Pixel-Based Texture Classification of Tissues in Computed Tomography

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1 Pxel-Based Texture Classfaton of Tssues n Computed Tomography Ruhaneewan Susomboon, Danela Stan Rau, Jaob Furst Intellgent ultmeda Proessng Laboratory Shool of Computer Sene, Teleommunatons, and Informaton Systems DePaul Unversty, Chago, Illnos, rsusombo@students.depaul.edu, {drau, furst}@s.depaul.edu Abstrat Prevous researh has been done to lassfy dfferent tssues/organs of nterest present n medal mages, n partular n Computed Tomography (CT) mages. ost of the researh used the anatomal struture present n the mages n order to lassfy the tssues. In ths paper, nstead of usng the anatomal struture, we propose a pxel-based texture approah for the representaton and lassfaton of the regons of nterest. The approah norporates varous texture features and deson trees to aomplsh tssue lassfaton n normal Computed Tomography (CT) mages of the hest and abdomen. Frst, we ntrodue a new dreton vs. dsplaement pars (DDP) approah to alulate a o-ourrene matrx for apturng all possble ombnaton between dretons and dsplaements neessary n alulatng the texture features at the pxel-level. Seond, we evaluate varous dfferent neghborhood szes for the pxel-based texture representaton n order to fnd the optmal wndow sze for dfferentatng among 8 organs/tssues of nterest: aorta, fat, kdney, lver, lung, musle, spleen, and trabeular bone. For all organs/tssues (exept for aorta), the optmal wndow was 13-by-13 allowng the lassfaton senstvty metr to be at least 96% for all organs/tssues. For aorta, the optmal wndow sze was 9-by-9 wth the lassfaton senstvty beng 81%. 1 Introduton Automat analyss of mages from varous medal magng modaltes s n hgh demand n order to nrease the produtvty of radologsts when nterpretng and dagnosng hundreds of mages every day. In medal magng researh, texture nformaton plays an mportant role for several reasons. Frst, the organ shapes are dfferent aross dfferent sldes due to the generated sequenes of two-dmenson (D) mages from three-dmenson (3D) struture. Sne sequenes of D mages represent a ross seton of human body, the shape of an organ throughout the entre slde of 3D s not onsstent. oreover, some organs an have dfferent szes from one patent to another. Therefore, the shape-based dsrmnaton tehnques [7, 8] may not be approprate to dentfy the organs. To avod these lmtatons, low-level features based on the gray-level nformaton present n the mage are used to apture the ontent of the medal mages. However, the gray -levels alone are not suffent as many soft tssues have overlappng gray level ranges [10]. Therefore, low-level features based on texture nformaton, that s

2 expeted to be homogenous and onsstent aross multple sldes for the same organ, are mostly used to perform automat mage analyss n the medal magng feld. The goal of the approah presented n ths paper s to aheve automat lassfaton of tssues of nterest n normal CT mages of the hest and of the abdomen. Our approah, dreton vs. dsplaement pars (DDP), s based on texture features alulated at the pxellevel nstead of a global-level as t has been done before n the texture analyss lterature: for eah pxel, we alulate a o-ourrene matrx for apturng all possble ombnatons between dretons and dsplaements wthn a small neghborhood entered on that pxel. The optmal neghborhood sze s determned by the wndow sze produng the best pxel-lassfaton auray of the regons of nterest. To lassfy the regons, 1) a Classfaton and Regresson (C &RT) deson tree s used to produe the pxel-level lassfaton and then ) a maorty vote sheme s appled to label eah of the regons of nterest based on the maorty of pxel labels wthn the orrespondng regon. The beauty of the proposed approah onssts n ts applablty to 1) perform automat segmentaton of regons of nterest by usng the lassfaton rules derved at the pxel-level; ) buld ontext-senstve reportng tools (for nstane, apply a omputer-aded dagnoss tool for lver only f the regon of nterest s a lver); and 3) develop eduatonal software for medne. Bakground Researh n the feld of mage lassfaton usng texture nformaton s mostly lmted to spef pathologes and a sngle organ tssue. In [11], Karkans et al. appled a multlayer feedforward neural network based on texture features to lassfy aner regons n olonosop mages. Baeg and Kehtarnavaz [13] proposed a three-layer bak-propagaton neural network based on two mage texture features to lassfy abnormaltes n dgtzed mammograms. Wroblewska et al. [15] proposed an automat feature seleton algorthm and multlayer feedforward bak-propagaton neural network to detet and lassfy of mro-alfatons n dgtal mammograms. Zaane et al. [14] proposed an automat