Local Adaptive Receptive Field Self-organizing Map for Image Segmentation

Transcription

1 Local Adaptve Receptve Feld Self-organzng Map for Image Segmentaton Aluzo R. F. Araúo, Dogo C. Costa Unversdade Federal de Pernambuco Centro de Informátca - CIn Departamento de Sstemas da Computação Av. Professor Luís Frere, s/n Cdade Unverstára , Recfe, PE, Brazl e-mal: { aluzoa, dcc, }@cn.ufpe.br Keywords: Self-organzng Map, Grow When Requred, Radal Bass Functon, Image segmentaton, Border segmentaton, Image processng Abstract A new self-organzng map wth varable topology s ntroduced for mage segmentaton. he proposed network, called Local Adaptve Receptve Feld Self-organzng Map (LARFSOM-RBF), s a two-stage network capable of both color and border segment mages. he color segmentaton stage s responsblty of LARFSOM whch s characterzed by adaptve number of nodes, fast convergence and varable topology. For border segmentaton RBF nodes are ncluded to determne the border pxels usng prevously learned nformaton of LARFSOM. LARFSOM-RBF was tested to segment mages wth dfferent degrees of complexty showng promsng results. Introducton Pattern Recognton and Computer Vson tasks are usually dvded n smaller problems or steps [5][3][3]. Fgure shows the fve steps wdely adopted to create an ntellgent or automatc mage recognton system whch s seen as a computer vson problem. Fgure Automated Image Recognton Processng Steps. Data acquston s the step n whch the mages generated by an magng sensor are obtaned. he pre-processng step ams to remove nose and dsturbance. Image segmentaton separates the obects or elements present n the data from the background. he recognton and nterpretaton step analyzes each segmented obect to dentfy them. Fnally, the post-processng yelds a report or other knd of dagnostc about the acqured mage. he present paper s focused on the segmentaton step. Segmentaton s the process of dvdng or separatng (segmentng) an mage n obects or elements that are coherent under some crtera [3]. hs dvson process should occur untl the desred nformaton s correctly separated. he hardest goal n automatc segmentaton s the determnaton of the moment to stop segmentng. he segmentaton technques are often based on two mages features [5][]: dscontnuty and smlarty. Dscontnutes are present n mage regons where there are abrupt color changes. he most common technques used for dscontnuty detecton are pont detecton, lne detecton and border detecton. he latter s the most used one; Sobel and Prewtt Flters are broadly employed technques. Smlartes are found n mage regons where there are not color changes or there are very slghtly color changes. Common technques for smlarty segmentaton n mage processng are: thresholdng and regon growth. A color value s defned as threshold and all mage pxels above ths value become whte, and below become black. here are dfferent ways to do thresholdng, ncludng ntellgent algorthms [7][]. here are also dfferent ways to apply regon growth segmentaton [3]. he smplest one s to go trough all mage pxels checkng ther color dfference, then, dfferent color regons are consdered as obect fronters. he defnton of the threshold and smlarty values s not a trval task. Intellgent tools have been proposed [3][], specally usng neural networks, to determne threshold and

2 smlarty values, because of ther capabltes of adaptng themselves to envronmental changes. Many artfcal neural network approaches have been presented that segment mages drectly from pxel smlarty or dscontnuty. In [3][] we fnd two surveys treatng mage processng wth neural networks and color mage segmentaton, respectvely. In [3] more than 00 applcatons of neural networks n mage processng are lsted and a novel two-dmensonal taxonomy for mage processng algorthms s presented. he [] summarzes many color mage segmentaton technques such as hstogram thresholdng, characterstc feature clusterng, edge detecton, regon-based methods, fuzzy technques, neural networks approaches and others. Recently, self-organzng map based technques have been used. Color segmentaton s successfully performed by SOM [9] related networks n the followng works [5][4][]. In [] a two-stage strategy s used, frst a fxed-sze two-dmensonal feature map (SOM) captures the domnant colors of an mage n an unsupervsed way, and then a second stage combnes a varable-szed onedmensonal feature map and color mergng to control the number of color clusters that s used for segmentaton. he model n [4] s based on an unsupervsed and supervsed