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Medical Image Analysis 10 (2006) 850–862

A biologically inspired algorithm for microcalcification cluster detection

Marius George Linguraru a,b,*, Kostas Marias a,c, Ruth English d, Michael Brady a

a University of Oxford, Medical Vision Laboratory, Oxford, UKb Harvard University, Division of Engineering and Applied Sciences, Cambridge, MA, USA

c Institute of Computer Science, Foundation for Research and Technology – Hellas FORTH, Heraklion, Crete, Greeced Churchill Hospital, Breast Care Unit, Oxford, UK

Received 29 August 2005; received in revised form 19 July 2006; accepted 19 July 2006Available online 1 September 2006

Abstract

The early detection of breast cancer greatly improves prognosis. One of the earliest signs of cancer is the formation of clusters ofmicrocalcifications. We introduce a novel method for microcalcification detection based on a biologically inspired adaptive model ofcontrast detection. This model is used in conjunction with image filtering based on anisotropic diffusion and curvilinear structure removalusing local energy and phase congruency. An important practical issue in automatic detection methods is the selection of parameters: weshow that the parameter values for our algorithm can be estimated automatically from the image. This way, the method is made robustand essentially free of parameter tuning. We report results on mammograms from two databases and show that the detection perfor-mance can be improved by first including a normalisation scheme.� 2006 Elsevier B.V. All rights reserved.

Keywords: X-ray mammography; Microcalcification clusters; Image normalisation; Anisotropic diffusion; Human visual system

1. Introduction

Breast screening programs attempt to detect anderadicate cancer at the earliest possible stage to reduce therate of mortality amongst women. However, detecting theearly signs of breast cancer that appear in X-ray mammo-grams presents a significant challenge to radiologists, notleast because such signs are often difficult to distinguishagainst the dense or highly textured breast anatomy. Studiesprove that the performance of radiologists is increasedwhen a good segmentation or classification system is used(Funovics et al., 1998; Giger et al., 2002; Petrick et al.,2002). However, such systems must have provably adequateperformance and robustness to be used in a clinical setting.

Most ductal and lobular cancers have secretions thatmay form calcifications (Highnam and Brady, 1999). The

1361-8415/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.media.2006.07.004

* Corresponding author. Address: Harvard University, Division ofEngineering and Applied Sciences, 60 Oxford Street, Cambridge, MA02138, USA. Tel.: +1 6174969098; fax: +1 6174969837.

E-mail address: [email protected] (M.G. Linguraru).

smallest of these (under 1 mm in diameter) are called mic-rocalcifications and represent some of the earliest signs ofbreast cancer. Microcalcification clusters may be the onlyindication of in situ tumours. Approximately 80% of micro-calcifications are benign (Highnam and Brady, 1999;Veldkamp and Karssemeijer, 1998), their shape and topol-ogy differentiating them from the malignant type.

In general, microcalcification detection algorithms con-sist of three stages: (i) a pre-processing step based on filter-ing the image, for example, subtracting a signal-enhancedimage from a signal-suppressed image (Nishikawa et al.,1993); (ii) a segmentation step, for example based on globalthresholding and morphological erosion (Nishikawa et al.,1993), on region growing (Shen et al., 1993) or adaptivethresholding (Betal et al., 1997); and (iii) a clustering step,typically using a fixed size kernel to eliminate noise pointsand isolated calcifications and to identify clusters. A majordrawback of such methods is their poor sensitivity to smalland faint microcalcifications. Other approaches use neuralnetwork classifiers (Edwards et al., 2000; Hara et al., 2000;Kim and Park, 1999; Rosen et al., 1996), several of which

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M.G. Linguraru et al. / Medical Image Analysis 10 (2006) 850–862 851

are trained on a single database and give poor results whentested on other databases. Wavelet filters have been used inAghdasi (1996) and McLeod et al. (1996) to highlight thehigh frequency signal from the background; unfortunately,noise also has significant power at high frequencies.

Yam et al. (2001) developed a structural approach tomicrocalcification detection, which exploits the StandardMammogram Form (SMF) representation (therein calledhint), which is introduced in Section 2 of the paper. Yamet al.’s technique detects tall thin structures in the hint

image and tests with the height of such a structure to itsfootprint in the image to detect possible calcifications.Noise is a major problem and some individual calcifica-tions are overlooked and so statistical analysis of a clusteris compromised. The results appear promising, though itshould be noted that they are from a considerably smallerdatabase (Yam et al., 2001).

