Classification of Melanoma Using Tree Structured Wavelet Transforms 2003 Computer Methods and...

8/18/2019 Classification of Melanoma Using Tree Structured Wavelet Transforms 2003 Computer Methods and Programs in Bi…

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Classication of melanoma using tree structured wa velettransforms

Sachin V. Patwardhan a , Atam P. Dhawan a, *, Patricia A. Relue b

a Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Uni v ersity Heights, Newark, NJ 07102, USAb Department of Bioengineering, The Uni v ersity of Toledo, Toledo, OH 43606, USA

Recei ved 18 June 2002; recei ved in re vised form 19 November 2002; accepted 25 November 2002

Abstract

This paper presents a wa velet transform based tree structure model de veloped and e valuated for the classification of skin lesion images into melanoma and dysplastic ne vus. The tree structure model utilizes a semantic representation of the spatial-frequency information contained in the skin lesion images including textural information. Results show thatthe presented method is effecti ve in discriminating melanoma from dysplastic ne vus. The results are also compared withthose obtained using another method of de veloping tree structures utilizing the maximum channel energy criteria with a

fixed energy ratio threshold.# 2002 Else vier Science Ireland Ltd. All rights reserved.

Keywords: Melanoma; Dysplastic ne vus; Tree structured wa velet transform; Ne voscope

1. Introduction

The rising rate of skin cancer is a growingconcern worldwide [1]. Skin cancer is the mostcommon form of cancer in the human population[2]. Mass screening for melanoma and othercutaneous malignancies has been ad vocated forearly detection and effecti ve treatment [3]. Thoughthe gold standard for the diagnosis of skin cancerwould still be the biopsy examination, the lesionfor biopsy can be selected utilizing the computer-aided analysis for impro ving the sensiti vity andspecificity of skin cancer detection. Thus, the

development of a non-in vasive imaging and ana-lysis method could be beneficial in the earlydetection of cutaneous melanoma.

Malignant melanoma [4] is the most lethal skincancer in which melanocytes in the epidermisundergo malignant transformation. The twophases in the growth of melanoma are the super-ficial spreading phase, during which the lesionincreases in size within the epidermis, and thevertical growth phase when the cells begin to mo veinto the dermis [5]. The le vel of the spread of melanoma within the epidermis and then thedermis is determined as the Clark le vel, whichindicates the stage (i.e. the se verity) of the spreadof melanoma [6].

Dermatologists use the ABCD rule (Asymme-try, Border, Colors, and Dermoscopic structures)

* Corresponding author. Tel.: /1-973-596-3524; fax: /1-973-596-5680; http://www.njit.edu/ece/dhawan.

Computer Methods and Programs in Biomedicine 72 (2003) 223 /239

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0169-2607/03/$ - see front matter # 2002 Else vier Science Ireland Ltd. All rights reserved.doi:10.1016/S0169-2607(02)00147-5


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to characterize skin lesions [7 /10]. To calculate theABCD score, the criteria are assessed semi-quan-titati vely. Each of the criteria is then multiplied bya given weight factor to yield a total dermoscopyscore [11]. The ABCD rule works well with thinmelanocytic lesions. The sensiti vity of the ABCDrule is reported to be between 59 and 88% [12,13].

The features used in the ABCD rule suggest thatchanges in the surface characteristics of the ne vusoccur as it progresses towards melanoma. In theearly stages of melanoma the features used invisual examination are hardly visible and may leadto a false diagnosis. Howe ver, if images of skinlesions can be collected that contain spatial/

frequency and texture information, then a non-invasive method of lesion classification based onthese surface characteristics may be de veloped.

