art and the new biology: biological forms and patterns || noise, form, art

Leonardo

Noise, Form, ArtAuthor(s): F. Molnar and V. MolnarSource: Leonardo, Vol. 22, No. 1, Art and the New Biology: Biological Forms and Patterns(1989), pp. 15-20Published by: The MIT PressStable URL: http://www.jstor.org/stable/1575133 .

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Noise, Form, Art

F. Molnar and V. Molnar

WHAT IS FORM? The concept of form is one of the most exciting notions that human consciousness has created, developed and manipu- lated. It is, in the words of Colin Cherry, "one of those rare

bridges between science and art" [1]. The concept of form, in the broadest sense of the word,

is reduced by computer scientists to a lack of randomness within an organised set of elements. By this measure, the fundamental property of form is a negative one: non- randomness. Computer scientists have tried to determine the features that distinguish form from randomness, or noise, which is itself a complex notion.

Objectively, noise is defined as a set of elements distributed randomly within well-defined parameters. Thus, a set of elements according to the Gaussian distribution, with

average m and variance v, is called white noise. There are several other 'colours' of noise, such as pink and gray. On the other hand, it is much more difficult to define noise

subjectively. A. Moles [2] thinks that Beethoven's Ninth

Symphony becomes noise for someone who wants to under- stand what his neighbour is saying, while for the person who is listening to the music, the neighbour is making noise.

To avoid confusion over the word 'form', many scientists

prefer to consider the detection of two- or three-dimen- sional objects. Obviously, nothing is gained by this for our

purposes, since the concept of object is at best a specific, highly constrained instance of form (for which the concept of boundary is essential as well). We are back where we started.

Although a large number of books and at least two

journals deal with this subject, in only a few instances is the

pattern-recognition problem treated as a problem of human

perception. Almost all research is directed towards algo-

Fig. 1. Pattern composed of two different probabilistic distribu- tions of elements. The central area seems to be emerging from a

background.

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rithms, which detect patterns, instead of towards mechanisms, which explain how the human

sensory system detects patterns. A number of engineers who are interested in understanding the human sensory system try to tackle the problem at the level of data discrimination. However, the sensitivity of electronic cam- eras does not match that of the human visual system. Therefore, processing pixels with 256 gray levels makes no sense; besides, the response of the human system is not linear but nearly loga- rithmic [3].

Thus, it is necessary to per- form a transformation, ex-

pressed as a mapping

z'= 4(z) from original gray level Zi to Z '. To encompass the human system the following boundary conditions are assumed:

ABSTRACT

The concept of form, related both to perception and to art, is one of the more exciting concepts that human consciousness has created. This ancient topic has received a new impetus from research on the automated recognition of form, closely linked to artificial intelli- gence. But this new branch of research often neglects the human aspect of the problem, the capacity of the human receptor. This paper considers the question of form chiefly with respect to human perception and human affectivity, i.e. with respect to visual art.

GL < Zi < GH

DL < Z'i < DH

where DL and DHare the limits of the dynamic range of dis- crete gray levels distinguished by the human system, and GL and GH are the same limits detected by the picture-processing system. -i and Z'i are the intensities at the ith level in the original and transformed image. The Zi values are

ranged in n classes, such that 1

Z2 Z Z (DH\GH-GL Z Z2 Zm - DL

This gray-scale transformation stretches and shifts the scale and increases the overall contrast.

NEUROPHYSIOLOGICAL MODELS OF VISION One other way of introducing the human receptor into the

pattern-recognition problem involves neurophysiological

F. Molnar (visual scientist) and V. Molnar (painter), Institut d'Esthetique et des Sciences de I'Art, Universite de Paris I, Paris, France.

Received 9 December 1987.

LEONARDO, Vol. 22, No. 1, pp. 15-20, 1989 15



mechanisms. For this, the digitised image is explored by a filter defined as

-r2

2 G(r) =bs4 on the G n- eaus

This filter, based on the Gaussian- Laplacian function, reproduces clear-

ly the behaviour of visual mechanisms located between the retina and the visual cortex. Marr and his colleagues showed that Gaussian-Laplacian curves are similar, even identical, to

sensory results obtained by electro-

physiological methods [4]. Marr and colleagues describe a se-

ries of representations, called sketches, that begin at the neurophysiological level and finish by identifying the

objects situated in space. By the detection of the variation of gray levels and so-called zero-crossings, one builds up the first level of representation, called

Fig. 2. Form emerging according to the function Pi - P2, for which the two curves are shown in the lower right corner (after Molnar [121).

