is a critical factor in the computation of lightness. We have re-cently provided additional support for this approach by showing that White’sillusion is largely determined by the luminance contrast across the edges of thetest patch (Betz, Shapley, Wichmann, & Maertens, 2015b). In that study, weused contour adaptation (Anstis, 2013) to selectively mask the edges of the testpatch that are either orthogonal or parallel to the inducing grating. We foundthat adapting to the orthogonal edges greatly reduced, and for some observersreversed White’s illusion. Adapting to the parallel edges had a smaller efect,and tended to enhance the illusion. hese results support our conclusion that


narrowband noise afects perceived lightness primarily in the frequency rangebetween 1 and 5 cpd because noise in that frequency range interferes with theedge detection that is a irst step in the computation of surface lightness.

9.2 E D G E - B A S E D M O D E L S A N D T H E F I L L I N G - I N P R O B L E M

here is one obvious advantage of spatial iltering models over models thatare based on luminance edges. Spatial iltering models sidestep the illing-inproblem, which refers to the problem that in order to perceive homogeneoussurfaces, information at the edges of a surface must somehow be used to ill-inthe entire surface area. Spatial iltering models rsolves the illing-in problemby including large ilters that are tuned to low spatial frequencies and theseilters produce a surface response.

he argument that the perceptual phenomenon of illing-in is mediated bylow spatial frequency signals was most prominently formulated by Dakin andBex (2003). hey stressed the importance of low spatial frequency content forlightness perception, but the precise meaning of plow’ was not deined. Insteadthey presented a demo using the Craik-O’Brien-Cornsweet (COBC) illusionin which either the high or the low spatial frequency content was shuled.Phase shuling the high frequency content left the illusion intact, whereasphase shuling the low frequency content destroyed it (Figure 17A-C).

At irst sight this demo seems in contradiction to the claim advocated here,that luminances edges, detected predominantly at frequencies within a bandof 1 to 5 cpd, are most relevant for lightness perception. However, Dakin andBex referred to all frequencies below 30 cpi as low frequencies. his would cor-respond to about 5 cpd in an image that is 4 cm wide and viewed at a distanceof 40 cm. heir original demo, thus, cannot distinguish between the alterna-tive hypotheses that all frequencies below 5 cpd are relevant for lightness per-ception, or that the efect is actually dependent on a speciic frequency bandsomewhere between 0 and 5 cpd. Figure 17 shows a demo that is analogousto the one used by Dakin and Bex, but with an additional stimulus, in whichthe phase shuling has only been applied to frequencies below 6 cpi (≈1 cpd)


Figure 17: COBC-type illusion (after Dakin & Bex) demonstrating the efect of shuf-ling the phase information in diferent frequency bands. A. Unshuledstimulus. he hair and cap look darker then the face, even though lumi-nance diferences are only present at the border between the regions. B.Shuling the phases below 30 cpi destroys the illusion. C. Shuling phasesabove 30 cpi preserves the illusion. D. Shuling phases below 6 cpi alsopreserves the illusion, in fact the shuling is hardly noticeable, since thereis by design very little energy in these low frequencies in the COBC-typeimage. his shows that the efect depends on some frequency band below30 cpi and above 6 cpi, not simply on all low frequencies. Note that at aviewing distance of 40 cm, these images subtend around 6 degrees visualangle, so the critical band is between 1 and 5 cpd. A-C recreated afterDakin & Bex(2003), but using a face image that is in the public domain,as done previously by J. Geier and M. Hudák (poster presentation at theEuropean Conference on Visual Perception 2013).


(Figure 17D). Readers can judge for themselves, but to us it seems that thismanipulation leaves the illusion intact. his demo supports the inding thatsome intermediate frequency band is important for lightness perception. heapparent conlict between Dakin and Bex’s demo and the present results canthus be resolved in favor of the importance of luminance borders. However, ifwe abandon spatial iltering models as accounts for the perception of surfacelightness in favor of models that are based on luminance edges, the illing-inproblem needs to be addressed in future experiments and modeling.

One might question whether the failure of four speciic models shown heresuices to argue against an entire class of models, and ask if there are possiblemodiications that could save the models. he current spatial iltering mod-els are incompatible with the idea that lightness perception depends on a twostage process, that irst computes luminance ratios across edges, and then ex-trapolates the lightness values that are based on these edge ratios to the entiresurface bounded by the edges. In spatial iltering models, surface lightness de-pends on the response of ilters that are centered on the surface, and whoseresponse may be inluenced by the surround through large receptive ields, andpotentially through normalization efects. here is no mechanism for extrap-olating edge responses to the center of a surface, and thus frequency speciicefects of noise masking will always be coupled to the spatial scale of the targetsurface. his holds independently of whether the speciic implementation ofthe ilters is explicitly designed as in the models tested here, or learned in aneural network approach (Corney & Lotto, 2007).

9.3 D I F F I C U LT I E S I N R E P L I C AT I O N E X P E R I M E N T

We found in pilot experiments that a one-to-one replication of Salmela andLaurinen’s study was diicult, because there was high variability in responseseven between experienced observers. While some observers, including the irstauthor, produced data very similar to observer VS in the original study, oth-ers showed very little efect of the noise masking. In conditions where the testpatch was hard to detect, and thus looked similar in lightness to the grating bar


on which it was placed, some observers looked at the stimulus for a very longtime trying to detect the test patch, while others simply matched the lightnessof the grating bar. In order to reduce the inluence of such diferent strategies,we attempted to make the task more objective by using a 2AFC paradigm,in which observers simply indicated which of two simultaneously presentedtest patches appeared brighter. However, close inspection of the psychomet-ric functions from that experiment revealed that for some noise frequencies,there is no point where test patches placed on dark and light grating bars ap-pear equal in lightness. When observers did not see the patches, they judgedthe lightness of the bars, and then the test location on a light bar is alwayslighter than the test location on the dark bar. However, when they did see thepatches, they almost always saw the patch on a light bar as darker, regardlessof the precise luminance values of the two patches. hus, if their response inthe 2AFC task was around 50% for some test luminance value, this was prob-ably because they saw the test patch in half of the trials, and did not see itin the other half. It was not because the test and the standard, if both werevisible, look equal in lightness at these luminance values. his implies thatanalyzing the 2AFC data by itting psychometric functions and estimatinga point of subjective equivalence is misleading when measuring White’s illu-sion masked by narrow-band noise. It also hints at the important connectionbetween edge visibility and perceived lightness of the patches. After furthertesting, we found that reducing the presentation time of the stimuli led tomore similar behavior across subjects, so we opted for a lightness matchingparadigm with short presentation times. But even then, two out of our 11 ob-servers showed behavior very diferent from the others, and the magnitude ofboth White’s illusion and the efect of noise difered widely across observers(see individual observer data in the supplemental material).

One possible explanation for these diiculties is that the noise may makethe matching task perceptually ill-deined. he luminance of the test patchesis not homogenous, and observers may have diferent strategies for arrivingat a single lightness value that they use for their match. In the low frequencynoise conditions, the noise can appear as a layer of clouds or haze in front of a


homogenous grating, and this layer separation makes the matching relativelystraightforward. At very high noise frequencies, the noise is so ine-grainedthat it is not diicult to get an impression of the average lightness of the testpatch, which in that case may appear as textured. At intermediate noise fre-quencies (i.e., those where we ind a reduction or reversal of White’s illusion)it can be diicult even to detect the test patch as a separate region, whichmakes the matching most diicult. In that case, most observers matched theaverage lightness in the region where the test patch would have been visiblewithout the noise, which explains why in this condition, test patches (or rathertest areas) on a light grating bar where often matched with higher lightnessvalues than test areas on a dark grating bar. To us, these observations suggestthat there is a close connection between image segmentation (i.e., the explicitperceptual separation of the test patches as a distinct region) and lightnessperception. Still, despite these diiculties with interpreting precisely what thelightness matches mean, the data consistently demonstrate that for most ob-servers, noise in the range from 1 to 5 cpd has the largest efect on perceivedlightness, and that the most efective noise frequency does not scale propor-tionally to the grating frequency.


We started from the question to what extent low-level visual mechanismsalone can account for diferent lightness phenomena. Our analysis showedthat the most popular class of low-level models, spatial iltering models, can-not provide an adequate explanatory account of White’s illusion. While thiscould indicate that higher-level factors are required for the explanation oflightness perception, the importance of edge information in the computationof surface lightness still leaves potential for a low-level mechanism.

here were other (low-level models) models of lightness perception that ad-vocated the importance of luminance edges (Watt & Morgan, 1985; Morrone& Burr, 1988; Kingdom & Moulden, 1992; Grossberg & Todorović, 1988;Kelly & Grossberg, 2000). According to Kingdom (2011), the problem with


some of these models (Watt & Morgan, 1985; Morrone & Burr, 1988; King-dom & Moulden, 1992) is that the integration of edge information over 2Dimages is intractable. A further argument against the models by Grossberget al. is that the proposed illing-in mechanism did not capture neurophysi-ological data (von der Heydt et al., 2003). However, r[t]he inal reason why[these] models have failed in their bid to account for brightness phenomenais that they have been superseded by another class of spatial-iltering models(Kingdom, 2011). In light of the failure of this new class of models that wasdemonstrated here, we believe that it may be time to reconsider the edge basedapproach to lightness perception.

Part III

C O N T O U R A D A P TAT I O N

his part has been published as:Betz T, Shapley R, Wichmann F A, Maertens M (2015). Test-ing the role of luminance edges in White’s illusion with contouradaptation. Journal of Vision, 15(11): 14, 1-16


In 1979 White presented a stimulus that caused a problem for contrast-basedaccounts of lightness perception (White, 1979). He showed that when graypatches were superimposed on a black-and-white square-wave grating, thosepatches that were placed on the black bars of the grating looked lighter thanthe patches that were placed on the white bars (Fig. 18). A lightness computa-tion based on luminance ratios would predict the opposite efect, because testpatches placed on black bars share more border with white bars, and henceshould appear darker than patches placed on white bars. Since the originalpublication, numerous attempts have been made to explain White’s illusion,and to integrate it with existing theories of lightness perception (White, 1981;Kingdom & Moulden, 1991; Spehar et al., 1995; Taya et al., 1995; Ander-son, 1997; Gilchrist et al., 1999; Blakeslee & McCourt, 1999; Ripamonti &Gerbino, 2001; Anstis, 2005; Howe, 2005; Robinson et al., 2007; Salmela &Laurinen, 2009). However, to this day there seems to be no consensus abouthow White’s illusion can be explained.

he most prominent low-level mechanistic explanation of the illusion isgiven by spatial iltering models (Blakeslee & McCourt, 1999; Dakin & Bex,2003; Robinson et al., 2007; Otazu et al., 2008). We have recently shown(Betz, Shapley, Wichmann, & Maertens, 2015a) that these models are un-likely to include the correct mechanisms to explain White’s illusion, becausethey cannot account for the efect of narrowband luminance noise on the per-ceived lightness of the test patches (Salmela & Laurinen, 2009). Instead, ouranalyses suggested that luminance edges at the test patch boundaries are cru-cial for the computation of their lightness. However, this raises the questionof how exactly the luminance contrast across the edges determines perceivedlightness in White’s stimulus. As we have pointed out above, a simple account

94 C O N T O U R A D A P T I O N

Figure 18: White’s illusion. he test patch on the black bar shares more border withthe white lanking bars than with the black coaxial bar, so based on edgecontrast alone, it should appear darker than the test patch on the whitebar. he opposite is the case.

that weights the edge contrast by the length of the border is insuicient be-cause it makes the incorrect prediction that the test patch on the dark barshould appear darker than the test patch on the light bar. herefore, if edgecontrast is indeed critical for perceived patch lightness, and if the length ofthe border is not critical for perceived patch lightness, then an alternative hy-pothesis would be that it is the orientation relationship between the edges andthe grating which is a critical factor.