lassfaton of bengn and malgn tumors n mammography mages based on an assoaton rule mnng approah. There s also some work done wth respet to the dentfaton of several organs at the abdomen level. In [9], a Hopfeld neural network was appled to perform organ dentfaton based on Haralk texture features appled at the pxel level. The advantage of ths tehnque s that t does not requre a pror knowledge. However, the tehnque gves poor results n dentfyng lver, spleen and musle beause of a blok-wse ontour effet from alulatng the texture features at the blok-level. Lee at al. [1] proposed a mult-module ontextual neural network and fuzzy rules to overome the dffultes n Koss s tehnque. The mult-module ontextual neural network segments mages by lassfyng the pxels nto dsont regon based on the gray-level and ontextual nformaton of neghborng pxels. Then, the fuzzy rule s appled to the regon features, nludng relatve loaton, relatve dstane, tssue-ntensty, area, ompatness, and elongatedness, n order to gve the fnal segmented organs. Furthermore, the texture feature analyss has been performed ether at the global-level (organ/tssue) or loal-level (small regon wthn the tssue/organ of nterest) rather than at the pxel-level. The DDP approah proposed n the paper wll extrat all possble texture haratersts wth respet to dreton and dsplaement nstead of onsderng all pxel par wthn a small neghborhood entered on the orrespondng pxel; furthermore, a deson tree s employed to do a pxel-based lassfaton. Sne ths proess s done at the pxel-level, the

3 lmtatons of the prevous approahes n dealng wth nonsstent organ shapes and postons, and overlappng gray-levels wll be overome by the proposed approah. The rest of ths paper s organzed as follows. The methodology of the approah for organ lassfaton s dsussed n Seton 3 and the evaluaton of the approah s desrbed n Seton 4. The prelmnary expermental results are presented n Seton 5; fnally, onlusons and future work are dsussed n Seton 6. 3 ethodology Our approah to pure path tssue lassfaton onssts of three stages: 1) pre-proessng; ) pxel-level texture extraton; and 3) lassfaton. Fgure 1 llustrates the overvew of our proposed system. Frst, the pre-proessng stage strengthens the ontrast n the mage and redues the nose n the data. Seond, the pxel-level texture stage extrats the haratersts of the texture at the loal level. Fnally, a supervsed learnng tehnque s utlzed n order to lassfy eah pxel, and further eah tssue of nterest. CT Images Pre-Proessng: Clpped Bnnng Enhane Image eghborhood of a pxel Pxel-Level Texture Extraton: Haralk Classfaton: Deson Tree (Pxel Level) Classfed Annotated mages 3.1 Pre-proessng: Gray-level reduton usng lpped Sne most of the soft tssues have overlappng gray-levels and the ontrast among the tssues s very low wthn the CT mages, espeally gven the large range of gray-levels n DICO (Dgtal Imagng and Communatons n edne) format of 4096 gray-levels for a 1 bt resoluton, an mage enhanement pre-proessng tehnque s needed to nrease the gray-level ontrast among the tssues. We apply a lpped bnnng tehnque [1] to enhane the ontrast wthn the soft tssues neessary for good texture feature extraton. The lpped bnnng tehnque norporates 1) a K- means algorthm that automatally determnes the range of the gray levels for the soft tssues n the gven CT mages; ) the gray-levels that are lower than the soft tssue range and the graylevels that are hgher than the soft tssue range wll be assgned to the mnmum bn and maxmum bn, respetvely; the gray values wthn the soft tssue range wll be lnearly dvded nto equal bns. 3. Pxel-level texture extraton Fgure 1: Dagram of the proposed system. Pxel-level texture extraton wll be used to dsover the texture of eah pxel wthn a small neghborhood. These overlappng regons allow a ertan ambguty to be norporated n the texture property for mprovng organ/tssue lassfaton. In order to apture the spatal dstrbuton of the gray-levels wthn the neghborhood, a two-dmensonal o-ourrene matrx

4 [3] s appled to alulate the loal texture nformaton around that pxel. Whle Kalnn et al. [4] and Koss et al. [9] alulated the loal texture based on an all-pars (AP) approah, whh onsders all the pxel pars wthn the neghborhood, we propose a new dreton vs. dsplaement pars (DDP) approah, whh onsders every dreton and dsplaement separately around the pxel of nterest. In ths way, the heker board problem ntrodued by the AP approah (two textures havng dfferent patterns wll have the same o-ourrene matrx f they have same values for the gray-levels) wll be overome by the proposed DDP approah. The DDP s based on the estmaton of ont ondtonal probablty of pxel par ourrenes P ( d, θ ). The P denotes the normalzed o-ourrene matrx by total