It is very difficult to gi ve the precise definition of texture that could be used in image analysis. Itshould describe local neighborhood properties of the gray le vels, but also include some intuiti veproperties like roughness, granularity and regular-ity. Texture is defined in [14] as the feature, whichdescribes spatial ordering of pixel intensities in aregion. According to Jain [15] the term texture

generally refers to repetition of basic textureelements called texels. Their placement can beperiodic, quasi-periodic or random. Texture can becharacterized using statistical properties of theregion in an image that has a set of local statistics,or other local properties that are constant, slowlyvarying or approximately periodic [16,17]. Amongthe different methods used for the analysis of spatial/frequency information and textural infor-mation, the Gaussian Marko v random field [18 /20] and Gibbs distribution texture models [21,22]characterize the gray le vels between nearest neigh-boring pixels by a certain stochastic relationship.The weakness in these methods is that they focuson the coupling between image pixels on a singlespatial scale and fail to characterize different scalesof texture effecti vely. Wa velet transform [23 /26],Gabor transforms [27 /30] and Wigner distribu-tion [27 /30] are good multi-resolution analyticaltools and help to o vercome this limitation. Treestructured wa velet decomposition determines im-portant frequency channels dynamically based onimage energy calculations within the different

frequency bands and can be viewed as an adapti vemulti-channel method [31]. The application of wavelet orthogonal representation to texture dis-crimination and fractal analysis has been discussedby Mallat [32]. Feature extraction for textureanalysis and segmentation using wa velet trans-forms has been applied by Chang and Kuo [31],Laine and Fan [33], Unser [34], and Porter andCanagarajah [35].

The tree structured wa velet transform decom-poses a signal into a set of frequency channels thatha ve narrower bandwidths in the lower frequencyregion. Decomposition of just the lower frequencyregion, as is performed in con ventional wa velet

transforms, may not be effecti ve for image classi-fication [27,36,37] . This is suitable for signalsconsisting primarily of smooth components withinformation concentrated in the low frequencyregions, but is not suitable for quasi-periodicsignals whose dominant frequency channels arelocated in the mid-frequency region. The mostsignificant spatial and frequency information thatcharacterizes an image often appears in the mid-frequency region. Thus, to analyze these types of signals wa velet packets are used [31]. In the

wavelet packet analysis the decomposition is nolonger applied to the low frequency channelsrecursi vely, but can be applied to the output of any channel.

Chang and Kuo [31] proposed a method for thedevelopment of wa velet transform based treestructure decomposition. In this method, a set of known images used during the learning phase isdecomposed using a two-dimensional wa velettransform to obtain the energy map and thedominant frequency channels. Decomposition of a channel is determined based on the ratio of theaverage energy of that channel to the highestaverage energy of a channel at the same le vel of decomposition. If the energy ratio exceeds a pre-determined threshold value, the channel is decom-posed. The dominant frequency channels are thenused as features for classification. Chang and Kuo[31] ha ve suggested that the filter selection dosenot ha ve much influence on the texture classifica-tion. On the other hand experiments preformed byUnser [34] imply that the choice of a filter bank inthe wa velet texture characterization could be an

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selecti vely decomposes them further. Each image isdecomposed into 4 sub-images at each le vel of decomposition. The mean energy, e, of a sub-image, or channel, f (m , n) was then calculated as

e1

MN X

M

m 1X

N

n 1

½ f (m ; n)½ (1)

where M and N are the pixel dimensions of theimage f (m , n) in the x and y directions, respec-

tively [31]. Further decomposition of the sub-image was determined by comparing the a verageenergy, e , of the sub-image with the largest a verageenergy value, emax , in the same decompositionlevel. Decomposition of the sub-image wasstopped if e /emax B /C , where C is a thresholdconstant; otherwise, the image was decomposedfurther into its 4 sub-images. The maximumnumber of decomposition le vels used was deter-mined by the resolution of the main image. Forour data set 4 le vels of decomposition were used.This method was implemented for threshold con-stant values ranging from 0.05 to 0.018. This rangeof the threshold constant resulted in selecti ve

decomposition from one to four of the first le velsub-images. For values below 0.018 all the chan-nels were decomposed and for values abo ve 0.05only channel 1 was decomposed further. For bothof these cases classification is not possible, asidentical tree structures would be obtained formelanoma and dysplastic ne vus images.