Here, we test the contribution of luminance edges to perceived lightness inWhite’s illusion experimentally by employing the method of contour adapta-tion. Anstis (2013) showed that adapting to a high contrast lickering contourfor a few seconds strongly reduced the perceived contrast of a luminance edgethat was subsequently presented at the adapted position. Luminance edgesthat are presented with a low contrast can disappear completely when pre-sented subsequently to an adapting contour. We used this technique to adaptthe edges of the test patches in White’s illusion and to observe the efect of


contour adaptation on the perceived lightness of the test patch. If the lumi-nance contrast across edges is indeed a major determinant of a surface’s light-ness, then adaptation should have a measurable efect on test patch lightnessin White’s illusion. In particular, incremental edges, i.e. higher intensity in-side than outside, should have a brightening efect and decremental edges, i.e.lower intensity inside than outside, should have a darkening efect on the sur-face. When the inluence of the edge is weakened by means of contour adapta-tion then its role in determining the lightness of a surface should be weakenedas well. Speciically, adapting at the location of incremental edges should re-duce the brightening efect and hence make a patch appear darker, whereasadapting at the location of decremental edges should reduce the darkening ef-fect and make a patch appear brighter. hus, adaptation to the edges parallelto the grating should make the patch on the dark stripe lighter and the patchon the light stripe darker, increasing White’s illusion. Adapting to the edgesorthogonal to the grating should make the patch on the dark stripe darkerand the patch on the light stripe lighter, decreasing White’s illusion. MoviesM1 and M2 illustrate adaptation to the orthogonal and to the parallel edges,respectively. Informal observations generally conirmed the edge-based pre-dictions above. hese demos suggest a role for both types of luminance edgesin White’s illusion. However, adapting to the edges orthogonal to the gratingseems to have a larger efect on perceived lightness. To substantiate and quan-tify the informal observations, we tested the efect of contour adaptation onWhite’s efect in a psychophysical experiment.

In the second part of this work, we analyze the implications of our indingsfor spatial iltering models of lightness perception. We focus our eforts onthese types of models because they are currently the only computational mod-els that allow the prediction of the lightness of an image region based on the lu-minance of an input image. In their original form, the models are not equippedwith mechanisms that are sensitive to temporal adaptation, and hence did notallow to make predictions about the response to contour adaptation. We there-fore implemented an adaptation mechanism in the most widely cited model(ODOG; Blakeslee & McCourt, 1999), and in two more recent spatial ilter-


Movie 1: Contour adaptation of the test patch edges orthogonal to the grating. hemovie consists of 5 s adaptation, and 1 s static presentation of White’s stimulus. Itshould be viewed in a loop, with constant ixation on the central circle. Most observerssee the test patches merge with the grating bar on which they are placed. Movie ilesare available with the published article at http://jov.arvojournals.org/article.aspx?articleid=2430776

Movie 2: Contour adaptation of the test patch edges parallel to the grating. Identicalto Movie 1 except for the orientation of the adaptors. Most observers see the testpatches bleed out into the neighboring bars.

http://jov.arvojournals.org/article.aspx?articleid=2430776



ing models that employ local normalization mechanisms and might thus bebetter suited to account for contour adaptation (Robinson et al., 2007; Otazuet al., 2008). We show that regardless of the choice of adaptation parame-ters, the models cannot reproduce the contour adaptation efects that wereobserved psychophysically. his analysis adds further evidence to our recentclaim (Betz et al., 2015a) that pure spatial iltering accounts are unlikely to bea correct explanation of lightness phenomena.

11M E T H O D S

11.1 PA R T I C I PA N T S

Ten naive observers (four female) participated in the experiment. Observers’mean age was 29 years (min 22, max 37). With the exception of one observer,they had normal or corrected to normal vision. Observer 6 had 20/25 vision.Observers were inancially compensated for their time.

11.2 S T I M U L I A N D A P PA R AT U S

he test stimuli consisted of a version of White’s illusion in which a squaretest patch was embedded. he grating contained six bars, three light and threedark bars, with a total size of 7.32°×7.32°. he test patch was 1.22°×1.22°

wide. he dark bars had a luminance of 39.6 cd/m2 and the light bars of48.4 cd/m2 corresponding to a Michelson contrast of 0.1. he contrast wasdeliberately chosen to be low, because the efect of contour adaptation is mostpronounced for low-contrast edges (Anstis, 2013). he background luminancewas 44 cd/m2. he comparison square was also 1.22°×1.22° in size. Its initialluminance was randomly set in each trial to a value between 26 and 44 cd/m2.It was presented on top of a random checkered background that consisted of13×13 checks of size 0.58°×0.58° with gray values sampled uniformly fromvalues between 35 and 53 cd/m2.

he test grating was centered horizontally on the screen, and placed abovea central ixation circle, so that its lower boundary was directly adjacent to theixation circle. he comparison background was placed directly below, and


in each trial the comparison patch was placed at the same distance from theixation circle as the test patch (Fig. 19.

Figure 19: Illustration of the screen during matching. he observer adjusted the com-parison square in the lower half of the screen to match the lightness of thetest patch in the grating. he gray background was actually larger, and hasbeen cropped for this illustration.

he adapting stimuli consisted of two parallel bars, each 0.13° (4 px) wideand 1.22° tall, and separated by 1.22°. Adapting stimuli were centered on thelocation of the edge, such that they had 2 px overlap with the test patch and2 px overlap with the background stripe of the grating.

Stimuli were presented on a linearized 21s Siemens SMM21106LS moni-tor (400×300 mm, 1024×768 px, 130 Hz) controlled by a DataPixx (VPixxTechnologies Inc. Saint-Bruno, QC, Canada) and custom presentation soft-ware developed in our lab and published at https://github.com/TUBvision/hrl. Observers were seated 70cm from the screen, and their position was ixedwith a chin-rest. Responses were recorded with a ResponsePixx button-box.

https://github.com/TUBvision/hrl

https://github.com/TUBvision/hrl

M E T H O D S 101

11.3 P R O C E D U R E

Our goal was to measure the efect of edge adaptation on the perceived light-ness of the test patches in White’s illusion. Our task and presentation parame-ters were similar to those employed by Anstis (2013). Adaptors and test stimuliwere presented in a loop as long as required by the observers to complete theirlightness setting. A trial started with the lickering adaptors that were shownfor 5s. he adaptors were contrast-reversing with a frequency of 5Hz and werepresented at 100% contrast (luminance changed between 0.24 cd/m2 and 88cd/m2; background luminance was 44 cd/m2). After the adaptation period,the test stimulus was shown for one second, and then the adaptation cyclestarted again.

Observers’ task was to adjust the lightness of the comparison patch so as tomatch the perceived lightness of the target patch that was embedded in thesquare wave grating of the White stimulus. Observers indicated when theywere satisied with their setting by a button press and continued to the nexttrial.

11.4 E X P E R I M E N TA L D E S I G N

he independent variable was the type of adaptor used, which could be or-thogonal to the grating, parallel to the grating, or none. he latter conditionwas included as a baseline in order to measure the strength of White’s illusionfor our experimental stimuli and presentation parameters. We included twomore controls to test the importance of the exact alignment between adaptorsand luminance edges. In these controls, the adaptors were shifted by half a barwidth orthogonal to their orientation and in a random direction (see moviesM3 and M4). Figure 20 illustrates all types of adaptors used.

We used two grating orientations (horizontal and vertical) so that the abso-lute adaptor orientation was not confounded with the adaptor type (i.e. paral-lel and orthogonal to the grating). Test patches appeared in one of four posi-tions: on the second (near) or third bar (far) relative to ixation, and immedi-


Movie 3: Contour adaptation with shifted orthogonal adaptors. Identical to Movie 1except for the shift of the adaptors. Most observers see little efect of these adaptors,and perceive White’s illusion similar to the unadapted condition.

Movie 4: Contour adaptation with shifted parallel adaptors. Identical to Movie 2except for the shift of the adaptors. Most observers see little efect of these adaptors,and perceive White’s illusion similar to the unadapted condition.

M E T H O D S 103

Figure 20: Illustration of the diferent types of adaptors used in the experiment. Fromtop left to bottom center: no adaptor, orthogonal to the grating, parallel tothe grating, orthogonal and shifted, parallel and shifted. he bottom rightstimulus illustrates the simultaneous contrast control condition, which didnot have an adaptor. Note that in the experiment, presentation of grat-ing and adaptors was separated in time, and adaptors lickered, i.e. theyswitched luminance between black and white. Also note that the gratingwas phase-shifted by 180° in half of the trials, making the test patch atthat location an increment instead of a decrement. he background of thesimultaneous contrast condition was dark in half of the trials.


ately to the left or to the right of the screen center. We had noticed in pilot ex-periments, and participants conirmed this observation, that the near positionwas easier to match. he far condition, on the other hand, had the advantagethat the test patch was located more centrally within the stimulus which is amore typical coniguration for White’s illusion. herefore we included bothconditions. Matches did not difer between the near and far condition how-ever, and thus we collapsed the data from the two in the analysis. he irst(i.e. topmost or leftmost) bar of the grating could either be light or dark, sothat every test patch position could become an increment or a decrement withrespect to the bar on which it was placed.

In order to prevent observers from using cognitive strategies that departedfrom pure lightness perception for their matching (e.g. use the backgroundluminance as a reference for their judgments if they assumed that the testpatch is always mean gray), we measured lightness matches for three diferentpatch luminances ( 42.2, 44, and 45.8 cd/m2). Finally, we included a controlcondition without adaptors in which the test patch was placed on a homo-geneous background (either 39.6 cd/m2 or 48.4 cd/m2), so that we couldcompare our efect sizes to simultaneous lightness contrast. Overall, the ex-periment consisted of 288 trials (2 grating orientations × 5 adaptor types ×4 test patch positions × 2 grating phases × 3 test patch luminances + 2 × 4× 2 × 3 simultaneous contrast controls).

12R E S U LT S

he critical features of the results are easiest to understand by looking irstat data from an individual observer (Fig. 21). Averages across observers areshown in Figure 23, and individual data from all observers are available assupplemental material with the published article (Figs. S1-S10 at http://jov.arvojournals.org/article.aspx?articleid=2430776).