number of the ourrene of two neghborng pxels between gray-ntensty at vertal dreton (row) and another gray-level at horzontal dreton (olumn) of spefy by dsplaement vetor d and angleθ. There are four dfferent dretons nludng 0, 45, 90, and 135 are generally used n mage proessng as n Fgure and (n-1) s a number of dsplaement vetor n n-by-n wndow sze, where n denotes resoluton vetor n row and olumn Fgure : From the entered pxel; pxel 1 represents 0 at d=1; pxel represents 45 ; pxel 3 represents 90 and pxel 4 represents 135 at d= Orgnal Image Co-Ourrene Fgure 3: Co-ourrene matrx for dstane 1, dreton 0 In terms of omputatonal tme, the DDP approah s Ο( n ) sne the number of pxel omparsons of DDP s gven by formula (1), where n denotes the sze of the wndow: n n n + (1) = 1 = 1 Furthermore, for omputatonal effeny purposes, the o-ourrene matrx mplementaton represents only the gray-levels that appear wthn the pxel neghborhood under onsderaton. One the o-ourrene matrx s alulated around eah pxel, ten Haralk texture desrptors [] measurng dfferent propertes of the texture are obtaned; 1) Entropy to measure the randomness of gray-level dstrbuton; ) Energy to measure the ourrene of repeated pars wthn an mage; 3) Contrast to apture the loal ontrast n an mage; 4) Homogenety to measure the homogenety of the mage; 5) Sum Average to provde the mean of the gray ntensty wthn an mage; 6) Varane to estmate the varaton of gray level dstrbuton; 7) Correlaton to measure a orrelaton of pxel pars on gray-levels; 8) axmum probablty to represent the most predomnant pxel par n an mage, 9) Inverse Dfferene oment (ID) to measure the smoothness of an mage and 10) Cluster Tendeny to measure the groupng of pxels that have smlar gray-level values. The alulaton of Haralk features are shown n Appendx. At the end of ths stage, eah pxel wll be haraterzed along eah dstane and dsplaement by a 10-dmensonal vetor: [ d,, d ]

5 3.3 Classfaton The lassfaton stage onssts of stages: pxel-based texture lassfaton and pure path lassfaton Pxel-based texture lassfaton. There are many types of lassfers that ould be used to dfferentate among the organs/tssues n pxel-based spae. Deson trees have a relatvely fast learnng speed ompared wth other lassfaton tehnques and also have the ablty to elmnate the rrelevant attrbutes from the set of features. Furthermore, the deson trees do not make any assumptons about the dstrbuton of the data and ths property makes them approprate to be used when the dstrbuton of the data s unknown. In our approah, a Classfaton and Regresson Tree (C&RT) lassfer s appled to dsrmnate the pxel-based pattern among dfferent tssues [16]. C&RT mplements the lassfaton proess based on splttng the urrent node nto two hld nodes based on the predtors values whh are the texture desrptors n our ase. The best predtor s hosen usng the Gn mpurty ndex suh that eah hld node s more pure than ts parent node [16]. The goal s to produe subsets, leaf nodes, whh are as homogeneous as possble wth respet to the lass label. In order to not overft the data, there are several stoppng rtera used for the tree growth [5]: axmum tree depth: d nmum number of ases for the parent node (nternal node): n p nmum number of ases for hld nodes (left/ termnal node): n nmum hange n mpurty: mp Dependng on these parameter values (d, np, n, mp), a dfferent tree wll be produed. The optmal tree wll be the tree whose parameters produe the hghest lassfaton auray at the pxel level on the testng data. One the optmal deson tree s developed, ts deson rules wll be used to lassfy eah pxel wthn the tssue regon of nterest Tssue lassfaton. The lassfaton of a tssue regon nvolves a maorty sheme n whh eah pxel from the regon s lassfed usng the rules derved from the C&RT. The most frequent label wthn the orrespondng regon wll beome the lassfaton label of that path. Therefore, the tssue lassfaton s the representaton of the maorty of predted tssues at the pxel level. Sne a set of rules s appled to eah pxel wthn the regon, the tssue lassfaton s ndependent of the tssue regons szes, so regons of dfferent szes an be automatally lassfed by our proposed approah. Ths advantage wll allow us to use the tehnque for mage segmentaton n regons havng not neessary equal szes as t s the ase for multple organs/tssues segmentaton n CT mages. 4 Evaluaton model The evaluaton of our approah s performed wth respet to eght dfferent pure tssue pathes nludng aorta, fat, kdneys, lver, lung, musle, spleen, and trabeular bone. The segmented pure tssues have been manually generated by a lnal expert. The proposed results wll be ompared aganst the lnal expert s manual path labels; n order to assess the auray of the approah, eah tssue wll be evaluated separately.