Once the tree structure was de veloped, theenergy in the lea ves of the tree defined the energyfunction in the spatial-frequency domain, or theenergy map. The energy map for a particular

image class was obtained by a veraging the energymaps o ver all the samples from the same class.This energy map was used in the texture analysisand classification of the unknown images, whereeach leaf of the tree corresponded to a feature.Each unknown image was decomposed to obtainits tree structure and energy map using the samedecomposition algorithm as used for the knownimages. The distance between the features of anunknown image and the corresponding features of the set of known images was used to classify thecandidate image to either the melanoma or dys-plastic lesion class. The Mahanalobis distance [42],D i , was used as the discrimination function forclassification of each unknown image. D i wascalculated for each unknown image as

D i XJ

j 1

(x j mij )2

cij (2)

where x j denotes the mean energy of the j thdominant channel for the unknown image, mij denotes the corresponding mean energy value of

Fig. 1. Epiluminesence images: (a) normal skin, (b) malignantmelanoma and (c) dysplastic ne vus. The images of melanomaand dysplastic ne vus are representati ve of those included in thedata set.



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the j th channel for the image class i , and c ij represents the variance of channel j for image classi . The first eight dominant frequency channelswere used in this analysis, so the value of J usedwas 8. For our data with only two-image classes,melanoma and dysplastic ne vus, the value of i waseither 1 or 2. An unknown image was assigned toimage class 1 if D 1 B /D 2; otherwise, the image wasassigned to image class 2.

2.4. Adapti v e wav elet-based tree structureclassication method

A new ADWAT method is presented here toaddress two major limitations of the tree structureclassification method described in Section 2.3 .First, additional features are selected so thatchannels are decomposed as a result of theirdiscrimination content and not solely on max-

Fig. 2. Two-dimensional wa velet decomposition of an image: (a) sample skin lesion image decomposed (b) the corresponding channeldesignation and (c) the corresponding tree structure. For the image illustrated here, channels 1,2 and 4 undergo second le veldecomposition and channels 1.2 and 4.1 undergo third le vel decomposition.

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imum energy. Porter and Canagarajah [35] pro-posed the ratio of the mean energy in the lowfrequency channels to the mean energy in themiddle-frequency channels as a criterion for opti-mal feature selection. These low to middle fre-quency ratios of channel energies emphasize thespatial/frequency differences in an image. Second,the threshold value used for selecting the decom-position channels is selected adapti vely based on astatistical analysis of the feature data. Thus,various ratios of channel energies or their combi-nation o ver a gi ven decomposition le vel are usedas additional features and a statistical analysis of the feature data is used to find the threshold values

that optimally partitions the image-feature spacefor classification. The ADWAT method for classi-fication is described below.

2.4.1. Feature setFeatures are computed so that channels are

decomposed as a result of their discriminationcontent and not only on maximum energy. Foreach le vel of decomposition, four sub-images arecreated and the a verage energy of each channel is

calculated according to Eq. (1) . In addition se veralenergy ratios are also calculated and used asfeatures as shown in Table 1 . The a verage energiesand energy ratios generate 11 features per channel,resulting in 11 features from the first le vel of decomposition, 44 features from the second le velof decomposition, and 176 features from the thirdlevel of decomposition.

2.4.2. Threshold selectionThe mean, variance and the histogram of the

feature values for each of the target classes areused to determine if a feature generated a unim-odal distribution or segregated into a bimodaldistribution between the image classes. The samplemode (most frequently occurring value) was usedas an estimator for the population mode. Thedescripti ve Statistics tool in Microsoft Excel wasused for this purpose. This analysis tool generateda report of uni variate statistics for the data in theinput range, pro viding information about thecentral tendency and variability of the data. Basedon the histogram of the data values, the number of

modes present in the data was estimated and themean and variance of the data was calculated.

During the learning phase the known set of melanoma and dysplastic ne vus images were used.For the classification of skin images, all imageswere decomposed up to 4 le vels using the db3wavelet. Thresholds for channel decompositionwere obtained by performing a statistical analysison the feature values deri ved from the a veragechannel energies.