In the single observer data (Fig. 21) light gray symbols indicate the matchesthat were made to a test patch placed on a light bar and dark gray symbolsindicate the matches that were made to a test patch placed on a dark bar of thegrating. Since in White’s illusion test patches on light bars appear darker andtest patches on dark bars appear lighter, in this representation White’s illusionshows itself as light gray symbols having lower values than dark gray symbols.his is what was observed in the no adaptor condition (Fig. 21 upper leftpanel) for all three test patch luminances. Illusion strength can be expressedas the diference in match luminance between the test patch on a dark and ona light bar. he average magnitude of White’s efect across patch luminancesfor this observer was 3.3 cd/m2.

he lower right panel in Figure 21 shows the simultaneous lightness con-trast efect which amounted to 3.9 cd/m2, and was hence of similar magnitudeas White’s efect. Note that, somewhat unconventionally, in our depiction asimultaneous lightness contrast efect has the same sign as White’s illusion.his is because we label the conditions with respect to the luminance of thebar on which the test patch is placed, and not with respect to the luminanceof the lanking bar. We chose this type of labeling, because in our version ofthe stimulus the test patches were squares and thus shared an equal amountof border with the carrier and the lanking bars. We found using the carrierbar as the reference most intuitive.




Figure 21: Lightness matching results for one observer. he small icons indicate the stimulus condition. hex-axis denotes the three diferent levels of test patch luminance and the y-axis the luminance of the matchingpatch. Light gray data points are for test patches on a light gray background (either a light gray bar in White’sillusion, or a light gray square in simultaneous contrast), dark gray points are for dark backgrounds. Smallcircles are individual trials, the squares indicate means across trials. Outliers are marked as red plus-signs, andwhere excluded for the computation of the means. he black horizontal line indicates the mean luminanceof the display, the solid gray lines the luminances of the light and dark grating bars, and the dotted lines thediferent test patch luminances. he strength of the illusion corresponds to the diference between the lightand dark squares at a given test patch luminance. Note that only in the condition where the edges orthogonalto the grating have been adapted (middle panel, top row) does the illusion disappear.

R E S U LT S 107

Figure 22: Lightness matching results for a diferent observer (fourth from the rightin Figure 23). Same conventions as in Figure 21. Note that for this ob-server, White’s illusion is not only absent, but reversed in the orthogonaladaptor condition (middle panel, top row). Test patches on dark stripes ap-pear dark in this condition, and test patches on light stripes appear light.


he efect of contour adaptation can be seen by comparing the data forthe orthogonal adaptor with those for the parallel one. After adapting to theedges orthogonal to the grating, White’s illusion for this observer was reducedto zero (Fig. 21 upper middle panel). Similar matches were made for testpatches on light bars and on dark bars. On the other hand, adapting to theedges parallel to the grating had a smaller efect on the perceived lightness ofthe test patches. For this observer, the magnitude of White’s efect was 5.0cd/m2 after adaptation with parallel adaptors. Similarly, adaptors that wereshifted with respect to the grating edges had no efect on White’s illusion. hedata for shifted adaptors look similar to the data in the no adaptor condition(Fig. 21 lower left and middle panel).

Figure 22 shows the results for a diferent observer. he results are compara-ble to the irst observer except for the orthogonal adaptation condition (uppermiddle panel). For this observer adapting to the edges orthogonal to the grat-ing did not only reduce the lightness diference between the test patches inWhite’s illusion but instead led to a reversal. he observer reported that adap-tation made the test patches invisible and hence they merged with the bar onwhich they were placed. hus, a test patch on a dark bar appeared as dark asthe bar itself and vice versa for a test patch on a light bar (Fig. 22). Such areversal of the efect occurred for four out of ten observers.

To summarize the results across observers, we expressed illusion strength asthe diference in match luminance between the test patch on a dark and ona light bar. We further averaged across the three test patch luminances. Wefound that six out of ten observers showed a signiicant White’s efect in thecondition without adaptors (Fig. 23); the other four did not (Fig. 24). For thesix observers that did perceive White’s efect in the no adaptor condition, it isevident from Figure 23 that the strength of White’s illusion was reduced, andfor some observers even reversed, after adaptation to the edges orthogonal tothe grating. Adapting to the edges parallel to the grating slightly increased theillusion, while the shifted adaptors had little or no efect.

To determine conidence intervals for the illusion strengths we drew 10,000bootstrap samples from the data. We resampled with replacement from the

R E S U LT S 109

eight data points that were measured in each condition (test patch luminance xcarrier bar luminance) and then computed illusion strength as described abovefor each of the samples. Data points that lay more than twice the interquartilerange away from the median of a condition (marked as outliers in Figure 21)were excluded from this analysis, as they were likely due to response lapses. Forive out of the six observers that showed White’s illusion, the 95% conidenceintervals show no overlap between the no adaptor and the orthogonal adaptorcondition, indicating a statistically signiicant diference.

Figure 23: Illusion strength for the six observers showing White’s illusion in the noadaptor condition. Colored circles represent mean values for individualobservers, errorbars indicate bootstrapped 95% conidence intervals forthe means. Large red circles are means across observers. Observers areordered by the illusion strength they show for White’s illusion withoutadaptors. he observers plotted in the two previous igures correspond tothe third and fourth datapoints from the right in this igure.


Figure 24: Illusion strength for the four observers not showing White’s illusion in theno adaptor condition. Same conventions as in Figure 23

here was considerable variability across observers. As mentioned above,four observers did not report perceiving White’s illusion (Fig. 24) and theyalso did not show an efect of simultaneous contrast. Some of these observers,on inquiry after the experiment, explained that they had tried to compen-sate their matches for putatively illusory lightness efects, although we hadinstructed them explicitly to match lightness as they see it and not as they inferit. According to their reports one can assume that cognitive factors had someinluence on these observers’ judgments. he efect of the adaptors, however,was preserved even in the four observers who reported no White’s illusion, asorthogonal adaptors reduced ’illusion strength’, parallel adaptors slightly en-hanced it, and shifted adaptors had no efect. We address the issue of cognitiveefects on perceptual judgments in more detail below (see Section 14.3).

13C O M P U TAT I O N A L M O D E L I N G

he efects of contour adaptation on White’s illusion provide a challenge forspatial iltering models with contrast normalization (e.g. Blakeslee & Mc-Court, 1999; Robinson et al., 2007; Otazu et al., 2008). hese models explainWhite’s illusion as the result of cortical iltering of the input stimulus with aset of ilters that span a large range of spatial frequencies and orientations. heoutputs of the individual ilters are weighted depending on the energy in eachilter response and then recombined to create a lightness image. he resultingoutput image has lower values at locations that observers tend to perceive asdark, and higher values at locations that observers tend to perceive as bright,although the luminances at these locations are identical in the input image.Spatial iltering models were not designed to treat luminance borders explic-itly, but the orientation and spatial frequency selectivity of their componentilters make the models responsive to contrast edges. We have recently ana-lyzed these models (Betz et al., 2015a), and concluded that they are unlikelyto be a correct explanation of lightness perception. However, the adaptationefects reported here might be the result of mechanisms that interfere withvisual processing at the same early level of processing at which spatial ilter-ing models presumably operate. We therefore wanted to test whether or towhat extent the models could capture the experimentally observed adaptationefect.

he models in their original form did not contain a mechanism that wouldimplement a temporal adaptation efect. We therefore augmented the ODOG(Blakeslee & McCourt, 1999), FLODOG (Robinson et al., 2007) and BI-WAM (Otazu et al., 2008) models by a respective adaptation mechanism. Togive the models a fair chance we tested them with favorable, even potentiallyunrealistic, choices of adaptation parameters. For the implementation we had


to decide between two candidate mechanisms of adaptation. Retinal adapta-tion would be modeled by changing the input to the model. Cortical adapta-tion would require a modiication of the model implementation, in particularit would require the possibility of attenuating the individual ilter responsesdepending on a ilter’s response to the adapting stimulus. Anstis (2013) hasargued that the contour adaptation mechanism is unlikely to be of retinal ori-gin, because the mean luminance of the adaptors over time is equal to thebackground, and the adaptors do not create an afterimage. Also, subjectivecontours do not adapt, which has been interpreted to suggest that the relevantadaptation happens in primary visual cortex (Anstis, 2013).

We therefore implemented a variant of cortical adaptation as a reduction inthe gain of the linear ilters, in close analogy to previous work (Goris, Putzeys,Wagemans, & Wichmann, 2013). First, we compute the response of each ilterto the adaptor. We then use these ’adaptor responses’ to determine the magni-tude of attenuation for the ilter responses to the stimulus. he ilter responsesat each location of the image are attenuated in proportion to the ’adaptor re-sponses’ at that location. he adaptors are changing luminance (back and forthbetween black and white on a mean gray background) over time. However, forsimplicity, we compute the response to the adaptor by computing the responseof the ilter to a dark adaptor on a gray background and by taking the abso-lute value as the maximal response of the ilter to the lickering adaptor overtime. his approach allows us to test whether it is possible to predict the ob-served contour adaptation efects qualitatively with the ODOG, FLODOGor BIWAM model.

In order to model this type of adaptation we need to consider two factors,the efect of maximum adaptation and the amount of response reduction toany stimulus between no adaptation and maximal adaptation. he maximumadaptation efect is the magnitude of response reduction when the ilter haspreviously been adapted with an optimal stimulus. We express the maximumadaptation efect as a fraction α of the response of an unadapted ilter. It hasbeen shown that iring rates in cat simple cells decrease on average to about20% of their pre-adaptation value after prolonged adaptation (Sanchez-Vives,

C O M P U TAT I O N A L M O D E L I N G 113

Nowak, & McCormick, 2000). he (physiologically unrealistic) limit for adap-tation would be a ilter response of zero at the adapted locations. Second, weneed to determine how the response of a ilter changes with varying amountsof adaptation due to stimuli that are less than optimal. his second factoris more complicated to implement, because none of the models contains anynon-linearities that would cause the ilter responses to saturate. herefore, thelevel of stimulation for complete adaptation of the ilter is undeined, and sois the function that relates the magnitude of adaptation to the level of stimula-tion. We modeled the adaptation level as an inverse cumulative Gaussian func-tion of the adaptor response. Free parameters are the mean and the standarddeviation of the Gaussian, µ and σ. µ deines the amount of response to theadapting stimulus that is required to reach 50% of the maximum adaptationefect. σ determines how quickly adaptation changes for diferent values of theadaptor response. Higher values of σ imply that adaptation drops quickly forsuboptimal stimulation, whereas lower values imply that even a weak responseto the adapting stimulus would still lead to substantial adaptation. hus, theadapted response of each ilter is given as

r = r0 ∗ (1− (1−α) ∗Φ (|ra|,µ,σ))

where Φ is the cumulative normal distribution function, r0 is the unadaptedresponse, and ra is the response to the adapting stimulus. Examples of thisfunction for diferent parameter values are shown in Figure 25. hese adaptedilter responses are then added and normalized in exactly the same way as theunadapted responses would be in the standard versions of the models.