6 Two lassfaton metrs are used to measure the lassfaton performane: TP senstvty = () TP + F T spefty = (3) T + FP n whh TP denote true postves, FP denote false postves, T denotes true negatves, and F denote false negatves. True postve s a number of the pathes that belong to that organ that are orretly lassfed as that organ. False postve s a number of pathes that belong to that organ that are norretly lassfed as that organ. True negatve s a number of pathes that belong to other organs that are orretly lassfed as other organs. False negatve s a number of the pathes that belong to that organ that are norretly lassfed as other organs. 5 Expermental results 5.1 Data In ths study, 440 pure pathes (55 pathes per organ/tssue) from multple, seral, axal normal CT mages derved from helal, mult-detetor CT aqustons of 5 patents were manually segmented and annotated by an expert radologst. The mages were n DICO format, sze of 51 by 51 wth 1 bt resoluton. The segmented tssues have been manually annotated n one of the followng ategores: aorta, fat, kdneys, lver, lung, musle, spleen, and trabeular bone; some examples of pure pathes are shown n Fgure 4. Kdney Lver Orgnal Clpped Orgna Clpped Spleen Trabeular bone Orgnal Clpped Orgna Clpped Fgure 4: Result of pure pathes ontrast enhanement usng lpped bnnng wth 56 bns. 5. Pre-proessng We found that the soft tssues n DICO format (wth 4096 gray levels) are nearly always plaed nto an approxmately gray-level range between 856 and Therefore, the lpped bnnng approah alloates all gray ntensty wthn a lower bound (0-855) to a sngle lowest bn and alloates a sngle maxmum bn to an upper bound ( ). The rest of the gray levels are equally dvded nto equal szed bns; by varyng the number of gray levels, we found that 56 equal-szed bns s an optmum number for ontrast enhanement of soft tssues n CT mages [1].

7 5.3 Texture features We assess the o-ourrene matrx alulaton for both the AP and DDP approahes: AP alulates the o-ourrene by onsderng all the pxel pars wthn the neghborhood; DDP s an ntegraton of every possble o-ourrene whh onsders dreton and dsplaement separately. For the DDP approah, we onsder four dfferent dretons of 0, 45, 90, and 135 ; n terms of dsplaement, sne DDP approah onsders every dreton and dsplaement separately, the values of the dsplaement wll vary aordngly to the pxel wndow sze. For example, n a 5-by-5 wndow, we wll have 4 dfferent dsplaements and thus, 16 (4 dretons by 4 dsplaements) o-ourrene matres n total. The ten Haralk texture features are alulated for eah o-ourrene matrx. 5.4 Classfaton To obtan the C&RT deson tree, we dvded the 440 pure pathes nto a tranng set ontanng a random samplng of 66% of the pxels and a testng set ontanng the other 34%. Sne the texture feature have dfferent value as a pre-proessng step, we saled all the features to the range 0 to 1; the salng was done usng the max-mn normalzaton approah [5]. The optmal tree was found for number of parents equal to 100 and number of hldren equal to 5. For ths tree, 155 rules and 188 rules were found for the AP and DDP approahes, respetvely, for a wndow sze equal to 13 by 13. In both approahes, the lowest number of rules was obtaned for fat, lung, and musle, and the hghest number of rules was obtaned for lver and spleen; ths ndates that there s not muh dfferene among the texture pxels for fat/lung/musle pxels, whle there s sgnfant dfferene among the tssue pxels of a sngle organ/tssue suh as lver or spleen. One all the pxels n the pure-path are lassfed usng the derved deson rules, the hghest frequeny of the organ/tssue label