Perhaps the best-known published statistical method isthat of Karssemeijer (1993) and Veldkamp and Karssemei-jer (1998). The authors use adaptive noise equalisation aspart of a Bayesian approach, using Markov RandomFields to detect clusters of microcalcifications. Though itset a new standard for feature detection at the time itwas published, the algorithm involves a large number ofparameters, and there have been questions raised aboutits robustness or generalisability to other databases (Pois-sonnier and Brady, 2000).

R2 Technology’s commercial product ImageCheckere

(Roehrig, 2005) is a CAD system that is widely acknowl-edged as the state of the art of microcalcification detection(though, understandably, few details of the detailed opera-tion of ImageCheckerTM have been published). Severallarge studies show the improvements from using Image-

CheckerTM to detect breast cancer by reducing the falsenegative rate, while increasing the mean sensitivity of radi-ologists (Roehrig, 2005). Freer and Ulissey (2001) reportthat radiologists improve the detection of malignant micro-calcification clusters from 68% to 100% after the use ofCAD. In a more recent study, Birdwell et al. (2005) notifythat the contribution of CAD increased by 7% the numberof detected cancers, but without clear benefit of CAD sys-tems in the detection of microcalcifications.

Herein we present a novel ‘‘foveal’’ segmentation algo-rithm that is based on a biological model of adaptivecontrast-detection, complemented with complex pre-processing steps. The rationale for adopting a modelinspired from the human visual system derives from thechallenge posed by the highly variable mammogram imagebackground that often confounds algorithms or humanobservers, especially when ‘bright’ microcalcifications arehidden within ‘bright’ dense tissue. The paper is structuredas follows. Section 2 presents the pre-processing of SMFimages (Highnam and Brady, 1999), in particular theoptional, but helpful, normalisation step, the removal ofshot-noise, curvilinear structures and image filtering. Anovel statistical approach to derive automatically theparameters of the enhancing diffusion filter is also pro-

posed. Section 3 introduces the ‘‘foveal’’ segmentationalgorithm. In Section 4, we perform a Free-Response Oper-ating Characteristic (FROC) curve analysis as a steptowards a validation of the microcalcification detectionalgorithm.

2. Pre-processing

Due to the complexity of mammogram image formation,we pre-process images before applying contrast-detection. The aim is to remove structures that may give riseto false positives (e.g. shot noise or curvilinear structures)and to smooth out noise in the image without removing mic-rocalcifications. Note that we also include in this section animage normalisation step SMF, which is optional to themethod, but which we have found that can improve detec-tion results, since it models the image formation processand removes variability in imaging conditions (e.g. time ofexposure, film speed). The pre-processing steps of ourmethod are described in the following paragraphs.

2.1. The standard mammogram form

A well-known normalisation method that results frommodelling the process of mammographic image formationis the Standard Mammogram Form (SMF) developed byHighnam and Brady (1999) and improved in Yam et al.(1999). The SMF algorithm corrects for scatter andextra-focal radiation, glare and anode heel effect. We havealso based our work on previous results by Highnam andBrady (1999) and Yam et al. (1999), which estimated radio-graphic mottle, and then used Wiener filtering to subtractits effect and estimate glare and local blur. Our paperstarted from the observation that sometimes Yam’s algo-rithm gave very poor results, and that led us to use – andanalyse – anisotropic diffusion.

Because of the relatively weak control over the imageacquisition process, it is difficult to eliminate variabilityin image characteristics, such as contrast and brightness.It is well known that such differences in imaging conditionslead to a complicated functional relationship between theintensities of temporal pairs of mammograms that variesfrom patient-to-patient (Marias et al., 2005). This is astrong indication that the non-linearities introduced byvarying imaging conditions may alter significantly theimage-intensity profile and reduce the efficiency of auto-matic microcalcification detection algorithms. After devel-oping a method for the calculation and correction forscattered radiation, Highnam and Brady (1999) discovereda method for mammogram image normalisation that elim-inates distracting variations. This was based on the follow-ing assumptions/observations:

– The X-ray attenuation coefficients of normal healthy tis-sue and cancerous tissue are approximately equal overthe range of tube voltages used in mammography; butare significantly different from that of fat.

852 M.G. Linguraru et al. / Medical Image Analysis 10 (2006) 850–862

– Fat is clinically uninteresting, therefore normal healthyand cancerous tissues are collectively referred to as‘‘interesting’’.

Highnam and Brady’s method estimates – in millimetres– the amount of interesting tissue in each pixel column, asillustrated in Fig. 1. This effectively provides objectivequantitative information about the breast anatomy. If,for example, the separation between the Lucite plates is6.5 cm, the amount of interesting tissue at a location(x,y) might be 4.75 cm, implying 1.75 cm of fat.