To evaluate whether the models are in principle capable of reproducing theobserved efects of contour adaptation we explored the parameter space of α,µ, and σ. We irst looked at combinations of low, medium, and high values forthe three parameters. Forα, the most extreme parameter setting is zero, whichwould correspond to complete response reduction of the ilter (Fig. 25, leftpanel, black line). A medium adaptation efect would require a more realisticparameter setting of about 0.2, and a mild adaptation efect could be modeled


Figure 25: Illustration of the efect of the three parameters on the function relatingthe response to the adapting stimulus to the level of adaptation. he x-axisshows the response to the adapting stimulus, the y-axis indicates the re-sponse strength resulting from this adaptation level. Each panel illustratesthe efect of changing one of the three parameters while keeping the othertwo ixed. Black lines indicate smaller parameter values.

with a parameter setting of 0.5. A meaningful range of parameter settingsfor µ and σ is less obvious. An important indicator for the upper limit is thelargest possible response of a ilter. Since all our stimuli are in the range [0, 1],the maximum response of a ilter would be achieved by a stimulus that is 1where the ilter is positive, and 0 where the ilter is negative. his responseis simply the sum of positive values in the ilters integration ield. For iltersin the ODOG and FLODOG models this value is ≈ 0.32. he exact valuedepends on the speciic parameters used in our model implementation. Sinceµ deines the value where the cumulative Gaussian function has a value of 0.5,setting µ to a value of 0.32 would mean that even ilters which are optimallyresponsive to the adaptors will reach only 50% of the maximum adaptationlevel. On the other hand, setting µ to 0 would mean that even ilters that donot at all respond to the adapting stimulus will reach 50% of the maximumadaptation level. Both options are too extreme, because an optimal stimulus


should cause full adaptation, and a stimulus that causes no response in theilter should not cause any adaptation. A meaningful range is somewhere inbetween these two values. We chose values of µ ∈ {0.08, 0.01, 0.001} for thepresent exploration. A iner sampling of the parameter space was requiredfor the BIWAM model because for that model the efect of changing theµ parameter was not monotonic. For BIWAM we tested µ values between0.1 and 0.0005. Having determined values for µ somewhat constrained theplausible range for σ. In order to ensure that there is (almost) no adaptationin ilters that have no response to the adaptor, σ should be at most half aslarge as µ. We tested model responses for values of σ ∈ {0.04, 0.005, 0.0001},skipping those combinations where σ > µ

2. For the BIWAM, we tested eight

linearly spaced values between 0.005 and 0.0001.Our results show that the efects of adaptation in ODOG and FLODOG

are similar. In both models, it was not possible to reproduce the efect ofcontour adaptation observed psychophysically (Fig. 26). Most of the testedparameter settings caused only mild adaptation efects, and failed to repro-duce the strong and speciic efect of orthogonal adaptors on perceived patchlightness. Only with extreme parameter settings the reduction or even rever-sal of the illusion in the orthogonal adaptor condition could be reproduced.However, these settings caused unspeciic adaptation efects in all conditions,including the parallel and the shifted adaptor conditions, which is in contra-diction to what was observed experimentally.

To accomplish this strong adaptation we had to use small values for µ,which implies that even ilters that responded only weakly to the adaptor werestrongly inhibited. his allowed the adaptation to afect also large ilters in themodels. Such large ilters are important for determining surface lightness faraway from the edges, but they are only weakly stimulated by the small adap-tors. hese ilters lack location speciicity and hence the location speciicity ofthe adaptors was lost. Results for the BIWAM model are diicult to visual-ize due to the larger parameter space sampled, so results are not shown here.However, none of the 3200 parameter combinations tested could reduce theillusion strength in the orthogonal adaptor condition close to or even below


Figure 26: Efects of adaptation in the two models. Top panel: ODOG model. Bot-tom panel: FLODOG model. Diferent symbols, colors, and sizes encodediferent values of the adaptation parametersα, µ, and σ, respectively. Redcircles replot means across observers from Figure 23, normalized to an il-lusion strength of 1 in the unadapted condition.


zero, without also afecting illusion strength in at least one of the other adap-tor conditions in a manner inconsistent with the data. We conclude that it isnot possible to explain the efect of contour adaptation on perceived lightnessin White’s illusion purely within the framework of spatial iltering modelswith contrast normalization. Our results leave open the possibility that therelevant adaptation takes place prior to the processing modeled by ODOG,FLODOG or BIWAM. In that case, the correct way to simulate the efectsof adaptation would be to modify the input to the models, rather than adaptingthe ilter responses. However, without an explicit theory about the processingsteps that occur prior to the iltering stage of the model it is unclear what typeof input modiication should exactly be performed. We would argue that ifthe pre-processing is complex enough to explain the efect of contour adapta-tion on perceived lightness, for example involving illing-in across weakenedborders, it might be that the spatial iltering computations are not needed asan explanation of lightness perception at all. At the very least, it would appearquestionable that the models are usually tested with unmodiied images if theassumption is that their actual input is already preprocessed.

14D I S C U S S I O N

We have shown that perceiving the luminance step between the test patchand the grating bar on which it is placed is a critical condition for perceiv-ing White’s illusion. If the contrast along this edge is reduced or even nulleddue to contour adaptation, White’s illusion is no longer perceived, and forsome observers, the illusion even reverses. For this efect to appear, it is es-sential that contour adaptation takes place exactly at the location of the lumi-nance edge. Shifting the adapting lines by half the bar width of the gratingeliminated the efect of adaptation and rendered the results indistinguishablefrom those obtained without adaptors. hese results are consistent with previ-ously reported efects of contour adaptation on perceived lightness (Anstis &Greenlee, 2014), and point to a critical role of luminance borders for surfacelightness. Our experiments extend that work by showing that not all lumi-nance borders that enclose a surface are treated equally in the computation oflightness in White’s illusion.

14.1 P O T E N T I A L C A U S E S O F T H E E F F E C T

We found that temporal adaptation selectively interfered with lightness per-ception in White’s illusion when we adapted the edges of the test patches thatwere orthogonal to the bars of the carrier grating. his inding is mirroredby results obtained when masking White’s stimulus using narrow-band noiseof diferent orientations (Salmela & Laurinen, 2009). In that study, noise ori-ented parallel to the grating increased the strength of White’s illusion, whereasnoise oriented orthogonal to the grating reduced or even reversed the illusion.Both sets of data show that White’s illusion is predominantly modulated bythe luminance contrast across the test patch edges that are oriented orthogo-


nal to the grating. However, the question how the visual system distinguishesbetween both types of edges, and in which ways they are subsequently treateddiferently, remains unanswered.

In the following we propose iso-orientation surround suppression (IOSS,see Gheorghiu, Kingdom, & Petkov, 2014, for a recent review) as a low-level candidate mechanism that could potentially account for the observedasymmetry. Iso-orientation surround suppression is a cortical mechanism bywhich neurons are inhibited by activity of other neurons in their local sur-round. he inhibition is orientation selective, i.e. cells with a certain orienta-tion preference are most strongly inhibited by other cells with the same prefer-ence (Blakemore & Tobin, 1972; Nothdurft, Gallant, & Van Essen, 1999; Ca-vanaugh, Bair, & Movshon, 2002; Henry, Joshi, Xing, Shapley, & Hawken,2013). he above-mentioned results suggest that lightness perception dependson the activity of edge sensitive mechanisms such as oriented odd-phase il-ters. Weakening the response of ilters with an orientation preference parallelto the grating while at the same time leaving the response of ilters with anorientation preference orthogonal to the grating intact, would lead exactly tothe asymmetry that was observed in White’s illusion (see Fig. 27).

In particular, ilters that are responsive to the grating would inhibit iltersthat are responsive to test patch edges parallel to the grating. Filters that areresponsive to the test patch edge orthogonal to the grating would not expe-rience such inhibition, and would consequently have a stronger response. Ifsurface lightness is determined by a mechanism that integrates the informa-tion from all edges of a surface, the test patch will appear more similar to theneighboring bars because of the reduced ilter response. Hence a test patch ona dark bar will look light and a test patch on a light bar will look dark. hisis what is observed in White’s illusion. Such a mechanism should also lead todiferences in the perceived contrast at the two types of edges of the test patch.his could be tested in future work.

We have suggested that White’s illusion results from a diferential weightingof the contrasts at edges orthogonal and parallel to the grating: a full contrastefect across the orthogonal edges outweighs a reduced contrast efect across


Figure 27: Illustration of the efect of oriented surround suppression on the ilters re-sponding to orthogonal and parallel edges of a test patch in White’s stim-ulus. Filters that respond to the test patch’s edges parallel to the gratingare inhibited by the response to the edges between the grating bars. heorthogonal edges are unafected by surround suppression because thereare no iso-oriented edges in their surround. his leads to the asymmetrybetween the two types of edges that is required for explaining White’sillusion.


the parallel edges. his interpretation is challenged by previous reports thattried to quantify the relative contribution of the two types of edges (Cliford& Spehar, 2003; Anstis, 2005). In these studies, the authors used a coloredinducing grating, and found that the perceived color of the gray test patcheswas inluenced by two factors, contrast with the color of the carrier bar, andassimilation to the color of the lanking bars. However, both studies foundassimilation efects speciically at spatial frequencies higher than the 0.4 cpdof the grating that was employed in our study. With gratings of low spatialfrequencies, only contrast efects were observed. It is possible that the assim-ilation efects at higher spatial frequencies result from chromatic aberration,and are thus an optical efect rather than the result of neural processing. It haspreviously been shown that White’s illusion increases with increasing spatialfrequency of the grating (Blakeslee & McCourt, 2004). he increase was mostprominent for grating frequencies above 2 cpd. It is thus possible that multi-ple mechanisms contribute to the perceptual efect, one being the edge-basedcontrast modulated by IOSS, as proposed here, and another that depends onassimilation due to spatial smoothing at high spatial frequencies. Whetherthis spatial smoothing is of optical or neural origin is an open question.

An experimental approach to test the question whether the edges parallelto the grating contribute at all to the perceived lightness of the test patches,would be to quantitatively compare the efect sizes of White’s illusion andsimultaneous lightness contrast within observers. Our model sketch predictsWhite’s illusion to be at most as strong as simultaneous contrast (assumingthat the inhibition of the parallel edges reduces their efect to zero). Due tothe diiculties discussed in Section 14.3, it is diicult to draw conclusionsfrom the present contrast data. he literature is divided with respect to thequestion which of the two efects is stronger: White (1981) and Anderson(1997) reported that White’s illusion is stronger, and Blakeslee and McCourt(1999), reported the opposite. Settling this question in future research wouldbe helpful to determine which individual factors determine the perceptual out-come known as White’s illusion.


14.2 T H E F I L L I N G - I N P R O B L E M

he above description raises the question how surface lightness is computedfrom edge contrast. An edge-based account of lightness perception is clearlyincomplete as long as it does not address this so-called illing-in problem. heconnection between contour adaptation and illing-in has been discussed be-fore (Anstis, 2013; Anstis & Greenlee, 2014), but at present there exists nosatisfactory mechanistic model of the process.

Some authors conceive of illing-in as the spread of information from oneneuron to the next in retinotopically organized visual areas, and the percept ofa surface depends on the iring of a corresponding patch of neurons (Grossberg& Mingolla, 1985; Paradiso & Nakayama, 1991; Ramachandran & Gregory,1991; Ramachandran, 1992; Rossi & Paradiso, 1996). Others have rejectedthis isomorphic notion of a surface representation either on philosophicalgrounds (O’Regan, 1992), or because of psychophysical (Blakeslee & Mc-Court, 2008; Robinson & de Sa, 2013) and electrophysiological evidence(von der Heydt et al., 2003; Zurawel et al., 2014) that is inconsistent withthe idea. Our results do not settle the discrepancy, but they underline theimportance of solving the illing-in problem in order to understand lightnessperception. One casual observation that we found noteworthy is that, for someobservers, the orthogonal adaptors rendered the test patch indistinguishablefrom the bar on which it was placed. In other words, the test patch was per-ceptually illed-in with the lightness of its background bar. his is interesting,because the parallel edges of the test patch to the neighboring bars were notadapted in this condition. hese edges were perfectly visible, having the samecontrast as in the no adaptor condition in which they were always perceived,and the contrast across these edges could have signaled that the lightness ofthe test patch was diferent from that of the bar. To us this suggests that per-ceived surface lightness need not be fully consistent with the edge contrastsignaled across all edges of a surface.