n the path wll be used as the label representaton of ths path n order to get the fnal lassfaton. In addton to the lassfaton task, the deson tree approah helps us dentfy the most mportane features for dsrmnatng among the organs/tssues. We found that the ID desrptor s the most mportant feature for the lassfaton task. 5.5 Path Classfaton Results Wth respet to the way of alulatng the texture features, n all ases, the DDP approah produed at least the same or better results than the AP approah (Tables 1 & ) regardless of the organ onsderaton. Varyng the wndow sze from 5 by 5 to 13 by 13, had a slght effet on the result of AP approah, but had a sgnfant effet on the DDP approah. An explanaton of ths result may rely on the fat that, as the wndow beomes larger, more loal texture propertes are aptured for the alulaton of the o-ourrene matrx, and thus of the texture features used for lassfaton. The wndow sze was vared from 5-by-5 to 13-by-13 beause 1) senstvty of aorta starts to derease from 9-by-9 wndow; ) at 13-by-13 most of tssue lassfatons get almost 100% lassfaton senstvty; and 3) the omputaton tme nvolved n DDP oourrene alulaton nreases ubally wth the sze of the wndow. Table 1 presents the sgnfant mprovement of the DDP approah s senstvty wth the wndow sze. For example, the senstvty of kdneys rses from 64% to 97% and there s a

8 sgnfant mprovement from 61% to 100% for spleen, when the wndow sze grows up from 5- by-5 to 13-by-13. The senstvty of aorta went up from 45% to 81% when wndow sze nreased from 5-by-5 to 9-by-9; however, the senstvty started droppng at that pont. Thus, from these prelmnary results, t seems lke there are dfferent patterns wthn the aorta tssue pathes and a 9-by-9 wndow sze wll be more approprate for aorta. On the other hand, the senstvty for fat, lver, lung and bakbone dd not nrease sgnfantly beause the senstvty was already almost 100% at a wndow sze of 5-by-5. Table presents the spefty results for the eght organs of nterest. Regardless of the wndow sze, the spefty value for eah organ was above 90% for both AP and DDP approahes. Table 1: Senstvty for the pure path lassfaton for DDP and AP Aorta Fat Kdney Lver Lung usle Spleen Trabeular Bone Wndow DDP AP DDP AP DDP AP DDP AP DDP AP DDP AP DDP AP DDP AP 5x5 45.8% 0.00% 98.18% 98.18% 63.64% 36.36% 100% 100% 100% 100% 100% 100% 60.47% 44.44% 100% 9.86% 7x7 67.9% 1.8% 100% 98.15% 81.48% 44.44% 100% 100% 100% 100% 100% 100% 83.33% 67.44% 100% 93.75% 9x % 7.7% 100% 100% 78.85% 51.9% 100% 98.18% 100% 100% 100% 100% 94.44% 83.33% 100% 95.4% 11x % 30.61% 100% 100% 86.67% 55.56% 100% 98.18% 100% 100% 100% 100% 94.34% 86.79% 100% 100% 13x % 30.43% 100% 100% 96.55% 7.41% 100% 100% 100% 100% 100% 100% 100% 96.67% 100% 100% Table : Spefty for the pure path lassfaton for DDP and AP Aorta Fat Kdney Lver Lung usle Spleen Trabeular Bone Wndow DDP AP DDP AP DDP AP DDP AP DDP AP DDP AP DDP AP DDP AP 5x % 99.44% 100% 100% 96.4% 96.08% 94.04% 91.60% 100% 100% 99.70% 99.7% 94.56% 90.78% 95.9% 91.08% 7x % 98.80% 100% 100% 96.39% 96.11% 96.37% 95.50% 100% 100% 100% 99.70% 96.79% 91.30% 96.55% 9.4% 9x % 99.3% 100% 100% 98.04% 95.96% 99.00% 96.60% 100% 100% 100% 100% 95.54% 90.17% 96.6% 9.18% 11x % 99.30% 100% 100% 95.43% 97.