This way, the interesting tissue representation refersonly to (projected) anatomical structures. The SMF algo-rithm estimates and then eliminates the effects of the partic-ular parameters that were used to form the mammographicimage. In short, the image can be regarded as standardised(hence the more recent name Standard Mammogram Formor SMF) and quantitative since the ‘normalised’ pixel val-ues are measurements in millimetres, not in arbitrary unitsof shading (contrast), and they convey anatomical informa-tion. The key point is that without normalisation, forexample by the SMF process, there is inevitably the riskof confounding anatomically useful information and imag-ing parameter effects, whose choice significantly affect con-trast, brightness and the level of noise. As we will show inthe results section, detection performance is improved if thenormalisation step is included.

The exception ignored in the generation of an SMF rep-resentation of a mammogram is the presence of microcalci-fications. The attenuation coefficient of microcalcificationis approximately 26 times that of normal/cancer tissue,and so, although microcalcifications are physically small,they appear in the SMF representation as non-fat tissuethat is 26 times as high as it actually is, that is as very high,tall thin towers. Thus, although the breast parenchyma isnormalised, calcifications remain small areas of higher con-trast. Hence, the contrast of a feature (microcalcification inour case) is largely independent of the film contrast curve.

Fig. 1. A schematic of hint calculation. In the normalised image each pixelvalue reflects the corresponding amount of non-fatty tissue instead ofacquisition-dependent attenuation measurements.

It is its presence in a fat or dense neighbourhood thatmakes it easy or difficult to detect/visualise.

We stress that the inclusion of a normalisation pre-processing step is not essential for our algorithm to work.However, our results indicate that the detection efficiencycan be improved by including such a step, probably as aresult of removing non-linearities and distracting varia-tions, which in turn improves the contrast.

2.2. Shot noise and curvilinear structures removal

An important pre-processing step is the removal of noise,which is a major source of false positives (FP). In this paper,shot noise refers to an intrinsic noise process during scan-ning, due to dust and artefacts present on the film or inthe scanner. Previous papers report the detection of film-screen artefacts associated with the SMF generation process(Ancelin et al., 2002; Highnam and Brady, 1999), for exam-ple, at the glare removal stage. Although shot noise appearsvisually similar to microcalcifications, it is introduced at theimage digitisation stage, that is, it is introduced to the imageafter the main blurring stage, and so the boundary shape ofshot noise tends to be quite sharp. The point spread functionof the intensifying screen (blur function) enables the identi-fication of image locations that are locally bright, but theenergy imparted becomes negative where shot-noise is pres-ent after glare compensation. Using the binary informationfrom the shot noise map (Fig. 2b), the artefacts can beremoved from the SMF image by interpolating betweentheir surrounding backgrounds.

Curvilinear structures (CLS) – ducts, blood vessels,ligaments or tumour spiculations – are locally linear, rela-tively thin structures, which often produce in a mammo-gram a characteristically textured appearance. Removingthe CLS turns out to be important for the method specific-ity (Highnam and Brady, 1999), but their identification andremoval remains a major challenge (Wai et al., 2004). TheCLS appear relatively bright, though not necessarily withhigh contrast. They are locally linear, but typically curveat larger scales. Their detection is difficult due to the largevariety of widths, contrasts, lengths and intersections.Intersections are either genuine bifurcations or may corre-spond to the overlap of two projected CLS in the com-pressed breast. The attenuations of the individual CLSadd, producing a localised region of higher attenuation.Such points also appear similar to calcifications rather thannoise.

The method we propose for CLS removal is based onthe local energy model for feature detection of Kovesi(1999) and is presented in Evans et al. (2002). From localenergy (LE) we search points with maximum phase congru-ency (PC) to detect and then remove CLS from mammo-grams. For the spatial frequency j, if the local Fouriercoefficients of a one-dimensional signal are as in Eq. (1),then LE and PC can be calculated according to Eqs. (2)and (3). In practice, logGabor filters were used to estimatethe local energy and phase, with a spreading function and


combination of responses from several discrete directionsto extend the analysis to 2D (Kovesi, 1999).

Several more assumptions are necessary: (i) the intensityprofile of a CLS perpendicular to its local orientation is anone-dimensional peak (e.g. cos(/)), with a phase within�p/ 2 6 / 6 p/2 and (ii) the phase congruency PCh+p/2 >PCh at a CLS of orientation h, since CLS are long and thinXN

j¼1

ðAj þ iBjÞ; ð1Þ

LE ¼XN

j¼1

Aj

!2

þXN

j¼1

Bj

!2

; ð2Þ

PC ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

LEPNj¼1

ðA2j þ B2

j Þ

vuuut : ð3Þ

Our implementation uses a small wavelength, whichmakes it more sensitive to smaller scales, and a reducednumber of scales over which features are detected by phasecongruency in order to avoid marking the CLS as calcifica-tions. The limitation is that there are discontinuities thatappear in the true CLS and their removal leaves brightareas on the mammogram similar to microcalcifications.