Pi1 - P2

the primary sketch, the primitive representation of the local geometry. With these primary sketches, Marr constructs the next level of representation, the 2 1/2-D sketch, and finally the 3-D sketch. The last is the actual

representation of visual forms. This is not yet an established fact but only a well-formulated model, which should be thoroughly tested. We should add that the detection of the zero-cross-

ings is done by a neurophysiological mechanism, but the construction of the 2 1/2-D and 3-D sketches is done by symbol-manipulation operations.

It is clearly established that the first elements of visual perception are elaborated by neurophysiological mechanisms. Those elements are des-

ignated byJulesz [5] as neurophysiological atoms, but Gibson [6] postu- lates that the visual world is filled with solid, stable objects. Our knowledge is considerable about the physiological basis of vision but not about what Julesz called psychological atoms, which concern the perception of the visual world.

These two approaches to the human visual system must be considered as but two examples amongst others. The main difficulty with these models is that they are based on a

sensory mechanism between the retina and the primary visual cortex; but, in fact, pattern recognition, identifica- tion and perception are processed at a higher level in the associative cortex. The primary cortex is not yet concerned with meaning, recognition or symbol.

Without going back either to the old Gestalt theory of perception or to behaviourism, we have to accept as fact

that certain visual stimuli provoke a reaction, a perceptive response, that cannot be attributed either to recognition or to labeling because there is nothing to identify. Something is per- haps detected but not identified, since the stimulus has no identity.

It is impossible to determine an identity because (1) the stimulus does not necessarily have one; (2) the information carried by certain stimuli is not sufficient for a logical deduction; and, finally, (3) the logical deduction by which a problem is solved, according to the theory of problem solving, needs much more time than the few milliseconds necessary for a perceptual reaction-perception is not

necessarily problem solving. The pattern in Fig. 1 is composed of

two types of random patterns. In a random distribution of a set of elements in a given area, it is assumed that any element has had the same chance of occurring in any sub-area as any other element and that the placement of each element has not been influenced

by that of any of the others. Without further scrutinizing this figure, the av-

erage person would interpret it to be a form arising from a background. Much experimental evidence suggests that the process responsible for the

perception of a pattern composed of random elements is an ordering mechanism within the spatial and energy domain rather than logical operations on a symbolic description. The function of the primary sensory system is therefore only to transduce the spatial structure inherent in the

light-intensity variation without a sig- nificant loss of information.

Our purpose in this paper is to ex-

Fig. 3. Random patterns: (a) The textures differ in dipole length variance, which is 0 for the surrounding area, and 1 for the central area; in this case, no discrimination occurs. (b) The same probabilistic distribution as in (a), but the dipole length in the central area is multi- plied by 0.2. (c) The same as in (a), but each dipole is linked as a line segment.

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16 Molnar and Molnar, Noise, Form, Art



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F Fig. 4. Some examples concerning the perceptual and aesthetic role of the probabilistic organisation of patterns.

amine and illustrate a method for ana-

lysing how a form can emerge out of a surface composed of visual noise, using psychophysical methods and with reference to the psychophysio- logical and physiological mechanisms involved. More precisely, we study how a visual display is segmented into parts on the basis of differences in the statistical organisation of the elements, i.e. the texture differential, and how such a display can eventually produce an aesthetic situation. Of course, this ap- proach can be compared to texture

segmentation studies, which several authors have been pursuing for the last 30 years [7].

SHAPE SEGREGATION BY TEXTURE It is well known that engineers can filter out some interesting types of form from dynamic noise. If a delimited area of a random surface begins to structure itself, to organise, this area will emerge as a form. On the psychological and the physiological levels,

the situation is not as well understood. To explain how a surface texture

emerges in a uniform distribution of luminance on the retina (Ganzfeld), the gestaltist Koffka states that the

light reflected by a homogeneously illuminated plane in front of the sub-

ject provokes a uniform excitation of retina photoreceptors, the intensity of which can be mapped on a graph by a horizontal line [8]. If the distribution of luminance on any area is different, the retinal activity will be different on the region corresponding to this area and a shape will be perceived against a background. Actually, the situation is not so clear. In fact, a homogeneous surface does not provoke homo-

geneous neural activity. There is spontaneous neural activity, which varies in

intensity and may be considered as the source of noise. In this situation, it is not so easy to draw the limits of the form, at least for low levels of illumi- nation; it is difficult to establish a threshold. Koffka's theory dates from 60 years ago and has nothing in com- mon with our current knowledge of the neurophysiological functioning of

the sensory system. Today, we instead must consider individual cells, recep- tive fields of spatial frequency and feature detection.

The problem of the measurement and description of pattern recently has been the subject of many impor- tant discussions [9]. Psychological and

physiological studies of vision gen- erate two divergent problems: how to describe a measure of the physical stimulus, and how to describe a subject response. This second question con- tains two sub-tasks: how to determine the presence or absence of a form, and how to prove that the stimulus has aesthetic merit.