neural network approach. he unsupervsed step s a SOM network to perform color reducton and then a smulated annealng seeks the optmal clusters from SOM prototypes. In the supervsed step segmentaton nvolves color learnng and pxel classfcaton n whch a procedure of herarchcal prototype learnng (HPL) s used to generate dfferent szes of color prototypes from the sample of obect colors. he mage pxels are classfed by the matchng of color prototypes. Edge detecton based on SOM networks was also successful appled. In [4] aeral low contrast mages were properly edge segmented usng booth a self-organzng map (SOM) and a grayscale edge detector. A color segmentaton algorthm should be adaptve wth respect to the number of remanng colors/obects. Fxed color algorthms often produce poor color segmentaton results. SmAR [5] s characterzed by varable number of nodes whch grows as new prototypes are needed. he new nodes are connected to two others under a trangle shape neghborhood. Instead of usng the topologcal map to mplement lateral plastcty control as SOM does, the topologcal relatons between nodes work as an adaptve learnng nhbtory functon upon the prototype vectors. Some color quantzaton mplementatons n neural network archtecture have been proposed [][][3]. In fact, color quantzaton and color segmentaton are based n the same process of reducng the mage colors. he man dfference s that color quantzaton usually results n a pre-defned fnal number of colors and the larger s the number of fnal color the better s the resultant mage. However, n color segmentaton each fnal color n the resultant mage wll represent an obect, therefore only few colors are desred or else too many obects or subparts of obects wll be detected. he proposed algorthm tres to overcome the lmtaton of mentoned models [][][3][5][4][4][]. LARFSOM s self-adaptve wth respect to the number of fnal colors, a sutable feature to color segmentaton, as opposed to fxed color quantzaton models [][][3] and even to the color segmentaton model [] wth ntal fxed sze map. he proposed model does not need supervsed tranng steps, as requred by [4], then ncremental learnng s vable. Dfferently from SmAR [5], LARFSOM-RBF does not have a restrcton to a trangular shape neghborhood for new nodes, whch lmt nodes to at most four neghbors. LARFSOM-RBF topology freely grows and modfes tself durng tranng. herefore nodes may have as many neghbor nodes as necessary yeldng an n-dmensonal map. Fnally, LARFSOM-RBF performs booth color and border segmentaton n a fully unsupervsed manner. Furthermore, n models such as [4], mages need to be converted to grayscales before border segmentaton, LARFSOM-RBF does not need t, then the resultng processng s faster. he proposed model presents a new node nserton strategy based on smlarty between an nput pattern and the exstng prototypes. he smlarty s determned through an actvaton value threshold calculated wth respect to a local neghbourhood receptve feld value. As new nodes are added to the network, the topology s modfed by creaton and deleton of edges and nodes are free to have as many neghbours as necessary. In the border detectons stage, RBF unts detect obect bundares employng the local receptve feld nformaton extracted from LARFSOM traned nodes. he remanng of ths paper s organzed as follows. Secton descrbes LARFSOM, as well as the two-stage LARFSOM-RBF network used for border segmentaton. Secton 3 shows the obtaned results and dscuss them. Fnally, Secton 4 brngs the concluson and ure work. he Model Descrpton he Local Adaptve Receptve Feld Self-organzng Map (LARFSOM) takes advantage of nce characterstcs of SOM [9] and Grow When Requred (GWR) [0] networks. From SOM the compettve-learnng and clusterng capabltes are preserved as well as the topologcal dstrbuton of learned data among the map neghbor nodes. As GWR the LARFSOM grows only when new nodes are requred, based on an actvaton threshold, and the topology s also varable. However, LARFSOM s smpler than GWR n the sense that the