Fig. 2. Removing artefacts in the pre-processing step: (a) the original image; (image.

We use a smooth interpolation process to remove CLSfrom mammograms. Fig. 2 shows an example of removalof shot noise and CLS.

2.3. Image enhancement

We have previously reported our work using anisotropicdiffusion to filter and analyse mammographic images(Linguraru et al., 2001). Anisotropic diffusion has the desir-able property of smoothing an image, that is reducing noise(hence increasing signal to noise, which is generally poorfor mammographic images) while at the same time largelypreserving image structure. In this paper, we also addressthe issue of automatically defining the appropriate diffu-sion parameters.

Previous methods used for noise reduction, such as theWiener filter (originally embedded in the SMF generation),have limitations (Linguraru, 2002), primarily arising fromdeconvolution and inevitably simplified models of the com-plex physical processes involved in mammography. Thesepossible sources of errors leave residual high-frequencynoise in mammographic images. Digitiser noise, also ofhigh frequency, adds to it. The anisotropic diffusion filteraims to smooth the remaining high-frequency noise that

b) the shot noise map (white dots); (c) the CLS map; and (d) the ‘‘clean’’


interferes with our specific application. We base ourapproach on Weickert’s solution (Weickert, 1998) for thediffusion tensor for which we define the correspondingeigenvalues in Eq. (4), where I is the initial image, Ir theGaussian smoothed image (r is the standard deviation orscale) and k is a contrast measure. I can be either an inten-sity or SMF image, depending if SMF normalisation hasbeen performed as a pre-processing step

k1 ¼1 jrIrj ¼ 0;

1� exp �1ðjrIr j=kÞ12

� �jrIrj > 0;

(

k2 ¼ 1:

ð4Þ

The parametric nature of anisotropic diffusion in generalmakes the process highly dependent on the fine-tuning ofits input parameters. In practice, the more complex andvariable the images in a dataset, the more problematicalit is to choose a single set of values for these parametersthat works well for the entire dataset. We address thisproblem by proposing an automatic scheme that definesthe diffusion parameters using image characteristics. Theparameters we deal with are: (a) a contrast gradient k, (b)the standard deviation r and (c) the number of iterations t.

Microcalcifications represent a tiny percentage of themammogram surface. Typically, they are very small,indeed are only present on average in about a quarter ofthe total number of screening mammograms (Highnamand Brady, 1999). For these reasons, we generouslyestimate that at most 5% of the mammogram pixels is suf-ficient to accommodate the entire population of microcalci-fication pixels. Microcalcifications often appear relativelybright in an X-ray image, indeed were it not for surround-ing dense tissue they would be the brightest/highest pixelsof the mammogram. As illustrated in Eq. (5), we computek as a measure of the gradient, where Kr(I) is the Gaussianof image I, M its derivative and N the number of pixels inthe neighbourhood di. k becomes a value with well-definedphysical meaning that discriminates between microcalcifi-cations (the brightest structures after noise removal) andbackground; more precisely, we chose the 4.4% structureswith highest contrast, according to the statistical value in

Fig. 3. An example of estimating k. (a) From the image shown on the left (afte(b) We note the zero mean value of g, as well as where the value of 0.47 of k

Eq. (5), given that mean(g) is 0. Fig. 3 illustrates the estima-tion and meaning of the value of k

k ¼ 2�stdðgÞ; where gi ¼Mi �1

N

Xj2di

Mj and M ¼ jK 0rðIÞj:

ð5ÞThe second parameter to be set is r, the standard devi-

ation of the Gaussian filter used to smooth the image.We need to choose a value for r so that, on the one hand,it removes high-frequency noise (which is very localised,typically spread over a couple of pixels at, for example,50 lm/pixel), but, on the other hand, preserves microcalci-fications (on average 0.5–1 mm in diameter). Digital imagesare convolved with a Gaussian kernel, whose width is givenby r (n*r, for example n = 10, where n gives the digitalfinite extent of the Gaussian). r must be sufficiently smallto clean noise and retain microcalcifications and is directlyrelated to the image resolution. For example, the widthof the kernel must be 300/50 = 6 pixels to preserve micro-calcifications over 0.3 mm (or 300 lm) in diameter at animage resolution of 50 lm/pixel.

Weickert (1998) notes that the number of iterations t isrelated to the spatial width of the Gaussian kernel. To blurfeatures of the kernel order it is required that t = (n*r)2/2,which gives excellent noise reduction results in the micro-calcification preservation framework.