In order to study the emergence of form from visual noise, first we must

formally define the meaning of random distribution for our purposes. In a random distribution of a set of elements (dots, for instance) in a given area, we assumed (1) that any element has the same chance of occurring in any sub-area as any other element; (2) that any sub-area of a particular size has the same chance of receiving any element as any other sub-area of

Molnar and Molnar, Noise, Form, Art 17



ME ED *niuum 1 S1 gf 1

1g RGi~

Fig. 5. V. Molnar, six images from the series Transformation/l, 1975. The complete series is composed of 24 pictures, each measuring 30 x 30 cm. This series starts as a group of patterns, each consisting of 10 concentric squares. The range of the controlling random variable was step-incremented in each group. Toward the end of the series, the geometri- cal organisation seems to disappear. Although progressively more hidden, the geometri- cal structure of the pictures remains.

the same size; and, finally, (3) that the placement of each element is inde- pendent of that of all the others. It is possible to construct a set of random elements by different methods, but it is difficult, or probably impossible, to determine a posteriori if a set of elements is distributed at random. We can never be sure that there are no hidden variables in the stimulus, non- randomly distributed. Even the depar- ture from random distribution is difficult to determine, and the significance of the difference in the distribution of two populations is hard to evaluate. The situation is made even more difficult by the fact that the visual system carries a certain organisation into an

unorganised pattern. To perceive is to grasp and to organise the information from the beginning of the visual process, from the instant when light pene- trates the ocular globe.

As far as the presence of a stimulus is concerned, there are no problems. And though we have encountered some difficulties detecting the absence of a stimulus, they are beyond the scope of this paper. For our purposes, shape or form recognition is a computational abstraction whose mechanisms do not concern us. These mechanisms may be connected to single neurons, to interconnected as- semblies of neurons or to any other biological structures.

It is much more difficult to answer the question of how form arises out of a background of noise. Under the most general conditions, the threshold of form detection depends on the statistical properties of the stimulus. Given that Pi represents the prob- ability of the distribution of features over a set X, it is possible to estimate (or to calculate) PI over a set A and P2 over a set B of elements surrounding set A. If the feature is effective, the chance of form arising is proportional to the difference between P1 and P2 (PI-P2). If we know the parameters of the statistical distribution of the elements, it is easy to construct a model, an ideal detector, that is able to detect the form with a required certainty, as is affirmed by signal-detection theory (see Fig. 2).

THE AESTHETIC SIDE OF THE EMERGENCE OF FORM But signal-detection theory concerns the decision process. The aesthetic quality of the visual stimulus poses still further problems. Once more, we are not looking for physiological or biological mechanisms able to produce aesthetic effects; the only aim of this paper is to establish a clear relation between a random distribution of elements over an area and the perceptual and aesthetic effects of the stimu- lation.

One of the simplest ways to produce random patterns is to change the density of elements (dots) within a well- defined area of randomly distributed elements. If the difference in density between the two areas is large enough, we see form emerging from the ground. But the density is closely related to the luminance. If the density of black dots on a surface increases, the surface becomes darker. The problem in this case, as mentioned earlier, is to determine the threshold of the density differences necessary to see form on a ground. On the other hand, the density of randomly distributed elements is related to the distance between adjacent elements. The distance from an individual element to its neighbour depends on the density of the black dots. In a population of N individuals having a specified density the mean distance rfrom each element to its nearest neighbour can be represented as




rA =

The mean distance that would be ex-

pected can be shown to have a value

equal to

1

2Vp The ratio r can then be used as a measure for degrees to which the ob- served distribution approaches or de-

parts from random expectation [10]. Under these conditions, it is pos-

sible to study the emergence of form not as the variation of the luminance on the retina but as the difference in the mean distance of neighbouring points. Julesz has demonstrated that, in general, this distance is not a useful variable for producing texture segregation; the texture system is sensitive to change in dipole orientation but not to change in dipole length. For ex-

ample, the probabilistic distribution of the distances between the dots in the center of Fig. 3a differs signifi- cantly from the distribution in the sur-

rounding area. In spite of this difference, the segregation of the pattern does not occur. Obviously, we can calculate the statistical difference between the adjacent regions, but we cannot see it segregate. The spontaneous segregation is neither a statistical calculation nor a conscious detection

process. By increasing the distance between dots within an area, we finally can obtain spontaneous form segregation (see Fig. 3b). But increasing the distance between the different dots, provokes, in general (although not in this case), an increase in the luminance of the region: the surface becomes clearer. It is well known that the difference in luminance is one of the

principal variables of form segregation. If we connect all pairs of dots (di- poles) by lines-that is to say, if we transform a set of points into a set of bars of different orientations, without

considerably modifying the statistical relations between the different areas-we obtain, surprisingly, a very good spontaneous form segregation (see Fig. 3c). From Julesz's perspec- tive, the bars and their terminators are assimilated, respectively, to simple and complex units in neurophysi- ology.