3 3 node wnnng counter s smpler calculated and only the best matchng unt s traned. he proposed segmentaton technque s based on a two stage neural network. Frstly, LARFSOM s used for color quantzaton, reducng the amount of data to be processed and creatng a color representaton of the mage. he acqured knowledge s then used for color segmentaton. Secondly, Radal Bass Functon [6] nodes are used to dentfy all edge pxels n the mage, resultng n border segmentaton. We call the whole model as LARFSOM-RBF.. Color Segmentaton Algorthm Color quantzaton [][][8] s a method to reduce the number of colors present n an mage consderng a mnmal vsual dstorton. Color quantzaton has two steps: () autonomous selecton of the most representatve colors from all colors present n the orgnal mage to form the color palette; and () mappng of each color n the orgnal mage to the nearest color n the palette. he fnal mage wll only have the selected colors and should be as smlar as possble to the orgnal one. Color quantzaton process usng LARFSOM s trggered by 3D-nput vectors: values of red, blue and green to compose the possble colors for every pxel of an mage, accordng to the RGB standard. As each pxel s an nput to LARFSOM, then, the weght vectors are also 3D. he RGB standard values vary from 0 to 55. hey are normalzed (0 to ) before gven as nput to the network. LARFSOM has 0 steps: () Parameter ntalzaton; () Selecton of nput pattern (pxel); (3) Best matchng unt (BMU) search; (4) Connecton nserton between two best unts; (5) BMU local receptve feld calculaton; (6) BMU actvty calculaton based on receptve feld; (7) Possble nserton of a new node; Else, update BMU weghts; (8) Check stop crteron; (9) Buld color palette; (0) Buld color segmented mage. hese steps are detaled as follows. Step : Parameter ntalzaton: fnal learnng rate ( ρ ), learnng rate modulator ( ε ), actvty threshold ( a ), number of wns of node ( d = 0 ), maxmum number of wns of each node ( d ), the tme teraton ( t = 0 ), the m mnmum error ( e mn ), and the ntal number of connected nodes ( N = ), whose weghts are coped from the RGB values of two randomly chosen mage pxels. Step : Present a randomly chosen mage pxel [ r g b] = to the network as nput data. f Step 3: Calculate the Eucldan dstance between the sample and the weght vectors ( w s) as follows: d (, w ) = w () ( r w ) ( g w ) + ( b w ) = r g b w () Calculate the shortest dstance between the nput and all weght vectors to fnd the best matchng unt (BMU): d w, ) d( w, ) d( w, ), N (3) ( s s where N s the all-node set. Increment the wns counter of BMU: d d S = + S Step 4: Insert a new connecton between s and s f t does not exst. Step 5: Calculate the receptve feld of s : ( w w ) + ( w w ) + ( w w ) s sr sr s g sg sb sb r = (4) Step 6: Calculate the actvty of s : a s ( w ) exp s = (5) r s Step 7: Insert a new node f BMU actvaton s bellow a threshold ( a ), else update the BMU weght vector: If a s < a Add a new node wth weght vector w n = Update the number of nodes N = N + Remove the connecton between s and s Calculate the dstances d w, w ), d ( w, w ), d ( w, w ) ( n s n s s s Insert connectons between nodes wth the two smallest dstances. Else w = ρ w ) (6) s ( s ( d / dm ) ε ρ f, d dm where ρ = ε ρ f, d > d m Step 8: Update the number of teratons t = t + and return to step unless f the stoppng crteron s reached: N 4 mn 0 current w former = N = 0 e = w e (7)

4 4 Step 9: After the tranng process, assgn each color represented by a weght vector to a color n the palette. Step 0: Replace each orgnal pxel color n the mage by ts closest one n the color palette. he number of nodes after the tranng process defnes the number of palette colors. o reconstruct an mage wth the palette color, an nterpolaton method s proposed to generate more colors based on the palette ones. hen, a small network map, wth ust a few nodes s sutable for color segmentaton of color full mages reducng sgnfcantly the tranng tme. If color nterpolaton s used Step 0 would be substtuted Step. Step : Replace each orgnal pxel color n the mage by a mean of the three frst BMUs of the current nput. hen, the nterpolaton for the red component of the mage s: R = where { s, s, s } m d( w 3 r d( w s s ) ) { s, s, s3 } (8) R G B s the new color for the actual mage pxel and m r s the color closest to the stmulus n the palette. he number of wnners was found heurstcally through tests wth dfferent wnner numbers. hree nodes were satsfactorly fast and precse for nterpolaton.. Border Segmentaton Algorthm An edge or border s the lmt between two regons suffcently homogeneous n whch dscontnuty between them can be located ust by analyzng the color changes. Edge detecton s a technque based upon the detecton of local dscontnutes, often correspondng to the boundares of obects n the mage. he varous optons of edge detecton of an mage [5][3] ams to reduce the amount of data to be processed and flters out rrelevant nformaton, preservng the man structural propertes of an mage. Edge detecton