The reasoning behind the parameter setting in the aniso-tropic diffusion process has been explained above. As aconcluding remark, we note that our method computesall parameters automatically: k is computed directly fromthe image and its meaning (it depicts the most outstandingfeatures in the mammogram) and is independent of thedata set; r is strictly related to the size of microcalcifica-tions and the image resolution; and t is set according tothe proposed value of r. We show a typical example ofautomated image enhancement for microcalcificationdetection in Fig. 4.

With the automatic tuning of parameters that we pro-pose, anisotropic diffusion becomes, for microcalcificationdetection, a robust process using little, but essential,a-priori knowledge. This is important since anisotropic

r increased display contrast) the histogram of g is computed from Eq. (5).(related to the 4.4% structures with highest contrast) falls.

Fig. 4. Automated image enhancement: (a) the original noisy image with a microcalcification cluster; (b) the map of features selected by the value of k; and(c) the enhanced image.


diffusion has often attracted criticism because of its strongdependency on a number of parameters.

3. Foveal segmentation

An important part in image processing and computervision is to understand and implement models of thehuman visual system (HVS), partly because understandingthe HVS is an important scientific goal in its own right, andpartly because expert radiologists have generally outper-formed computer systems, especially for the detection ofsubtle microcalcifications and/or masses in dense texturedbackgrounds. There is over a century of research behindtrying to fully understand the way HVS functions, particu-larly how it responds to intensity transitions and texturevariations. A major contribution to this on-going researchwas made by Holladay (1926) and later by Moon andSpencer (1943). They developed several of the fundamen-tals of the way the human processes visual scenes, at leastin the early stages. Nevertheless, the process is very com-plex and still not fully understood (Ashdown, 1996).

The adaptation of the eye to light changes is a continu-ous process in the HVS. We perceive objects differently ifthey are against a bright surface (for instance a windowon a sunny day) or dark area (a dark wooden panel).The adaptation luminance proposed in (Moon and Spen-cer, 1943) is the response of the eye in adding an averageluminance within the central visual field or fovea (Lfov)

Fig. 5. An illustration of the lightness assimilation. We show three synthetic imhave central objects of the same size and intensity, but are perceived different

and an equivalent veiling luminance caused by surfaces sur-rounding the peripheral field of view (Lseq) as in the follow-ing equation:

La ¼ Lfov þ Lseq: ð6ÞHowever, foveal adaptation stems mainly from the lumi-

nance within the foveal field and relates to approximatelyonly ten percent to the luminance of the field of view out-side that of the fovea (Moon and Spencer, 1943). Further-more, the visual perception of the eye is dependent on thespatial perception of the object we visualise. This effect iscalled lightness assimilation. The same object may appearlighter on a dark background and darker over a light sur-face (see Fig. 5).

In mammography, the main advantage of human eyeover CAD methods is the detection of microcalcificationsin dense areas of the breast, usually the clusters that makethe True Positive (TP) ratio inferior to the 100% of theground truth. At the same time, neither the radiologistnor a computer program must pick FP in the dark areas.This is the result of the adaptation to background, whichis equivalent to lowering thresholds in bright areas (toincrease the TP ratio by detecting clusters in dense breastareas) and increasing them in dark areas (to decrease theFP number), basically an inverse proportionality to thebackground. In a mammogram we must consider the neigh-bouring area of the foveal kernel, as shown in Eq. (6). Theadaptive thresholding model that we propose for the detec-tion of microcalcification applies the above-mentioned

ages with dark (left), medium (middle) and bright (right) backgrounds. Allly by our eyes, due to the variance in background lightness.


concepts in the mammographic setting for the improvementof abnormality detection in the breast.

The classical contrast (Cclassic) is calculated at every pixelas the difference between that pixel value (p0) and a weightedsum of the pixel values in an immediate neighbourhood (N),as in Eq. (7), where n is the number of pixels in N (Gonzalesand Woods, 1993). In mammography, such contrast mea-sures were used in (Karssemeijer, 1993) combined withnoise/contrast equalisation and (Kegelmeyer and Allmen,1994) together with local thresholding. In a simpler sce-nario, Cclassic is compared with a fixed threshold, Cthresh,over the whole image and microcalcifications are marked.The variation in height in a SMF image or intensity in a typ-ical mammogram makes it far easier to detect microcalcifi-cations (or contrast changes) against a fatty (dark)background but more difficult to detect correctly against adenser (bright) background (Highnam and Brady, 1999).The HVS, however, adapts to the local image contrast,and detects faint contrast changes in a manner essentiallyindependent of the background. We adopted a model ofcontrast detection similar to HVS for mammography withthe aim of improving the accuracy of the detection