All pooled feature values that generated unim-

odal distributions were rejected. Out of the total231 features, 214 features were rejected for thisreason. For all features that segregated intobimodal distributions between image classes,thresholds were calculated. If more than onefeature within a particular channel were distrib-uted bimodally, then the feature that generatedlinearly separable pure clusters for the two classes

Table 1Feature calculations at each le vel of decomposition illustrated with decomposition of channel 1

Features

Sub-image or channel A verage energy a Maximum energy ratio b Fractional energy ratio

1.1 e1.1 e1.1 /emax e1.1 /(e1.2 /e1.3 /e1.4)1.2 e1.2 e1.2 /emax e1.2 /(e1.1 /e1.3 /e1.4)1.3 e1.3 e1.3 /emax e1.3 /(e1.1 /e1.2 /e1.4)1.4 e1.4 e1.4 /emax e1.4 /(e1.1 /e1.2 /e1.3)

At each le vel of decomposition, the a verage energy of each sub-image is calculated with the corresponding energy ratios. Thesefeatures are used in a statistical analysis to select the optimal feature set for image classification.

a Of the four a verage energies calculated, the greatest is designated emax .b Since emax is the maximum a verage energy (either e1.1 , e1.2 , e1.3 , or e1.4 ) only three of the ratios to maximum energy are used as

features; the fourth ratio is always 1.



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was used in the analysis. For all such features,energy ratio thresholds were calculated by a ver-aging the highest value from the lowest valuedclass with the lowest value from the highest valuedclass. According to the minimum distance classi-fier, taking the a verage value of the means of thetwo classes as a threshold would be optimum inthe Bayes sense [43]. This requires that the distancebetween the means is large compared to the spreador randomness of each class with respect to itsmean. Since this is not true for any of the linearlyseparable features, a verage of the separationbetween the two classes was used as a threshold.For all the remaining channels ha ving features

with bimodal distribution that did not producelinearly separable pure clusters, the feature withgreater separation of the two class means com-pared to the variance of the two classes was used inthe analysis. All such features were assumed tofollow a Gaussian distribution with each of thetwo texture classes ha ving the same probability of occurrence equal to 0.5. The optimal energy ratiothreshold for these features with the minimalclassification error was calculated as the a verageof the means of the two Gaussian distributions

[43]. 2.4.3. De v elopment of tree structure signatures

Based on the thresholds selected abo ve, theimage decomposition algorithm was de veloped toobtain the tree structure for each of the imageclasses. Decomposition was stopped for a channelif all of its features for the two classes followedunimodal distributions. Each channel that had atleast one feature that was bimodally distributedwas decomposed further if its feature value satis-fied the corresponding energy ratio threshold.Since the thresholds were selected to optimallypartition the two image classes, one of the twoimage classes was preferentially decomposed. Inthis analysis, many more dysplastic ne vus imageswere a vailable than melanoma images. Thus, thedysplastic ne vus class was used as the referencegroup and the thresholds were set such that imagesof this type were not decomposed. The treestructures that resulted from this decompositionform the signatures of the melanoma and dysplas-tic ne vus image classes.

2.4.4. Classication phaseDuring the classification phase the tree structure

of the candidate image obtained using the samedecomposition algorithm described pre viously wassemantically compared with the tree structuresignatures of melanoma and dysplastic ne vus. Aclassification variable (CV), is used to rate the treestructure of the candidate image. CV is set to avalue of 1 when the main image is decomposed.The value of CV is incremented by one for eachadditional channel decomposition. When the algo-rithm decomposes a dysplastic ne vus image, onlyone le vel of decomposition should occur (channel0). Thus, for values of CV equal to 1, a candidate

image was assigned to the dysplastic ne vus class. Avalue of CV greater than 1 indicates furtherdecomposition of the candidate image, and theimage was accordingly assigned to the melanomaclass.