14.3 D I F F I C U LT I E S W I T H M AT C H I N G TA S K S

In the following we will discuss some general diiculties with matching tasksas we think that they were not speciic to our setup or our stimuli. We wouldlike to encourage an open discussion of these issues because that would makethe comparison and evaluation of results from diferent experiments moretransparent, in particular when they are inconsistent (c.f. Bindman & Chubb,2004).

It is known that instructions can have an efect on lightness matching (Arend& Reeves, 1986; Bäuml, 1999; Reeves, Amano, & Foster, 2008; Troost & deWeert, 1991). We observed that, although observers were explicitly instructedto set the match luminance according to the perceived lightness of the test,some of them still adopted a diferent strategy and tried to act like a photome-ter, i.e. they tried to infer the veridical luminance of the test. his tendencymight be attributable to observers’ strong desire to please the experimenter (cf.Durgin et al., 2009).

If observers believe that they are confronted with an poptical illusion’, andif they further believe that they found a way of knowing the pcorrect’ answer,then their responses are likely to be biased by their cognitive strategy (seeRuneson, 1977, for an illustrative example of such strategic behavior). For ex-ample, when the test patches have the same luminance as the background ofthe screen (which is a common experimental setup), observers could adjusttheir matches relative to the background luminance instead of matching testpatch lightness. To counteract such tendencies, we adopted a ’perturbation’approach and measured lightness matches for three diferent test patch lumi-nances. Observers did not know in advance how many values of test patchluminance were tested. If they had used a strategy such as setting the matchluminance always to the same value to counteract a presumed illusion, thiswould have been evident in constant match values across the diferent testluminances. hus, although this pperturbation’ does not necessarily preventobservers from strategic matching, it would at least allow us to identify suchlawed matches.


In our data, match luminance generally increased with increasing test patchluminance, indicating that observers were indeed matching individual stimuli.However, three of the four observers that did not perceive White’s illusionand that did not show a simultaneous contrast efect (Fig. 24), also did notshow this increase in matched luminance with increasing test luminance inthe simultaneous contrast condition. his is a further indication that these ob-servers followed some strategy, but it does not allow us to understand whatexactly they were doing. he downside of this kind of control condition is thatit considerably increases the number of experimental trials without contribut-ing much to answering the main research question. Clearly, even with suchsafeguards in place observers might still engage in other strategies.

Another observation is the large variability across and within observers.Variability within observers might not simply be variance in setting the re-sponses. With simple stimuli of the kind used here, the perceived lightnessof diferent image parts can change over time. Readers can try that for them-selves. It is very much possible to psee’ test patches on dark and light back-grounds as identical, especially if one has the background knowledge that theyare in fact identical. hus, response diferences across trials may relect the factthat observers did indeed perceive the stimulus diferently in some trials. Inthat case, the mean across trials may not be a good indicator of subjective expe-rience. he variability across observers in lightness illusions seems to indicatethat there really are large individual diferences in how pronounced certainlightness phenomena are (e.g. Robinson et al., 2007; Ripamonti et al., 2004).For example Ekroll and Faul (2013) have demonstrated that observers per-ceived an additional transparent layer for similar stimuli when they were oflow contrast. So in stimulus conditions with relatively low contrast some ob-servers may have perceived an additional transparent layer which could makethe matching task ill-deined. his makes it diicult to argue which of twolightness illusions is stronger and it might also explain the inconsistent resultswith respect to the relative strengths of White’s illusion and simultaneous con-trast.


Finally, as can be seen in the data from individual observers (see supplemen-tal material), observers sometimes selected match lightnesses that were outsidethe luminance range spanned by the grating. his is surprising, as it is diicultto imagine how a test patch that has a luminance somewhere in between thetwo luminances of the grating could appear much brighter than the brightbar or darker than the dark bar. hese data points cannot be easily attributedto response lapses, because they were not accompanied by particularly shortor long response times and they were diferent from the random start value.hus, observers seem to have deliberately chosen these extreme luminances tomatch the test patch luminance. A possible explanation for this inding mightbe that the luminance range in the match background was larger than the lu-minance range in the grating. If observers performed a contrast normalizationbetween the test display and the match display (see Singh & Anderson, 2006;Zeiner & Maertens, 2014), this could explain why they used a higher lumi-nance range for their matches than the range that was spanned by the grating.his is just one further example that lightness matching is not such an easyand straightforward task as it might appear on the surface.


Our experiments show that luminance edges play a central role in White’s il-lusion. he illusion seems to be predominantly caused by the luminance edgebetween the test patch and its background bar while the edge contrast to neigh-boring bars is largely ignored. he efect of contour adaptation on White’s il-lusion could not be replicated by spatial iltering models which adds furtherevidence against the adequacy of such models as a mechanistic explanation ofWhite’s illusion in particular, and lightness perception in general. Our resultshighlight the importance of further investigating the question how surfacelightness is computed from edge contrast.

Part IV

C O N C L U S I O N

15G E N E R A L D I S C U S S I O N

In the previous two parts, I presented evidence against spatial iltering modelsas explanations of lightness perception. I showed that these models, whichconstitute the only low-level account of lightness perception that is currentlyformulated precisely enough to be testable through model simulations, are un-likely to capture the processes underlying lightness perception in the humanvisual system. his failure was made apparent by the inability of the modelsto capture the efect of narrowband noise on human lightness perception. henoise results could be explained under the assumption that luminance contrastacross edges is crucial for the computation of surface lightness. I supported thisconclusion by providing direct experimental evidence showing that localizedinterference with edge processing afects the perception of an entire surface.he inadequacy of the spatial iltering approach may appear obvious in hind-sight, but it is important to keep in mind that at the time of writing of thisthesis, these models represented the state of the art in the ield, were widelyendorsed, and the articles by Blakeslee and McCourt presenting the ODOGmodel alone had collectively been cited over 400 times (Blakeslee, Cope, &McCourt, 2015). And while the models have always been unpopular withresearchers favoring mid- to high-level explanations of lightness phenomena(e.g. Gilchrist, 2006), a clear refutation of the approach was lacking.

he stated goal of this thesis was to improve our understanding of the low-level processes that must constitute the irst steps in a complete account oflightness perception. So far, I have mainly made a negative argument againstthe currently most popular low-level explanation. While I believe this to bean entirely worthwhile contribution towards a better understanding of themechanisms that are involved in lightness perception, the refutation of one hy-pothesis eventually calls for an alternative. Fully developing a lightness model

130 C O N C L U S I O N

based on luminance ratios across edges is beyond the scope of this thesis. Asa starting point for future work, I will instead develop the ideas presented inSection 14.1 in more detail, and propose some experiments that may help toconstrain the proposed model. I will then take a broader perspective, and fo-cus on some questions that the results presented in this thesis raise, and thatneed to be addressed in future research to improve our understanding of theprocesses that enable us to distinguish black from white.

15.1 S K E T C H O F A N E D G E - B A S E D M O D E L O F L I G H T N E S S P E R C E P T I O N

Our experimental and modeling results suggested that while current spatialiltering models are inadequate as an explanation of White’s illusion, a difer-ent low-level approach, based on the explicit treatment of luminance ratiosacross edges, may be successful in accounting for the efect. he main prob-lem facing an edge-ratio based account of White’s illusion is how to integratethe two diferent luminance ratios computed between the test patch and thebar on which it is placed, and between the test patch and the neighboring bar.his integration has to account for the fact that the relative length of the twotypes of edges has little or no inluence on the strength of the illusion. Asdescribed in Section 14.1, iso-orientation surround suppression (IOSS) maybe a suitable mechanism to solve this problem. IOSS could decrease the in-luence of the edges parallel to the grating on the perceived lightness of thetest patch, because these edges would be inhibited by the edges of the grat-ing, which have the same orientation, but a higher contrast (see Figure 27 inSection 14.1).

Such a model could account for the results obtained in our experimentswith both narrowband noise and contour adaptation. In the case of isotropicnoise, ilters oriented parallel to the grating and ilters oriented orthogonal tothe grating should both be inhibited by the noise, which would reduce thediference between the two ilter responses, and thus reduce the strength ofthe illusion. In the extreme case where the noise renders the edges entirelyinvisible, it is unclear what the model would predict without a more concrete

G E N E R A L D I S C U S S I O N 131

implementation in mind, but assimilation of a patch without edges into thebackground, as was observed, should be one possibility. For the contour adap-tation results, the case is even clearer. he model predicts that the luminanceratio across the edges orthogonal to the grating is responsible for White’s illu-sion, while the luminance ratio across the edges parallel to the grating worksin the opposite direction. Our results show that masking the edges parallel tothe grating slightly increases the illusion, while masking the orthogonal edgesreduces or reverses the illusion. his is precisely what the IOSS model wouldpredict.

here are a number of other well-known properties of White’s illusion (seeChapter 3, and speciically Table 1), and it is informative to consider how theproposed model would fare with regard to these properties. One obvious short-coming of the proposed model at this stage is that it lacks a concrete mecha-nism that computes a surface response from the edge responses. he generalproblem of illing-in is discussed in more detail in Section 15.3. One conse-quence of this shortcoming is that it is diicult to fully evaluate the merits ofthe proposed model, and also to falsify it. Still, it will be elucidating to con-sider which properties of White’s illusion are easily explained already withinthe IOSS framework, which need to be accommodated within the illing-inmechanism, and which are generally diicult to reconcile with such a model.

he model correctly predicts that White’s illusion is largely independentof the aspect ratios of the test patches, because the inluence of an edge onperceived lightness is based on its response strength after IOSS, not on itslength. However, edge length might still become a factor in the unspeciiedsurface computation, so this property of the illusion will need to be considered.

he model does not predict an increase in illusion strength with increasingspatial frequency. It may be that this increase is caused mostly by an increasein assimilation due to spatial smoothing at higher frequencies (whether opti-cal or neuronal in origin), which may be a factor independently contributingto White’s illusion. In that case, the efect of grating frequency on illusionstrength is compatible with our model, but it is certainly not directly predictedby it.


he model presently makes no prediction regarding the efect of changingthe number of test patches or the extend of the grating beyond the test patches.Without a more speciic illing-in mechanism in mind, it is also impossible tosay what should happen with test patches shifted in phase within the grating.Such shifts have been reported to lead to perceptual gradients within the testpatches, but these reports are based on few observations, and would need tobe independently veriied.