Cclassic ¼ p0 �1

n

Xi2N

pi: ð7Þ

We initially pre-process the images as described in theprevious section (shot-noise and CLS removal, etc.). Then,we compute a set of mean intensity values of the inner areaof the object to visualise (i.e. within the boundary of calci-fication), its neighbourhood (the local area around theobject) and background (the rest of the breast tissue).The histogram of the inner foveal surface provides themean of the object (lO), as the histogram of the wholeimage will give us the mean of the background (lB) anda measure of the density of breast. The mean of the neigh-bourhood (lN) is found from the intensities of pixels withinthe neighbourhood and excluding the object pixels accord-ing to Fig. 6. lN determines whether the visualised object ison a dense (bright) or a fat (dark) area of breast. The sizeof the kernel of the inner object (O) used to compute lO isestablished according to the average size of microcalcifica-tions (Highnam and Brady, 1999) and the resolution of the

mB

mN

mO

Fig. 6. The foveal masks used for the computation of lO, lN and lB. Theobject O is the area of the fovea centralis, N its neighbourhood (twice thesize of O in our applications) and B the background.

tested images, in a similar manner to the kernel of theGaussian in Section 2. It is desirable to have a slightlysmaller kernel than the microcalcification diameter toassure the detection of small calcium salts, which are over-looked by larger kernels. Still, the size of O must not be toosmall to avoid overlapping O and N for slightly bigger mic-rocalcifications. In our application N is set twice the size ofO. Then the perceivable contrast C is calculated in agree-ment with the following equation:

C ¼lO�lN

lN; if lO > lN;

0; otherwise:

(ð8Þ

We then compute Cmin (9), a measure of contrast sensi-tivity, where lA = wlN + (1 � w)lB and w is a suitableweight between 0 and 1 affecting the amount of back-ground implied in the computation of contrast. Cmin setsthe threshold from which objects in the image are visiblefor the observer, a measure of the eye’s ability to perceiveluminance gradients. The literature proposes 7.7% of theadaptive luminance to be due to the background luminance(Heucke et al., 2000), which gives a value of 0.923 to ourweight w. In practice, we studied the effect of varying w

with 10% more or less than the proposed value. We usew = 0.923 as the default value in comparative studies.For parameter b in Eq. (9), we have found that the litera-ture proposed value b = 0.0808 (Heucke et al., 2000) givesgood results. Areas in the image having C > Cmin aremarked as microcalcifications

ð9ÞThe segmentation parameters are established automati-

cally based on the image-adapted value of k, as computedfrom the statistical analysis (discussed in Section 2).Through the use of the minimal perceivable contrast cw,we include a measure of the image contrast (previouslydenoted as k) – imagine varying the amount of objectswe can distinguish with the naked eye by using a pair ofsunglasses. cw is a crucial variable for assessing our methodand is consequently used for producing the FROC curvesin the results session. From the FROC analysis, we notedthat adapting the value of cw to the image characteristicsgives a better balance between TP and FP than a constantcw. We performed simple preliminary tests on 13 randomcropped mammograms digitised at 50 lm resolution andcontaining 10 pre-labelled isolated coarse calcifications.These images originate from Oxford, but are not part ofthe Oxford database on which the algorithm is evaluatedin the next section. We found that cw ¼

ffiffiffikp

=200 is appro-priate for conservative detection of microcalcifications.

Cthresh

Cthresh Cmin

Cmin

Intensity/Height

X dimension

Fig. 7. The simulation of a plot of a mammogram section containingmicrocalcifications over height/intensity variation. The variation of theperceivable contrast in the detection of microcalcifications is suited to thelocal characteristics for the adaptation of HVS using Cmin. The classicalminimal perceivable measure, (here called Cthresh) is a global characteristicof the mammogram and less flexible in the elimination of FP in thedetection of microcalcifications.

Fig. 8. The diagram of the biologically driven algorithm to detectmicrocalcifications. The top row underlines the optional image normal-isation that generates SMF images. The rest of the diagram highlights thesteps introduced by our algorithm, which are described in this paper.


Using Cmin instead of Cthresh, the contrast is adaptedlocally, not just globally, in a manner similar to that ofHVS. Fig. 7 shows how the variation of perceivable con-trast varies with the background in the HVS adaptationmethod versus classical methods. While Cmin varies withthe local image characteristics, Cthresh is constant over thewhole image. Microcalcifications can be easily depicted ina fat background for both contrast measures, but Cmin

reduces the number of FP. The main advantage of usingCmin becomes clear in a dense background, where its adapt-ability facilitates the detection of microcalcifications.