% 98.93% 97.48% 100% 100% 100% 100% 96.30% 91.43% 96.50% 9.78% 13x13 100% 100% 100% 100% 9.97% 95.43% 98.43% 97.13% 100% 100% 100% 100% 97.64% 96.55% 99.4% 96.59% 6 Conluson and future work Our prelmnary results show that that the o-ourrene alulaton sheme at the pxel level and the wndow sze have a sgnfant nfluene upon the lassfaton results, espeally for the soft tssues. Wth respet to the DDP approah, the optmal wndow sze was 13-by-13 allowng the senstvty metr to be at least 96% for all organs exept for aorta. For aorta, the optmal wndow sze was 9-by-9 wth the lassfaton senstvty beng 81%. Therefore, dfferent wndow szes are approprate for dfferent organs and the larger the wndow sze, the more loal nformaton wll be aptured to alulate the texture. In terms of the overall lassfaton result and operatonal effeny, we suggest that the best wndow sze for dentfy regons of nterest s 9-by-9. As future work, the proposed approah an be extended to 1) nlude other texture features; and ) assgn probablst labels to the regons of nterest nstead of ust the label whh most predomnant wthn the orrespondng regon. Ths wll allow applyng the proposed approah for 1) probablst annotaton of unknown pure pathes; ) automat probablst segmentaton of pure pathes n CT mages usng splt and merge segmentaton algorthms; and 3) reaton of ontext-senstve tools for CAD systems. We also plan to nvestgate the effet of

9 usng three dmensonal texture models and norporatng more sophstated deson algorthms to move from a pxel lassfaton to a path lassfaton. Fnally, we wll begn testng the applablty of texture-based lassfaton to ertan pathologes. Referenes [1] R. Lerman, D. S. Rau, and J. D. Furst, Contrast enhanement of soft tssues n Computed Tomography mages, SPIE edal Imagng, 006. [] R.. Haralk, K. Shanmugam, and I. Dnsten, Textural Features for Image Classfaton, IEEE Trans. on Systems, an, and Cybernets, vol. Sm-3, no.6, pp , [3] R. Jan, R. Kastur, and B.G. Shunk, ahne Vson, ew York: Graw-Hll, [4]. Kalnn, D.S. Rau, J. Furst, and D.S. Channn, A lassfaton Approah for anatomal regons segmentaton, IEEE Int. Conf. on Image Proessng, 005. [5] D. Channn, D. S. Rau, J. D. Furst, D. H. Xu, L. Llly, and C. Lmpsangsr, "Classfaton of Tssues n Computed Tomography usng Deson Trees", The 90th Sentf Assembly and Annual eetng of Radology Soety of orth Amera (RSA04), 004. [6]. Kass, A. Wtkn, and D. Terzopoulos, Snakes: Atve ontour models, Int l. J. of Comp. Vs. 1(4), [7] E. Persoon, K. S. Fu, Shape dsrmnaton usng Fourer desrptors, IEEE Trans. Pattern Analyss & ahne Intellgene., vol. Pam-8, no. 3, pp , [8] R.. Dave, T. Fu, Robust shape deteton usng Fuzzy lusterng: Pratal applaton, Fuzzy Sets Syst., vol. 65, pp , [9] J. E. Koss, F. D. ewman, T. K. Johnson, D. L. Krh, Abdomnal organ segmentaton usng texture transform and a Hopfeld neural network, IEEE Trans. edal Imagng, vol. 18, no. 7, pp , [10]. Kobash, L. G. Shapro, Knowledge-based organ dentfaton from CT mages, Pattern Reognton, vol. 8, no. 4, pp , [11]S. A. Karkans, et al., Detetng abnormaltes n olonosop mages by texture desrptors and neural networks, Pro. of the Workshop ahne Learnng n ed. App., pp 59-6, [1]C. C. Lee, P. C. Chung, and H.. Tsa, Identfyng multple abdomnal organs from CT mage seres usng a mult-module ontextual neural network and spatal fuzzy rules, IEEE Trans. on Info. Teh. Bomedal, vol. 7, no. 3, 003. [13]S. Baeg,. Kehtarnavaz, Texture based Classfaton of ass Abnormaltes n ammograms, Pro. of IEEE CBS Symposum, 000. [14]O. R. Zaane,. L. Antone, A. Coman, ammography Classfaton by an Assoaton Rule-based Classfer, Int. Workshop on ultmeda Data nng., 00 [15]A. Wroblewska, P. Bonnsk, A. Przelaskowsk, Kazubek, Segmentaton and feature extraton for relable lassfaton of mro alfatons n dgtal mammograms, Opto- Eletron. Rev., vol. 11, no. 3, 003. [16]R. O. Duda, P. E. Hart, D. G. Stork, Pattern Classfaton, A Wley-Intersene, 001

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