3. Results

The diagnostic accuracy of a test is measured bythe sensiti vity and specificity of correct classifica-

tion [44]. For the classification of skin lesions inthis study, the sensiti vity, or true positi ve fraction(TPF), indicates the fraction of melanoma lesionscorrectly classified as melanoma. The specificity,or true negati ve fraction (TNF), indicates thefraction of dysplastic or non-melanoma lesionscorrectly classified as non-melanoma. The rela-tionship between sensiti vity and specificity calcu-lated for all possible threshold values of thediscriminant function, or for this case the thresh-old constant, is represented graphically as theRecei ver operating characteristic (ROC). Thevertical axis of the graph represents the sensiti vityor TPF, while the horizontal axis represents thefalse positi ve fraction (FPF), which is 1-TNF [44].Results obtained from the ADWAT classificationmethod are presented and are then compared withthose obtained using the method proposed byChang and Kuo [31].

In the ADWAT Classification Method, 11features were considered for each decomposedchannel for the tree structure de velopment. Fromthese features, threshold values were calculated for



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those features that segregated into bimodal dis-tributions between lesion classes. If more than onefeature within a particular channel segregatedbetween lesion classes, then the feature for whichthe separation between the mean values of the twoclasses was maximum compared to the variance of each class was used in the analysis. The feature setand threshold values used in the de velopment of the tree structure are summarized in Table 2 . Forchannels 1 and 4, all features generated unimodaldistributions and were not decomposed further orused for classification.

Feature data values used to generate the thresh-old values gi ven in Table 2 are illustrated in Fig. 3 .Channels 2 and 3 had bimodal feature segregation,but the clusters were not linearly separable.Thresholds were obtained for these channels byaveraging the means of the features for the twolesion classes. This method of threshold selection isillustrated for channels 2 and 3 in Fig. 3 a /b. Forchannels 2.1, 3.1, and 2.1.4, the feature databetween the melanoma and dysplastic ne vusclasses segregated into linearly separable classes.These data are illustrated in Fig. 3 c /e. Thresholdsfor these data were selected by a veraging the

highest value from the lower valued class withthe lowest value from the higher valued class.

No features from channel 1 or channel 4 andany of their sub-images segregated into bimodaldistributions between the image classes. Sincethese features contained no discrimination value,further decomposition of these channels wasstopped. For classification of candidate images,decomposition of each channel was determinedbased on the value of a specific feature and thefeature threshold value gi ven in Table 2 .

The resulting tree structure signatures of mela-noma and dysplastic ne vus are shown in Fig. 4 .Note that for melanoma, only channels 0, 2, 3, 2.1,3.1 and 2.1.4 are decomposed. The decompositionof all the other channels was stopped since thesefeatures produced unimodal distributions betweenthe lesion classes. Also note that due to theselection of the thresholds, the algorithm doesnot decompose dysplastic ne vus images beyondthe first le vel. A dysplastic ne vus will thus generatea tree structure with only one le vel of decomposi-tion as shown in Fig. 4 b.

The results of the classification of the test datausing ADWAT method are summarized in Table3. For the 10 images of melanoma used during theclassification phase, the algorithm was able tocorrectly classify 9 images to the melanoma ne vusclass. Histological e valuation confirmed that all of these lesions were melanoma. For the 20 images of dysplastic ne vus, 18 were correctly classified to thedysplastic ne vus class while 2 images were incor-rectly classified to the melanoma ne vus class. Theresulting TPF obtained for this classifier was 90%with a FPF of 10%.

The results from the Chang and Kuo [31]

classification method are summarized in Table 4 .The number of melanoma and dysplastic ne vuscorrectly classified and the resulting TPF and FPFare gi ven. The resulting ROC cur ve obtained forthe tree structure wa velet transform analysismethod is shown in Fig. 5 . This tree structuremethod gi ves a maximum true positi ve value of 70% and a false positi ve value of 20% for athreshold constant value of 0.026.