s often the maor step of mage segmentaton n computer vson systems. Fgure llustrates the two-stage procedure of the proposed model. he proposed edge detecton algorthm s based on a two stage neural network. In the frst stage, a partcular mage s color segmented by the LARFSOM. In the second stage, two RBF [6] nodes are responsble for dentfyng all pxels formng edges. he RBF nodes are not traned,.e., ther parameters are extracted from the LARFSOM weght vectors. Despte the absence of an explct tranng stage, the RBF layer has ts parameters adapted through the learnng of LARFSOM, then, for dfferent cluster formatons, the RBF layer parameters are also updated. After the color quantzaton stage, every pxel, n, of the quantzed mage s analyzed and classfed accordng to the RBF nodes whch are defned by complementary levels of actvaton ( U,U ). he current pxel, n, s an edge pxel f U < U. M past M U = exp (9) rn U = U (0) where, r n s the radus of the RBF functon defned by Eq. as functon of the output of LARFSOM whereas M and M past are the ure and past pxel color averages, respectvely, calculated by (3) and (4). o fnd vertcal edges the pxels are consder from left to rght, lne by lne. In ths case the M and M past would be the rght and left neghbor pxels value average, respectvely. o seek for horzontal edges pxels are taken from top to bottom, column by column. When both edges are desred, the two prevous procedures are executed. he radus s calculates as follows. r n C far = α C () where C = BMU M ) () ( and 0 < <, C s the quantzed color, represented by the BMU LARFSOM, of the ure pxel color average, and C far s the farthest node of LARFSOM from the BMU node. he ure pxel color average, M, s used nstead of the current pxel value to make the actvaton functon more dscrmnatng for local sharp contrasts, usually nose that should be removed. he radus, r n, controls the color dfference degree to dentfy an edge. he past and ure edges are determned as follows: [ R( n), G( n), B( n ] M = ) (3) Fgure - Proposed two-stage edge detecton algorthm. M past = R( n), G( n), B( n) (4)

5 5 where R (n) s the average of the red values of the ure pxels and R (n) s the average of the red values of the past pxels descrbed by (5) and (6), respectvely. R( n) = ρ R( n) + ( ρ) R( n + ) (5) R( n) = ρ R( n ) + ( ρ) R( n ) (6) where 0 < < ; R(n) s the red value of the current pxel; defnes the nfluence of ure and past pxels upon the average. he green, G (n), G (n), and blue, B (n), B (n), averages are calculated as n Eq.5 and Eq.6. 3 Results and Dscussons hs secton presents the results of the proposed segmentaton technque tested by means of four real world mages : house, pepper, Lena and baboon are shown n Fgure 3, respectvely. (5x5) has 30,47 colors and plenty of soft and abrupt color changes, t s the hardest color segmentaton. he peak sgnal-to-nose rato ( PSNR ) [] s gven by: 3 55 PSNR = 0 log (7) MSE MSE = Nt ( ( X X ' ) ) = 0 N t (8) where X and X are the pxel values of the orgnal and quantzed mage, and N t s the total number of pxels. A hgher PSNR value ndcates a better qualty mage, usually above 30 s consdered a good qualty level []. he mage wth hgher number of colors wll have hgher PSNR due to ther smlarty to the orgnal mages, however ths does not ensure better segmentaton. 3. Color Segmentaton Results LARFSOM parameters ( ρ f =0.05, ε = 0. 3, d m =00) were emprcally chosen. hree actvty threshold values ( a ) were used,.65,.65, and.0, also the color nterpolaton was llustrated for the.65 resultant mage. Fgure 3 he orgnal mages used to test the proposed algorthm: house, pepper, Lena and baboon. Color segmentaton complexty s dfferent for the four mages. he house (56x56 pxels) s the smplest one havng 33,95 colors and few domnant and contrastng colors. Pepper (5x5) has 83,55 colors and more domnatng colors, however the obects border are defned by color contrasts. Lena (5x5) has 48,79 colors and few domnant and smlar colors then, the obect segmentaton s harder than the prevous cases. Baboon House, Lena, pepper and baboon mages were collected at the USC-SIPI Image Database: Fgure 4 LARFSOM color segmentaton of house mage. A combnaton of many parameters was tested wth the mages n Fgure 3. he chosen parameters showed to acheve good results for all four mages. Fgure 4 to Fgure 7 shows the results of the color segmentaton performed by LARFSOM. ables to 4 provde further detals such as threshold value, the use of the nterpolaton (step ), and the fnal network parameters.