An interesting case are the efects of the relative luminance relations in thestimulus on the illusion. Stimulus conigurations where the test patch is ei-ther lighter or darker than both of the grating bars (sometimes referred to asinverted White’s illusion) have been reported to result in an illusion oppositeto the classical White’s efect: the test patch on the darker bar appears darkerthan the test patch on the lighter bar. Although this phenomenon has usuallybeen taken as evidence in favor of higher-level explanations such as anchor-ing theory (Spehar et al., 1995), it might also be explained within the IOSSframework. If the test patch is darker (or brighter) than both grating bars, theluminance ratio between the grating bars has to be smaller than that betweenthe test patch and at least one of the bars, which is not the case in the classicalWhite’s illusion. his reduced grating contrast should lead to a reduction ofthe efect of IOSS, in which case other factors, such as edge length, could endup determining the perceptual outcome.

he present model does not predict the efects of perceived depth or trans-parency on the strength of the illusion. However, if edge detection and IOSSare taken as simply the irst steps in a more complex lightness computation,our account could be part of a larger theory that also explains these efects.

he model explicitly predicts that White’s illusion should be at most as largeas simultaneous lightness contrast, because in the model, White’s illusion isthe net efect of two opposing contrast efects, one of which is weakened dueto IOSS. Even if IOSS weakens the contrast efect which is opposite in sign tothe perceived illusion to zero, the total illusion strength cannot be larger thanthat of the contrast efect unafected by IOSS. Since the question whetherWhite’s illusion is stronger or weaker than simultaneous lightness contrast


has not been settled empirically, it can at present not be used to evaluatethe model (see also Chapter 16). he same is true for the question whetherWhite’s illusion results mainly from a lightening of one test patch, a darkeningof the other, or both. In summary, none of the clearly established propertiesof White’s illusion speak strongly against our proposed model, while some areeasily explained by it.

here are also a number of variations of the classical White’s stimulus thatare informative with regard to our model sketch. he model makes no predic-tion regarding Anderson’s (2003) textured illusion, because that illusion de-pends mainly on the matching strategy observers use to make their response.A response mechanism is so far not part of our model sketch.

he radial White’s illusion (Robinson et al., 2007) is an interesting test casefor the model. Depending on the tuning width of IOSS, this stimulus may beexplained by our model. It could be elucidating to test whether the width ofthe sectors in the stimulus has an efect on the strength of the illusion. If thereis some width at which White’s efect disappears, this could be related to thetuning width of IOSS.

he circular White’s illusion (Howe, 2005) presents a challenge to our pro-posed model. In this stimulus, the edges orthogonal to the grating are entirely

Illustration of thestimulus suggestedby Anstis to test theIOSS model.

absent, and still the illusion persists. he efect also does not seem to rest purelyon assimilation due to spatial smoothing, because making the surround of thetest rings homogenous results in a regular simultaneous lightness contrast, notin assimilation. his stimulus may indicate that our present account is insui-cient. Perhaps the weakening of edges through IOSS results in more than justa reduction of the contrast efect acting across those edges, but can actuallylead to assimilation across the weakened edges.

Two more stimuli that Stuart Anstis pointed us towards in his review ofone of our articles may also help to determine the parameters of IOSS. heunpublished stimulus suggested to us by Anstis (see margin) changes the par-allel lines of the grating to a zig-zag. hus, it is no longer the case that the testpatch’s edges rparallel to the gratings have exactly the same orientation as theedges of the grating itself. If White’s illusion is indeed caused by the weak-


ening of these edges through IOSS, one would expect this manipulation toweaken the illusion. However, the manipulation need not immediately abol-ish White’s illusion (as Anstis implied). he exact efect of this stimulus ma-nipulation depends on how narrow the orientation tuning of IOSS is. herelationship between the angle of the zig-zag lines and the weakening of theillusion could thus help to quantify the orientation tuning.

Reproduction of thestimulus used by

Cliford and Spehar(2003).

he stimulus by Cliford and Spehar (2003) can be interpreted as takingAnstis’s stimulus discussed above to the extreme, and increasing the zig-zagangle to 90°. However, the test patches that are superimposed on white linesstill look darker than test patches superimposed on black lines in this stimulus(Cliford & Spehar, 2003). his phenomenon is diicult to explain with theIOSS account, because both decremental and incremental test patch edges areconnected to an edge with equal orientation on one side, and to an edge withorthogonal orientation on the other side. here is no asymmetry that wouldexplain the diference in perceived lightness. Interestingly, Cliford and Spe-har (2003) found that the illusion was essentially abolished if the stimulus waschanged to make the test patches square. In that case, the symmetry predictedby the IOSS model seemed to hold. It remains an open question what mech-anism is responsible for the illusion in the case with elongated test patches.

A diferent possible experimental test for our proposed model is based onthe temporal properties of cortical inhibition. he reduction of an edge re-sponse through IOSS should take longer than the initial computation of thatresponse, because it requires at least one additional synaptic transmission. hus,one might expect that White’s illusion (in the standard version where testpatches share more border with the neighboring bars than with the bar onwhich they are placed) turns into simultaneous contrast at presentation timesthat are too short for IOSS to take efect. Robinson and de Sa (2008) havemeasured the temporal properties of White’s illusion, and found that the illu-sion is observable with a presentation time of 82 ms. However, assuming thatWhite’s illusion is indeed the result of IOSS in primary visual cortex, given theknown response latencies 82 ms might just be enough time for the suppressionto take efect. hus, one would need to test presentation times around 50-60


ms. Robinson and de Sa (2008) reported that simultaneous contrast could beobserved also at 58 ms, but did not measure White’s illusion for that presen-tation time. It would be informative to test whether White’s illusion can alsobe observed at 58 ms presentation time.

A further issue that is of relevance for further developing our proposedmodel is the perceived lightness of blurred patches. An extreme position, claim-ing that lightness perception depends exclusively on edge ratios, will have dif-iculties explaining how the lightness of regions that have no clear edges isdetermined. Maertens et al. (2015) proposed that blurred ellipses are not in-terpreted perceptually as surfaces, and therefore are subject to diferent light-ness or brightness computations than ellipses with sharp edges. One possibleapproach to answering the question of how a region without perceived edgescan have a perceived lightness difering from its surround is to consider edgedetectors at multiple spatial scales. Low spatial frequency ilters could pick upa smooth gradient as an edge that is relevant for lightness computation, butnot as a perceptually sharp edge. If diferent ilters are responsible for edgeperception and for the lightness efects of edges, this could explain how im-age regions without perceivable edges nevertheless have a lightness distinctfrom their background. he results of lightness matching in the presence ofnarrowband noise (see Part II) suggested that the relevant spatial frequency forlightness perception lies in the range 1-5 cpd. Whether this frequency rangecoincides with that required for perceiving a luminance diference as a sharpedge is an open question. We also observed that the exact frequency rangescales to some degree with the size of the target surface. his may suggestthat the visual system can dynamically adjust which ilter responses are usedto compute lightness in order to adapt to stimulus properties.

How does our approach relate to previously proposed explanations of White’sillusion (see Section 3.3)? Our proposed model could be considered as one pos-sible implementation of the pattern-speciic inhibition idea (White, 1981):he pattern, through edges oriented parallel to some of the test patch’s edges,inhibits the contrast that would usually afect the perceived lightness of thetest patch. However, the way White originally presented the idea, it did not


explicitly involve an edge contrast computation, but assumed that a ilter di-rectly signaling the surface lightness of the test patch is inhibited, which maybe more similar to the standard spatial iltering models. In the form describedabove, the model is also more local than what White had in mind, because itonly assumes inhibition from edges in the close vicinity. Whether the edgesof neighboring grating bars also have an inluence on the inhibition would beimportant to determine in future experiments.

here is no direct connection between the present approach and the accountbased on the corner response of center-surround ilters. Since that account hasnot been developed thoroughly, it is diicult to critically evaluate.

he explanations based on contrast mediated by T-junctions are stronglyrelated to our approach, and might be seen as a diferent level of description ofthe same mechanism. he T-junction approach claims that contrast across thestem of the T has a larger efect on perceived lightness than the contrast acrossthe top of the T. IOSS could be precisely the mechanism that is responsiblefor this diference.

Anchoring theory operates on a diferent abstraction level than our ap-proach. It is in principle possible that the two are compatible, and that some ofthe computations postulated by anchoring theory are in fact performed not onthe retinal image, but on the output of a irst processing stage that resemblesour model. However, the explanation that anchoring theory ofers for White’sillusion, namely that the test patches are perceptually grouped with the bars onwhich they are placed, and then anchored to white within the framework con-structed through this grouping, is diferent from the weighted edge contrastcomputation we propose.

he same holds true for the explanation based on perceptual scission of thestimulus into diferent layers (Anderson, 1997). Our model at present does notdivide the image into diferent layers, and our explanation of White’s illusionis thus diferent from Anderson’s. IOSS might be one mechanisms that aidsthe scission process, and it is thus possible that a future lightness model willcombine the two approaches, but at least in the present form, our approach isnot related to the scission account.


Finally, the edge-ratio model with IOSS also difers from the spatial ilter-ing models that have previously been proposed as explanations for White’sillusion, as has been discussed in depth in the previous parts of this thesis.

he edge based approach with IOSS as outlined here is of course still in-complete as a model of lightness perception. First, the idea so far only coverssimple stimuli, where the only relevant edges are directly adjacent to the regionof interest, and where no diferentiation between relectance edges and illumi-nation edges is possible (see next section for a more detailed discussion of thisproblem). Second, and related to the irst point, the model cannot explain e.g.why Adelson’s famous checkerboard-shadow illusion is much stronger than alocally identical simultaneous contrast efect where the global cues to illumina-tion, shadow, and scene layout have been removed. hus, the model developedhere should be seen only as an attempt to mechanistically understand the ini-tial processing stages in a complex lightness computation that will ultimatelyrequire the consideration of more global image properties, and thus mid- orhigh-level vision.

I do not want to appear naively optimistic regarding the feasibility of someof the research ideas proposed here. Quantitatively itting parameters of themodel – such as the orientation tuning width of the surround suppression, orthe frequency tuning of the relevant edge-responsive ilters – to psychophysicaldata, may well be impossible, or at least very diicult. While I have suggestedsome theoretically interesting experiments that may help to it the model, Ibelieve that some efects may in practice be too hard to quantify with enoughprecision to really inform computational modeling, given the diiculties withaccurately and reliably measuring perceived lightness that were discussed inthe experimental parts of this thesis, and that are a recurring theme in the ield.It seems that for some lightness efects, a qualitative description of the direc-tion of the efect (lightening or darkening) is all that can reliably be measuredacross diferent observers. I thus do not envision that rigorous model selec-tion approaches that are used in other areas of psychophysics (e.g. Goris et al.,2013) are likely to be adopted in the ield of lightness perception without anaccompanying breakthrough in experimental techniques measuring subjective


experiences such as lightness, however theoretically appealing this increasedrigor may be.

One idea that ofers some promise is to take inter-individual diferences inlightness perception more seriously (Ekroll, personal communication). It maybe that part of the variability between observers, which makes drawing con-clusions about relative and absolute illusion strengths so diicult, is not dueto problems of accurately measuring subjective perception, but instead due toactual diferences in how a certain stimulus appears to diferent observers. Inthat case, it would be interesting to measure responses of the same observersacross a range of diferent stimuli, and investigate whether there are regular-ities. E. g., do all observers for whom White’s illusion is particularly strongalso perceive some other illusions strongly? If it is possible to ind clustersof observers with lower internal variance, this may help to better it modelparameters to these speciic groups. In addition, comparing the parametersacross diferent groups may be informative for understanding inter-individualdiferences in perception.