The different threshold constant values selecteddictated the number of channels that were decom-

Table 2Features obtained for the ADWAT classication method

Channel Energy feature Distribution type separable/bimodal Threshold for decomposition

2 e2/e1 Bimodal /0.03663 e3/e1 Bimodal /0.0432.1 e2.1 /(e2.2 /e2.3 /e2.4 ) Linearly separable /0.343.1 e3.1 /(e3.2 /e3.3 /e3.4 ) Linearly separable /0.3152.1.4 e2.1.4 /e2.1.1 Linearly separable B /0.837

Selected features obtained from a statistical analysis were either linearly separable or segregated bimodally between classes. Thechannel, corresponding energy feature ratio, and the threshold values obtained for maximum separation of the two classes are gi ven.



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posed. For high values of the threshold constantonly the channel 1 energy ratio was high enough tomeet the energy ratio criteria for decomposition.Howe ver, as the threshold constant value wasdecreased, other channel energy ratios satisfiedthe threshold and were decomposed. Increasingthe number of decomposed channels does notnecessarily add useful information to the discrimi-nation, as the dominant energy channels may

remain the same. As shown in Fig. 5 , the ROCcur ve shows a peak in sensiti vity for an inter-mediate value of the threshold constant andnumber of channels decomposed. This methodwith a constant threshold value has both a smallersensiti vity and a smaller specificity than theADWAT method presented in the pre vious sec-tion. Thus, by adapti vely selecting the thresholdbased on the discrimination content of the data, abetter classification can be achie ved with the samedata.

4. Discussion

In this section, the ad vantage of adapti velyselecting the threshold values for image decom-position is discussed in relation to the energydistribution and the information within the chan-nels. Result analysis and interpretation are alsopresented followed by pointing out the potentialapplications of the ADWAT method.

4.1. Threshold selection

For the epiluminesence images used in thisstudy, the energy is non-uniformly distributedamong the channels. At the first le vel of decom-position, the image total energy is distributed withabout 82 /87% in channel 1, 3 /4% in channel 2, 4 /5% in channel 3 and 4 /11% in channel 4. Theenergy in channel 1, the low /low frequencychannel, primarily corresponds to the skin sur-

Fig. 3. Feature data values for dysplastic and melanoma training data. Scatter plots and thresholds are shown for features selected forchannels: (a) 2, (b) 3, (c) 2.1, (d) 3.1 and (e) 2.1.4. Threshold values used to separate classes are shown as a dotted vertical line in (a) /(b)and as dotted horizontal lines in (c) /(e).



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rounding the lesion and is of no significance in thelesion classification. Channels 2 and channel 3, themid-frequency channels, correspond to the ne vus-skin boundary and some portions of the ne vusitself. These two channels are importantfrom the classification point of view as theycontain most of the information that would allowdiscrimination between lesions according to theABCD rule. The energy in channel 4, the high /high frequency channel, corresponds to portionsof the lesion boundary where the boundary iswell defined and also to regions of une ven reflec-tion from the surface due to air gaps and skinlayering.

In the method proposed by Chang and Kuo[31], a threshold value is selected and the ratio of channel energy to maximum channel energy withina decomposition le vel is calculated. The decom-position of channels 2 and 3, which contain mostof the rele vant discrimination information, isdependent on the value of the threshold constant.Selecting a threshold constant value higher than

the a verage e2/e1 or e3/e1 energy ratio for a lesionclass will thus result in a loss of this information.For the test images, an e3/e1 ratio of 0.043 and ane2/e1 ratio of 0.0366 optimally segregate themelanoma and dysplastic ne vus classes. For athreshold value greater than this e3/e1 ratio value,the tree structure de veloped for many candidatemelanoma images results in decomposition of onlythe low /low frequency channel. This method willthus produce identical tree structure and energymaps for the melanoma and dysplastic imageclasses, resulting in nearly all the images fromthe data set being classified as dysplastic. Forvalues of the threshold constant below 0.043, thetree structure and the energy maps are highlydependent on the value of the threshold constant.Hence, rather then randomly selecting a thresholdvalue without any criterion, this classificationcould be impro ved by using an adapti ve methodfor selecting the threshold value.