4. Results

In this section we present comparative Free-ResponseReceiver Operating Characteristic (FROC) curves to testthe outcome of our method with variations in algorithmand input images. We used a database of 102 samples ofdigital SMF images from 83 mammograms. Seventy-eightof the samples contain between 1 and 3 clusters per image,while 24 are normal mammogram samples. An experiencedradiologist annotated a total of 98 microcalcification clus-ters, which had previously been proven by biopsy. Theground truth for the validation of our detection algorithmwas the contour drawn by the radiologist on the filmaround each detected cluster of microcalcifications. Thefilms were subsequently digitised using the Lumisys scannerat a resolution of 50 lm. The cluster positions were thentranslated into x–y coordinates on the digital images. Thecropped image sizes are of maximum 1500 · 1500 pixels.

Fig. 8 shows a schematic of the method flow describedin the previous sections. As noted earlier, the normalisa-tion step in the flow is optional and results are reportedfor both original and normalised (SMF) images. A clus-ter is detected if it contains at least three microcalcifica-

tions, where a distance of maximum 5 mm connects eachcalcification to the rest of cluster. When a cluster is iden-tified at the position indicated by the radiologist, wecount a TP. If a cluster is detected outside the markedareas or more than one cluster are found at the approx-imate location of a single contour indicated by the radi-ologist, we count a FP. Recursively, we noted that thedistribution of detected FP/image is equal in sampleswith microcalcifications and in normal samples. InFig. 9 we note the impact of CLS removal, imagesmoothing and image normalisation (SMF images) ondetecting microcalcification clusters. The results are supe-rior when the proposed algorithm (Fig. 8) is employed(the top line in the FROC curve); when the algorithmis applied to intensity (not normalised) images the resultsare also very satisfactory.

In Section 3 we noted the significance of the value of w

in setting the minimal perceivable contrast for obtainingthe best detection results when our algorithm is applied.We ran parallel tests to test the consistency of our conclu-sion to use the value 0.923 for w, by varying the value of w

over 5–10%. Fig. 10 shows the comparative detectionresults with the variation of w. A small variation of w

around the proposed value of 0.923 does not influencethe evolution of our algorithm.

The results used in building the FROC curves in Figs. 9and 10 are based on processing cropped samples of mam-mograms. To illustrate results on whole mammograms,we used a total number of 83 mammograms in SMF for-mat from the Oxford Screening Database. Fifty-nine ofthem contain between 1 and 5 clusters/image, adding thetotal number of clusters to 85, while 24 mammograms haveno sign of abnormality. The pooled opinions of cliniciansat the Oxford Breast Care Unit established the groundtruth. The breast margin is detected in SMF, thus a thresh-old above 0 removes the background. Now we can com-pute the value of k (see Section 2) for the inner area ofthe breast. The detection results are accurate and similarto those achieved on mammogram samples (see Fig. 11).The presence of CLS remains the main source of FP, ormore precisely their imperfect removal. A few isolated

Fig. 9. The comparative FROC curves for the detection of microcalcifications. s – represents the detection on SMF images; } – are the results withoutnoise removal by anisotropic diffusion; h – are the results without CLS removal; n – shows results on intensity images, when no SMF generation ispresent. All algorithms reach 100% TP fraction with a clear better performance on SMF images, which were de-noised and CLS-removed.

Fig. 10. The comparative FROC curve when w is varied over a range of 5–10% of its default value of 0.923. The difference in detection results is quitesmall and all four algorithms converge smoothly to 100% TP ratio.


calcifications were also depicted, but they were not labelledas microcalcification clusters. The method is more robustto detecting microcalcification in samples because the prob-ability of generating FP is increased when applied to thewhole image (i.e. the search space for microcalcificationdetection is larger).

The ultimate goal of any CAD algorithm is to performcorrectly on any given similar database, no matter where

it originates from. As is acknowledged by many authors,without image normalisation this is hard to achieve. TheSMF generation algorithm is designed to help in this diffi-cult situation, but excepting the Oxford database, no otherimage collections have mammograms in SMF format. Ourdetection algorithm, through its extraction of parametersfrom image attributes, facilitates the generalisation ofdetection standards.

Fig. 11. The comparative FROC curve of the detection of microcalcifications when mammogram samples are used versus full mammograms. Thebehaviour of the algorithm is similar and robust with the image size.


We used for comparison a collection of images from theUniversity of South Florida Digital Database for ScreeningMammography (DDSM). The new database consists of 82image samples, of which 58 show abnormalities in the formof microcalcification clusters and 24 are normal. The abnor-mal images contain between 1 and 4 clusters/image and thetotal number of annotated clusters is 82. All images areintensity images, as termed before, digitised at 43 lm/pixel.