15.2 P R O B L E M S O F E D G E C O D I N G

Since I am promoting the resurrection of a classical account of lightness per-ception, namely that perceived lightness is inluenced by the luminance ratiosacross edges, I should not conceal the diiculties that lie in this approach,and that have been recognized by others before. One problem already men-tioned in Chapter 2 is that of edge integration: how are the multiple edges in acomplex stimulus weighted and integrated to arrive at a lightness estimate forevery single surface? he weighting of edge responses based on iso-orientationsurround suppression discussed in Chapter 14 ofers one mechanism that maycontribute to a solution for this problem. However, while such a mechanismcould successfully account for the diferent contributions of the two types ofedges of the test patch in White’s illusion, it ofers no explanation for the ef-fect of remote edges discussed by Arend et al. (1971) and Shapley and Reid(1985) (see Chapter 2).


A further issue with edge-based accounts of lightness perception is thatedges caused by diferences in illumination must be treated diferently fromedges caused by changes in surface relectance (Gilchrist et al., 1983; Gilchrist,1988). While contrast ratios across relectance edges allow the correct com-putation of the relative relectances of diferent surfaces within a commonillumination, integrating contrast ratios across illumination edges would leadto errors in lightness perception. Gilchrist (1988) has shown that human ob-servers make diferent lightness matches depending on whether contextualcues about the source of an edge, such as light sources and shadow casters, arevisible. his may indicate that a low-level account based on edge-sensitive il-ters and local surround normalization is insuicient to account for all aspectsof edge integration. Still, one should not fall into the trap of assuming that anefect has to have a single cause, and that a mechanism which does not explainall aspects of a phenomenon has no role in causing the phenomenon at all.

Gilchrist (2006, p. 148) also discusses the fact that the lightness of objectsis not greatly afected when they are placed on diferent backgrounds. Heargues that, while this type of background independent constancy is unsur-prising under the naive assumption that perceived lightness corresponds tolocal luminance, it actually poses a problem for edge-ratio based explanationsof lightness perception. If local edge ratios were all that determines perceivedlightness, one should expect a gray piece of paper to look much darker whenit is placed on a white cardboard then when it is placed on a black one. hefact that the actual diference in lightness for the two backgrounds is muchsmaller than one would predict based on edge ratios proves that the computa-tions going on in the visual system are more complex than suggested by sim-ple experiments using only disc-annulus stimuli. Integration of remote edgescould in principle help to solve the problem of background independent con-stancy, because the remote edge ratios of the white cardboard, e.g. against thetable, will difer from those of a black cardboard. hus, we are back at theproblem of edge integration, which at least from a low-level perspective thatstarts at the image and tries to explain the computations of the visual systemin terms of local features, appears very diicult. One may conclude that while


edge ratios do igure prominently in the computation of surface lightness evenin complex scenes, a simple account like the ratio principle (Wallach, 1948)fails to appreciate the subtleties apparently involved in the computation. Butthis failure of a simple edge-based approach does not negate the important roleluminance edges play in lightness perception.

15.3 F I L L I N G - I N

Even assuming that the problems of edge classiication and edge integrationcan be solved, there remains the question of how we perceive lightness asa surface property. Areas of uniform relectance usually also appear uniformin lightness, despite the fact that responses of edge-sensitive ilters in the vi-sual system will difer dramatically between ilters placed at the border of thesurface, and ilters placed in its center. his implies that the lightness valuecomputed at the edges has to be extrapolated to the entire surface. his is-sue, known as the illing-in problem, was briely touched upon in Chapter 14.Here, I will discuss some phenomena related to illing-in in more detail, andhighlight a few gaps in current explanations that I believe may be promisingstarting points for further investigation of the topic. First, however, it is im-portant to diferentiate two potential meanings of the term pilling-in’: some-times, the term is used to describe a speciic mechanism by which informationthat is encoded in neurons responding to the edges of a surface is transferred,through an active process, to neurons whose receptive ields are located in thecenter of a surface. I will use the term pisomorphic illing-in’ to refer to thisspeciic idea (cf. von der Heydt et al., 2003; Weil & Rees, 2011). pFilling-in’without any qualiier is here used simply to imply that at some level of visualprocessing, the perceived lightness at the center of a surface depends on stim-ulus information at the edges of that surface, and thus needs to be perceptuallyilled in from those edges, without commitment to any speciic mechanism. Iwill not discuss aspects of the illing-in problem that pertain to the lack of aperceptual representation of the blind spot or of scotomas, but limit myself tothose questions directly pertaining to the perception of surfaces.


An edge-contrast based account of surface perception requires a notion ofilling-in. Some authors have argued that this illing-in need not be a specialprocess at all, but that the absence of an edge-signal from a certain area isenough for the perceptual interpretation of a homogenous surface at a higherlevel of the visual hierarchy (Dennett, 1991; O’Regan, 1992; O’Regan & Noë,2001). While these arguments are valid, and perceptual illing-in could in the-ory also occur without an active neuronal illing-in process, the visual systemdoes nevertheless seem to be using an active isomorphic illing-in mechanismat least in some cases, as evidenced by electrophysiological recordings in cat(Rossi, Rittenhouse, & Paradiso, 1996) and macaque V1 (Huang & Paradiso,2008). Some doubt is however cast on this interpretation by reports that thetime course of edge vs. surface responses to black or white squares on a graybackground speaks against isomorphic illing-in as an explanation for the mea-sured surface responses (Zurawel et al., 2014). In a series of experiments aimedat understanding the connection between perceptual illing-in and neuronalilling-in, von der Heydt et al. (2003) trained macaque monkeys to report aperceptual color change of a blurred red or green disc on a complimentarysurround. First, they found that perceptual illing-in was observable in thesemonkeys. In some trials, the color of the central disc was gradually changedfrom red to green or vice versa, while on other trials, the color remained con-stant, but could change perceptually due to fading of the edges after prolongedixation. he iring pattern of surface responsive cells in V1 and V2 followedthe actual color of the central disc. Cells preferring red decreased their ir-ing when the color of the disc changed from red to green. Crucially, on trialswithout a physical change in disc color, surface responses remained constantdespite the fact that perceived surface color changed over time. hus, whilethere are surface responsive cells in V1 and V2, their responses do not seem todetermine perceived surface color, which speaks against the idea that percep-tual illing-in depends on an isomorphic illing-in process. Spillmann (2011)suggested that the discrepancy between the data of Huang and Paradiso (2008)and von der Heydt et al. (2003) may be explained by diferences in processingof colored and achromatic stimuli. However, this argument cannot explain


why Zurawel et al. (2014) ind no evidence of isomorphic illing-in, since inthat study, stimuli were also achromatic. hus, there is no inal answer to theempirical question of whether and under what conditions the visual systemuses an active isomorphic illing-in process to encode surface properties suchas lightness.

Psychophysically, insights on potential mechanisms of illing-in can be gainedfrom experiments studying the time course of surface perception, because lat-eral spreading of neuronal responses should take time. Paradiso and Nakayama

Illustration of themasking experiment

by Paradiso andNakayama (1991).

Top: stimulus.Center: mask.

Bottom:approximate percept.

(1991) reported that backward masking of a white disc on a dark surround witha smaller white ring leads to a dark percept in the center of the disc (see illustra-tion in the margin). hey interpreted this inding as implying that the whitecolor at the disc’s center is encoded at the disc’s edge, and spreads towardsthe center. If the spreading is disturbed by the introduction of an additionaledge in the form of the mask, the center appears dark. his interpretation issupported by the fact that the longest time delay at which the mask was stillefective was positively correlated with the distance between the disc’s edgeand the masking ring. he further the mask location is from the edge, thelonger the edge signal should take to reach that location, leaving more timeto interfere with the spreading through masking.

Blakeslee and McCourt (2008) have argued against the idea that perceptualilling-in depends on the lateral spreading of neuronal activity. hey showedthat there is almost no time lag between perception of a grating induced ona homogenous test stripe by two lanking gratings, and the perception of anactual grating on the test stripe, and concluded that there is no slow illing-inprocess for the induced grating. However, this interpretation does not takeinto consideration how the percept of the actual grating is formed, and im-plicitly assumes that this happens without illing-in or a temporal delay. Ifthe perception of all surfaces is based on edge signals, there is no reason toexpect a time lag between a real grating and an induced one, because bothwould take time to ill in. hus, the absence of such a time lag does not initself show that the induced grating does not result from isomorphic illing-in.


But the conlicting results of a time lag appearing in some experiments andnot appearing in others are puzzling.

Data on the critical licker frequency at which lightness induction breaksdown are potentially informative to answer the question if there is a diferencebetween immediate surface responses and induced edge responses. De Valois,Webster, De Valois, and Lingelbach (1986) reported that a central square os-cillating between black and white on a mean gray background was perceivedto change in lightness over an oscillation frequency range from .05 - 8 Hz,without much efect of the frequency. If, on the other hand, the square washeld constant, and the background oscillated between black and white, a coun-terphase oscillation was induced in the square, which appeared to be changingin lightness itself. his induction greatly diminished at oscillation frequenciesabove 2 Hz. De Valois et al. (1986) interpreted their indings to imply thatsurface lightness is mediated by two processes, a fast one depending on theluminance of the surface itself, and a slow one that depends on the luminanceratios at the edges, and takes time to ill in. A similar dichotomy has beenpostulated by Yarbus (1967). He concluded from his results on image fadingafter retinal stabilization that only changes in stimuli (and not constant stim-ulation) generate a signal that is transmitted to the brain. He assumed thatat the irst moment of perception of a surface, its lightness is signaled by theresponse to the stimulus onset at every point of the surface. Only later, afterthis onset response has faded, are surface properties computed from signalsat edges that continuously change due to small eye movements, and thus donot fade, while the center of the homogeneous surface ceases to generate asignal. Such a two stage model, while being compatible with the licker data,raises the question of how lightness constancy is achieved in the initial surfaceresponse. If edge-based surface perception is really just a mechanism to coun-teract image fading, and recreate the direct surface responses that are presentupon stimulus onset, we are back to square one regarding the question of howlightness can be extracted from the retinal luminance pattern.

Even more puzzling are the details of Yarbus’s results regarding the tempo-ral aspects of lightness or color induction (see Figure 28). First, he showed


that if the color of the background surrounding a stabilized bipartite black-white circle was changed after the circle had faded and taken on the colorof the background, the illed-in color of the circle followed the change inthe background. However, the change in the stabilized region lagged behindthe change of the background, rendering the circle temporarily visible unlessthe background change was very slow. It should be noted that the circle wasperceived as homogenous, having the original background color, during thisperiod, not as black and white. he circle’s color slowly faded into the newbackground color, starting at the edges and spreading to the center. his timelag of the illed in color behind the inducing background color is evidence infavor of an active isomorphic illing-in process.

Figure 28: Illustration of the illing-in stimulus by Yarbus(1967). A bipartite circlesuperimposed on a red background is stabilized on the retina. After a fewseconds, the circle fades from perception. hen, the background is changedfrom red to blue, and the circle reappears, but in homogenous red, insteadof bipartite black and white. After a few more seconds, the red circle fadesfrom perception again, starting at the edges, and progressing towards thecenter.