Obtaining the threshold values from a statisticalanalysis of the channel energies and their ratios

Fig. 3 ( Continued )



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pro vides the required adapti vity to the tree struc-ture de velopment. Statistical selection of thethresholds at each le vel of decomposition makesthe ADWAT method more robust and a goodcandidate method for surface characterization andtexture representation. It should be noted thatsince the thresholds were obtained from bimodaldistributions, re versing the inequalities on thethresholds would re verse the tree structure signa-tures de veloped for the two classes. The dysplasticnevus was a logical choice as a basis for classifica-tion instead of the melanoma since moredysplastic ne vus data was a vailable. The numberof images used during the learning phase is thesame for both the classes, although the number of dysplastic ne vus images used in the classificationphase is more. Also the natural population of dysplastic ne vus class is very large compared tomelanoma, hence we do not see any risk of obtaining bias.

4.2. Analysis of results

In the ADWAT method, it is necessary foreither channel 2 or channel 3 to be decomposed inorder to generate a value of CV /1 and to classifya lesion as melanoma. A summary of the decom-position of the test images is gi ven in Table 4 . Of the 9 images classified as melanoma, 8 imagesdeveloped the complete tree structure signature of melanoma with the value of CV equal to 6. Theremaining image correctly classified as melanomaproduced a value of CV equal to 5, failing todecompose channel 3.1. The melanoma image thatwas misclassified as non-melanoma is shown inFig. 6 . This lesion is a late stage melanoma thatwas easily diagnosed by the physician. As can beseen in the image, a significant amount of reflec-tion is contained in the image as a result of flakingskin on the lesion and skin surface. As a result,more energy was distributed in channel 4, while




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the energy in channels 2 and 3 decreased below thethreshold values needed for decomposition. Thealgorithm failed in this case due to this change inthe energy distribution. The imaging artifactresulting from non-uniform reflection can beminimized by use of a polarizing filter or byapplying a lotion to the skin prior to imaging tominimize refracti ve index mismatch.

The two images of dysplastic ne vi that wereincorrectly classified as melanoma were decom-posed beyond the first le vel. For both of theseimages, channel 2 was decomposed one le vel.These images produced a value of CV equal to 2and were thus classified as melanoma. The treestructure de veloped for these two images is differ-ent from the tree structure signature of melanomasince channels 2.1, 2.1.4, 3, and 3.1 were notdecomposed. This misclassification can be inter-preted in two primary ways. One le vel of decom-position beyond the main le vel is a result of theclosely valued features between the melanoma anddysplastic in channel 2. As a result, it may be

worthwhile to reconsider the definition of the CVor to increase the CV to a value greater than 1 todelineate the melanoma and dysplastic ne vus classboundary. An alternate interpretation of the mis-classification of these dysplastic ne vi may be thatthese two ne vi are in the early stages of malignanttransformation, but are not showing any visiblefeatures to be identified as melanoma by aphysician. Since none of the lesions visuallydiagnosed as dysplastic ne vus were biopsied, thesetwo lesions could potentially be at the very earlystage of melanoma. This possibility deser vesfurther consideration as it may show that theADWAT method is more sensiti ve than theABCD rule in making diagnosis of early mela-noma. Further in vestigation and patient follow-upis needed before this hypothesis can be confirmedor dispro ved.

The ADWAT classification method requiresapproximately 15 /20 s for image decomposition,computing the feature values and making adecision about the image class of the unknown.




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Fig. 4. Tree structure signatures for: (a) melanoma and (b) dysplastic ne vus. Based on the threshold values gi ven in Table 3 , severalchannels are decomposed beyond the rst le vel because of the selection of the threshold values.



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The method suggested by Chang and Kuo [31]

requires more time due to the distance calculationsinvolved in the classification phase.The same set of features used during the training

phase of the ADWAT classification method wereused to train a 3 layer feed forward neural networkwith backpropagation training algorithm [45,46].The backpropagation training algorithm is aniterati ve gradient algorithm designed to minimizethe mean square error between the actual outputsof a multiplayer feed forward perceptron percep-tion and the desired output. Various configura-tions with an input layer, two hidden layers andone output layer were tested. The best results wereobtained with 10 neurons in the first hidden layerand 6 neurons in the second hidden layer. Theoutput layer had 1 neuron. The two hidden layershad a nonlinear log-sigmoid transfer functionwhile the output layer had a linear transfer

function. It required 957 cycles of iterations

through the training set for the error to go below0.00001. The feature set used in the classificationphase of the ADWAT classification method wasthen presented to this trained network. It pro-duced a TPF of 90% with a FPF of 25%.