From an aesthetically oriented

In addition, we observe that this aesthetic effect is related closely to the

probabilistic structure of the stimulus. In Fig. 4, we present some examples to illustrate these statements. The figure comprises a complex relationship between three factors: the statistical structure, the form segregation and the aesthetic effect of the stimulus. For instance, the relationship between aesthetic effect and statistical structure is neither linear nor simple. Ob-

viously, the figures that are easiest to discriminate are far from being the most aesthetic, but, on the other hand, this also holds true for those that are hardest to discriminate. It seems that features such as bar length and bar orientation are not the most appropri- ate for the study of aesthetic quality. But these two variables are not the only ones that provoke form segregation; many others intervene and influence human perceptual mechanisms. For instance, it seems that a 3:1 ratio between spatial frequencies provokes spontaneous form segregation; this is, however, the topic for another paper currently in preparation [ 11].

Julesz was able to provoke sponta-

neous pattern segregation by using the capacity of the human visual system to detect colinear or quasi- colinear detectors. It is not our task to

posit whether specific detectors of this kind of feature exist. It is also outside the scope of this discussion to justify the introduction of the colinear detector in pattern segregation. But we have to admit that the hypothesis of the colinear detector could explain the aesthetic qualities of certain patterns in

Figs 4c and 4d. In these figures, the co-

linearity is detected, in fact, with great likelihood, and so chance intervenes once more in the visual composition [12].

We do not mean to explain perception by the probabilistic organisation of the stimulus, even less by its aesthetic effect. Nevertheless, the statistical description of the stimulus is useful for aesthetic research done by scientists as well as by artists. In fact, art has often used random processing tech-

niques. Leonardo da Vinci recom- mended that artists take inspiration from small cracks in old walls and transform them into good form. The

process of composing music using

Fig. 6. V. Molnar, six images from the series Transformation/2, 1976. The complete series is composed of 32 pictures, each measuring 30 x 30 cm. In this series of concentric

squares, the range of the random variable, controlling the distortion of the position of the corners, was step-incremented. From the twelfth figure onwards, a sine curve was

applied to the lines linking the corners. The drawings obtained are organized random patterns: disorder in order.

l --_

r- XI I - l~

point of view, we must notice that the

pattern obtained by the random distribution of the orientation of the bars

begins to produce an aesthetic effect.

Molnar and Molnar, Noise, Form, Art 19



Fig. 7. V. Molnar, Hypertransformations, acrylic on canvas, 150 x 150 cm, 1976. (Private collection)

dice games was very popular in Mozart's time, and in our dayJackson Pollock's drippings are obviously random processes as well.

The works presented in Figs 5, 6 and 7 are by one of the authors, V. Molnar.

Obviously these drawings are not at all stochastic; they are the products of a conscious work guided by an obvious Kunstwollen but with respect to the science of vision. Random process techniques served nevertheless at different stages of their elaboration.

References and Notes

1. Colin Cherry, On Human Communication (New York: Wiley, 1957).

2. A. Moles, Theorie de l'information et perception esthetique (Paris: Flammarion, 1958). Translated byJ.E. Cohen under the title Information Theory and Esthetic Perception (Urbana, IL: University of Illinois Press, 1956).

3. B. Chanda, B.B. Chandhuri and D. Dutta Ma- jumder, "Some Algorithms for Image Enhance- ment Incorporating Human Visual Response", Pattern Recogn. 17, No. 4, 423-428 (1984). 4. D. Marr, Vision (San Francisco: Freeman, 1982).

5. B.Julesz and A. Schumer, "Early Visual Percep- tion", Ann. Rev. Psychol. 32, 575-627 (1981).

6. J.J. Gibson, The Perception of Visual World (Bos- ton: Houghton Mifflin, 1950).

7. See, for instance, W.R. Uttal, A 7axonomy of VisualProcess (Hillsdale, NJ: Erlbaum, 1981).

8. K. Koffka, Principles of Gestalt Psychology (New York: Harcourt, Brace, 1935).

9. A. Rosenfeld, Picture Languages (New York: Academic Press, 1979).

10. P.J. Clarck and F.C. Evans, "Distance to Near- est Neighbor as a Measure of Spatial Relation- ships in Population", Ecology 35, No. 4, 445-452 (1954).

11. F. Molnar and C. Weikart, FourierAnalysis as a Toolfor Visual Aesthetics Research (in preparation).

12. F. Molnar, "Perception de la Pluralite d'un Stimulus Compose d'Elements Discrets", Psycho- logieFrancaise 13, 219-228 (1968).




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