At the time when the background began changing in color, the entire circlebecame visible at once, which is consistent with the idea that the background


change is signaled by surface receptors that do not require time to ill in. Ifthe background color oscillated at a frequency above 1 - 3 Hz, the color of thecircle could no longer follow the oscillation, and remained a mixture of thechanging background colors. his inding is similar to the brightness induc-tion results of De Valois et al. (1986). While both Yarbus and DeValois et al.interpret their indings to show that illing-in is a slow process, this conclusiondoes not follow directly from the data. A slow illing-in process does not au-tomatically predict that induced oscillations stop at a certain frequency. Onemight also expect that the induced surface color becomes inhomogeneous, be-cause the regions closer to the edges could have a smaller phase lag than thecenter. he fact that this does not happen could indicate that cells encod-ing induced surface colors cannot change their response at a rate faster thanabout 2 Hz, unlike hypothetical cells responding directly to surface luminance.However, this is in conlict with a further result by Yarbus: if the licker rateexceeded 3 - 6 Hz, the diferences between the circle and the backgrounddisappeared again, and the illed-in area changed in synchrony with the back-ground. his inding is puzzling, because it appears to indicate that a surfacecolor which depends entirely on edge signals (there is no physical change inthe circle) can change quickly. Yarbus also pointed out that if only a single cy-cle of background change at these high frequencies was presented, the circledid reappear. Only under continuous oscillation did the perceptual impressionat the location of the stabilized circle follow the background change withoutdelay. he general possibility of perceiving relatively high frequency inducedoscillations in surface color raises the question why illing-in was not perceivedabove 2 Hz by De Valois et al. (1986), a result that has been supported andextended in a later study (Rossi & Paradiso, 1996). I have at present no answerto this question, but I believe it should not be ignored by future attempts tounderstand the underlying causes of perceptual illing-in.

A further phenomenological fact about illing-in that requires an explana-tion is that not all illing-in seems to result in homogenous surfaces: gratingsand gradients can also be induced from edge signals. his fact is highlightedby two contour adaptation demonstrations (Anstis, 2014).


Figure 29: Illustration of two contour adaptation stimuli inducing a gradient. Left:actual stimulus. Center: adaptor. Right: approximate percept.

In one of these, the central border of a bipartite circle is masked throughcontour adaptation. If both halves of the circle are increments (or decrements)with respect to the background, the circle appears homogenous after adapta-tion. However, if the background luminance is in between the luminances ofthe two halves of the circle, a gradient is perceived from one half to the other(see Figure 29, top). In the second demonstration, a half-ring adaptor rendersone half of the contour of a circle invisible, while the other half of the circle’sedge is still visible against the background. Perceptually, the unadapted righthalf of the circle is clearly lighter than the background, but the, physically ho-mogenous, left half appears to gradually darken towards the background gray(see Figure 29, bottom). hus, even in displays with only two or three uniquegray values, edge coding and illing-in can apparently induce the percept ofgradients, a phenomenon that seems relevant to a theory explaining surfacelightness based on edge signals.

Finally, a theory which assumes that surface lightness is illed-in perceptu-ally, and that any edge will stop this process, efectively blocking the spreadingof lightness, faces an additional diiculty, illustrated in a stimulus by Boyaci,


Fang, Murray, and Kersten (2010, see margin). In this stimulus, two equi-

he stimulus used byBoyaci et al. (2010).he two outer lanksare equiluminant,but each appears tohave the same grayvalue as the centralsegments on itsrespective side of thestimulus.

luminant outer lanks are connected to two central surfaces that difer in lu-minance. he luminance steps from the inner surfaces to the outer lanks arehidden behind occluders. Perceptually, most observers report to perceive onlytwo surfaces difering in lightness, both of which are partially occluded. hatis, the lightness of the central surfaces, which partially depends on the edge ra-tio between these surfaces, appears to spread across the occluders to the outerlanks.

his percept is similar to what would be expected if contour adaptation wasused to render the edges between the lanks and the central surfaces invisible.However, the fact that lightness seems to spread not only across edges thatare no longer signaled, but also across edges that are hidden behind occluders,implies that the mechanism is sensitive to non-local factors. After all, locallythe edge between the central region and the occluder is even more prominentthan the edge between the central region and the lank would be if the occluderwas removed. It is therefore clear that the low-level, edge based account oflightness perception that has been argued for in this thesis is incomplete, andneeds to be augmented by mid- or high-level vision to account for even slightlymore complex stimuli than the ones that I have focused on. his conclusion,however, does not undermine the importance of understanding the low-levelprocesses of edge integration and illing-in that are likely to form the basisalso for more high-level aspects of lightness perception.

16O U T L O O K

he results presented in this doctoral dissertation demonstrate the need for anew model of lightness perception that replaces the spatial iltering approach.Processing of luminance ratios across edges has been highlighted as one centralfeature that this new model should be based upon, and a rough sketch of such amodel has been introduced. In the previous section, numerous diiculties thatstill need to be addressed on the path to a better lightness model have beendiscussed. In this inal chapter, I will make some suggestions for empirical aswell as theoretical work that I believe could continue the research approachtaken here.

One empirical issue that remains unanswered despite its theoretical rele-vance and ostensible simplicity is whether White’s illusion is stronger, weaker,or equally strong as simultaneous lightness contrast. If White’s illusion is in-deed stronger, as has been suggested (see Section 3.1.8), this would imply thatour proposed model needs to be augmented. he reduction of the edge signalfrom the lanking bars due to surround suppression would not suice to pro-duce an efect that is stronger than the contrast efect from the carrier baralone. It might be necessary to posit an active assimilation process that makesthe lightness of two areas between which no edge is perceived similar.

he main issue that makes statements about the relative efect size of thetwo illusions diicult is that both illusions can be inluenced by many parame-ters, making the choice of which comparison to pick appear arbitrary. Havinga speciic explanatory mechanism in mind may help in this respect. Under ourcurrent model hypothesis, we would expect the illusion to increase if the testpatches were kept constant, but the width of the carrier bar was increased sothat all edges of the test patch become either incremental or decremental. hisprediction follows from the fact that we assume the edges to the neighboring


bars to have an efect that goes in the opposite direction from the ultimatelyperceived illusion, but is outweighed by the efect from the edges between thetest patch and the carrier bar. While this experiment cannot settle the, po-tentially ill-posed, question which illusion is stronger in general (e.g. becauseincreasing carrier bar width decreases grating frequency, which may inluencethe efect), it would still produce important data that would help assess ourspeciic model hypothesis.

Another question that is raised by both the noise masking and the contouradaptation experiments regards the relationship between edge visibility andlightness perception. It appeared that once an edge becomes invisible, the en-closed area is completely assimilated to the background. If an edge is perceived,on the other hand, it causes the diference between the surface and the back-ground to be enhanced. his is reminiscent of the crispening efect (Whittle,1994, p. 64f ). he question is: what happens if all edges of the test patch inWhite’s illusion become invisible. Since the surround of the test patch is nothomogenous, the patch cannot be assimilated to both the carrier bar and the

Possible percepts ofWhite’s illusion ifboth parallel and

orthogonal test patchedges become

invisible.

lanking bars at the same time. hus, it is not possible for both types of edgesto become invisible together, without the edges between the grating bars alsobecoming invisible, resulting in the perception of a completely homogenousgray surface. Two possible percepts are conceivable, illustrated in the margin.he test patch could take on the color of the carrier bar, resulting in the per-cept of a square wave grating. his is what most observers reported in thenarrowband noise experiment in conditions where the test patch was invisible.Alternatively, the test patch could also merge with the lanking bars, form-ing a shape that looks like the letter H. Why this percept was not reportedin our noise masking experiments is an open question, since the noise wasisotropic, and should have afected both types of edges equally. In fact, ouriso-orientation surround suppression account suggests that the edges parallelto the grating should become invisible irst due to the suppression, favoringthe letter-H percept. In any case, both percepts also require the perceptionof some edges to be strengthened. In the square wave percept, the edges be-tween the test patch and the lanking bars appear to have the same contrast

O U T L O O K 151

as the edges between the individual grating bars, which is not the case as longas the test patch is perceived as a distinct surface. his may hint at a mutualinhibition between the two types of edges, and further experiments with lowcontrast versions of White’s illusion that directly measure detection thresh-olds for these edges may help to better understand the mechanisms involved.he fact that observers always saw the square wave grating and never the H-coniguration in our experiments suggests that some Gestalt-like groupingfactors are involved. If that is the case, this phenomenon may also provide alink to mid-level vision accounts of lightness perception. In addition, experi-ments on the detection threshold of the individual edges may be informativeregarding the IOSS account of White’s illusion, because one would expectIOSS to raise the threshold for detecting the edges parallel to the grating.

Some further questions are raised by our replication study of the noise mask-ing efects on White’s illusion. While conirming the general results of Salmelaand Laurinen (2009), we found that the frequency of the carrier grating inWhite’s illusion and the noise frequency that most afects perceived lightnessare not completely independent. However, it is also clear from our data thatthe two frequencies do not scale in direct proportion to each other (i. e., adoubling of the grating frequency does not result in a doubling of the mostefective noise frequency). he exact numerical relationship between the twoproperties is diicult to quantify in lightness matching experiments due to thehigh variability between and within subjects in this task. Still, it is a centralempirical question that is relevant for implementations of lightness modelsbased on edge processing, if these models are to ground their edge detectionmechanism in psychophysical data. hus, further experiments are required onthis issue. he fact that the most efective noise frequency is not completely in-dependent of the grating frequency may imply that the spatial scale at whichedges inluence surface lightness can be dynamically adjusted by the visualsystem to a certain extent. Alternatively, the dependence could be a result oftwo diferent mechanisms contributing to surface lightness, one edge basedand one surface based. If the edge based mechanism is always sensitive to thesame noise frequency, while the noise efect depends on the stimulus size for


the surface based mechanism, the net result could be a partial scaling of themost efective noise frequency with the frequency of the grating.

A inal question that follows from our noise masking data is why, at least forsome observers, low frequency noise increased White’s illusion above the base-line level measured without any noise. It may be that the addition of the lowfrequency noise, which could generate the perceptual impression of a semi-transparent haze overlaying the grating stimulus, prompted observers to basetheir judgements more on the perceived surface character of the test patch,and resort less to direct luminance matches, which are diicult to make inthe presence of noise. hus, even in our experimental stimuli that were de-signed to investigate the low-level factors contributing to lightness perceptionin White’s illusion, we cannot avoid the inluence of mid-level vision on theexperimental results.

his observation brings us back to the motivation and goal of this thesis.he low-level approach to understanding lightness perception can only takeus part of the way. It was clear from the outset that mid- or high-level factorsplay a large role in this ield. Still, understanding these factors and their efectsis diicult when not even the low-level computations that constitute the irststages of visual processing are well described. I hope that the work presentedhere has made a meaningful contribution to our understanding of these low-level computations, and will ultimately enable research to progress to higherlevel aspects of lightness perception in a more systematic fashion.

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D E C L A R AT I O N

I hereby declare that this thesis and the work reported herein was composed byand originated entirely from me. Information derived from the published andunpublished work of others has been acknowledged in the text and referencesare given in the list of sources.

he two studies that have been published with co-authors and make upparts of this thesis were devised and carried out by myself, and I wrote thearticles. My co-authors provided supervision, discussed the interpretation ofthe results, and revised the manuscripts.

Berlin, September 2015

Torsten Betz

arguments for a new early vision model of lightness perception

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