The sensiti vity of the ADWAT classificationmethod is better then the sensiti vity of the ABCDrule [12,13]. The TPF and FPF values are muchimpro ved as compared to the method suggested byChang and Kuo [31]. Compared to the neuralnetwork backpropagation method [45,46], theADWAT classification method has better specifi-city. Also the physicians find more information inthe epiluminesence images obtained using theNe voscope [40,41] than normal visual examina-tion. But still we think more data need to beanalyzed before the ADWAT classificationmethod can be used in a clinical setting.

Table 3Summary of the test data classied using the ADWAT method

Lesion type Number classified CV Classification Channel decomposition errorMelanoma 8 6 Melanoma /Melanoma 1 5 Melanoma No decomposition of 3.1Melanoma 1 1 Dysplastic No decomposition of 2, 3Dysplastic 18 1 Dysplastic /Dysplastic 2 2 Melanoma Decomposition of 2

Note that lesions with a value of the CV greater than 1 are classified as melanoma; those with CV equal to 1 are classified asdysplastic ne vus. The resulting TPF is 90% with a FPF of 10%.

Table 4Classication of melanoma and dysplastic ne vus by the method of Chang and Kuo [31]

Threshold constant Melanoma correctly identified, TP ( n /10) Dysplastic ne vus correctly identified, TN ( n /20) TPF FPF0.018 6 20 60 00.022 6 18 60 100.026 7 16 70 200.030 5 15 50 250.034 5 14 50 300.038 4 13 40 350.042 3 13 30 350.046 3 12 30 400.050 1 10 10 50

The results obtained from the tree structure wa velet transform analysis method are gi ven for a range of threshold constant values.The highest correct classification of melanoma occurs for a threshold constant of 0.026.



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4.3. Potential application

The ADWAT classification method is especiallyeffecti ve and fast as compared to that of Changand Kuo [31] when images with different surfacecharacteristics but similar dominant frequencychannels are to be classified. Instead of measuringthe distance between features and iterati vely add-

ing new features into the classification process, theimages can be classified by using a semanticcomparison of the tree structure signatures, mak-ing the classification process simpler. Although theADWAT method has been illustrated here withtwo image classes, it can be adapted easily toaccommodate more classes. Instead of using asingle threshold, multiple thresholds and treestructures will be obtained, depending upon thenumber of classes. Howe ver, the learning phase,especially the procedure for obtaining the thresh-

Fig. 5. ROC cur ve for the tree structure wa velet transform classication based on the method of Chang and Kuo [31]. The maximumsensiti vity of 70% correct diagnosis of melanoma occurs with a false diagnosis of melanoma of 20%. Each data point represents a

different value of the threshold constant.

Fig. 6. Melanoma image misclassied as a dysplastic ne vus.Note the light areas in the upper right quadrant of the imagethat represent reection from aking skin.



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old values may become tedious with an increase inthe number of classes.

5. Conclusions

Results of this work show that the ADWATmethod using the mean energy ratios with statis-tically selected threshold values is effecti ve andsimple for classification of the images based ontheir spatial and frequency information. The treestructure model de veloped by using this method ismore robust than the one employing a fixedthreshold of the maximum energy ratio. This

work also shows that the epiluminesence imagesof the skin lesions obtained using the Ne voscopeare promising in the early diagnosis of melanoma.

Acknowledgements

The authors would like to thank all the patientswhose data was used in this study. We would alsolike to thank The Medical College of Ohio, Toledoand Dr Prabir Chaudhari for his contribution in

the data collection. We would also like to thankthe Whitaker Foundation for pro viding partialfunding for this research under the WhitakerFoundation Research Grant RG-99-0127.

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