Fig. 12. The comparative FROC curve between the detection results on intensitFlorida Digital Database for Screening Mammography. Note that the results

The major difference between these images and the onesfrom Oxford is the image resolution. To compensate forthis difference, we converted the values of r in the imageenhancement step and that of the kernel of fovea in thefoveal segmentation change accordingly. These conversionsare done automatically in agreement with the user specifiedimage resolution. The FROC curve shown in Fig. 12 com-pares the performance of the microcalcification detection

y images from the Oxford Screening Database and the University of Southare for mammogram samples without SMF normalisation.

Fig. 13. The FROC curves of the three microcalcification detection methods on SMF images; the Foveal approach yields the best results.


algorithm between the Oxford Screening Database inintensity form and the DDSM database on original images.The algorithm performs better on the Oxford Screening

Fig. 14. Two examples of microcalcification detection. On the left we presmicrocalcification clusters, on bottom an image with faint microcalcifications inmethod.

database, but the detection results on the two databasesconverge at about 0.5 FP/image and they both achieve100% TP fraction in the vicinity of 2 FP/image. The

ent the input images in SMF format: on top an image with two largevarying background, while on the right we note the results of our detection


DDSM database was chosen for its availability; no similar-ity between databases was considered and no additionaltuning of parameters performed. It remains desirable totest the detection algorithm on the DDSM database whenimages will be available in SMF form, as normalisationwould improve the flexibility of the results of the algorithmon other databases.

Finally, this section compares three algorithms to detectmicrocalcification clusters that operate upon the SMF rep-resentation of mammograms from the Oxford Database.The first has been described previously in this paper andis addressed as the ‘‘foveal algorithm’’; the second one isYam et al.’s physics based approach that was describedin Yam et al. (2001). The third is a variation of the statis-tical analysis introduced in Section 2, here addressed as the‘‘statistical approach’’, and is presented in Linguraru andBrady (2002). Using FROC analysis, we demonstrate thesuperiority of the foveal algorithm in Fig. 13. In Fig. 14we present examples of microcalcification detection.

5. Discussion and conclusion

We have presented a novel method for detecting micro-calcification clusters based on a biologically inspiredcontrast detection algorithm in combination with a pre-processing step (shot noise and CLS removal, imageenhancement), as well as an optional image normalisationstep. Many methods to detect microcalcifications attemptto tune the variety of parameters used in the implementationof the algorithm to best suit the studied cases. The consis-tency and reproducibility of results becomes highly depen-dant on the operators and their capability to find the bestparametrical configuration for the detection. We proposeda fully automated method to detect microcalcificationsand we reported results on both SMF and intensity images.

The first contribution of the presented work is the auto-matic tuning of the parameters of anisotropic diffusion.The contrast k is found from its direct relation to the imagegradient and the percentage of features that we desire toenhance. The second parameter r reflects the scale of fea-tures of interest and must be set according to their sizeand given the image resolution (multiscale analysis maybe performed). In our application, both r and k becomemeasures that related to the anatomy of breast. The lastparameter, the number of iterations t, is derived as a func-tion of r to remove noise in the context of preserving mic-rocalcifications. In a general application for featureenhancement, the automatic tuning of t may prove to bemore difficult than in our particular framework. With theautomatic tuning of parameters that we propose, aniso-tropic diffusion, a method with a solid theoretical basis,but controversial for its parametrical dependency, can beused as a robust process using little, but essential, aprioriknowledge.

However, the main contribution of the paper is themethod for adaptively thresholding the filtered results inorder to segment microcalcifications. Based on the biolog-

ically driven idea that human eye is a better feature detec-tor than a computer algorithm and that both local andglobal adaptability are necessary for subtle contrast detec-tion, our detection model mimics the human eye’s functionfor improved segmentation results. Therefore, the algo-rithm combines filters, analysis of image characteristicsand adaptive thresholding based on a human visual systemparadigm.

The robustness of the algorithm has been demonstratedby the FROC analysis performed over a range of parame-ters. It is important to note that the parameters are setaccording to the image attributes and the method is fullyautomated. The method converged in each case to 100%TP ratio. Similar results were obtained on intensity images,although for the lower scale of FP/image there is a moresignificant difference in results. We also compared the per-formance of our algorithm on data from different data-bases with good detection results. The results indicate thatadding adaptive contrast segmentation based on character-istics of the human visual system significantly enhances thedetection of microcalcifications.

Acknowledgements

This work was supported in part by a Scatcherd Euro-pean Scholarship from the University of Oxford and anOverseas Research Scholarship from the Committee ofVice-Chancellors and Principals of Universities of UnitedKingdom. The authors would like to thank Dr. DjamalBoukerroui from Compiegne University of Technologyfor his assistance.

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