6 6 able Parameters for color segmentaton of house mage. Image a Interpolaton Iteratons PSNR Nodes Colors.65 no yes no no Fgure 6 - LARFSOM color segmentaton of Lena mage. able 3 - Parameters for color segmentaton of Lena mage. Fgure 5 - LARFSOM color segmentaton of pepper mage. able Parameters for color segmentaton of pepper mage. Image a Interpolaton Iteratons PSNR Nodes Colors.65 no yes no no Image a Interpolaton Iteratons PSNR Nodes Colors.65 no yes no no LARFSOM dd not need many teratons to capture the mage color dstrbuton. Images havng 6,44 pxels, for a =.65, needed less than 0,000 teratons to learn. Despte the fast convergence, LARFSOM can determne the most sgnfcant colors (Fgure 4 to Fgure 7). he self-adaptve number of nodes also appears as an nterestng feature. wo nodes (able ) were enough to dstngush the house from the background. Pepper was easly segmented due to ts very abrupt color contrast wth four or fve nodes. Also, four nodes segmented most of the obects of Lena mage whereas the poorest segmentaton of baboon was reached wth four nodes. he PSNR values were also satsfactory due to the ntense color reducton durng the color segmentaton. Fgure 7 - LARFSOM color segmentaton of baboon mage. able 4 - Parameters for color segmentaton of baboon mage. Image a Interpolaton Iteratons PSNR Nodes Colors.65 no yes yes no

7 7 he nterpolaton of the palette colors generated many fnal colors makng t harder the color segmentaton. Even though, the nterpolaton capablty may be very useful for precse mage reconstructon. 3. Border Segmentaton Results he edge detecton must neglect all color nformaton and preserve the relevant structural nformaton,.e., only sgnfcant color changes should reman n the mage. he edge detector was appled to the orgnal mages (Fgure 3), after the color segmentaton stage, to produce the results shown n Fgure 8. he chosen parameters for color segmentaton were the same as before, wthout color nterpolaton and a =.65. he emprcal border segmentaton parameters were =0.80, and =0.66. Once more, dfferent parametrc combnatons were tested to fnd a good parameter combnaton. Whte pxels are borders whereas black pxels are not. In house and pepper mages the border segmentaton was very accurate. In Lena due to ts soft color changes, edge detecton s harder, but even so the most relevant edges were determned. Border segmentaton of baboon s easy because t s formed of very contrastng colors. he RBF unts can determne f a partcular pxel s an edge. Flters lke Sobel gve dfferent ntenstes of gray values to each pxel. herefore a further processng s necessary to threshold the Sobel fltered mage and chose the gray ntenstes to be defned as borders. algorthm s;.e., the growth of causes senstvty only to hgh contrasts. he parameter controls the border wdth crteron; hgh values of causes detecton of thck edges. For nstance, for = 0.50 the number edges detected n (Fgure 9 ) are hgher than those n Fgure 8. For = 0.90, only wder edges were preserved n pepper mage Fgure 9 as opposed to Fgure 8. Fgure 9 - Segmentaton of Lena mage wth =0.80 and =0.50 and of pepper mage wth =0.90 and = Further Comparsons he most sgnfcant feature of LARFSOM s ts fast convergence wth sutable PSNR values. Comparng LARFSOM wth SOM and SmAR, one may notce these features. able 5 shows that LARFSOM needed 64 teratons and 0.0 seconds to be traned for Lena mage leadng to nodes. SOM needed.3 teratons to converge wth nodes for the same mage and ts PSNR was sgnfcant lower. SOM parameters were ntal learnng rate of 0.0 and ntal neghbourhood nfluence of 0.5 and the same convergence crtera as LARFSOM was used. able 5 Compares SOM and LARFSOM performance for Lena mage. Network Nodes Iteratons PSNR CPU me (seconds) SOM LARFSOM SmArt acheved a MSE rate for Lena mage of 56.9 (PSNR of 5.40) wth nodes and learnng rate of 0. as shown n [5], whle the LARFSOM PSNR was Concluson and Future Work Fgure 8 Results of applyng two-stage LARFSOM-RBF border segmentaton to mages of Fgure 3. he parameters and allow fne-tunng for the edge detecton crteron. he greater the more selectve the he usage of ntellgent algorthms for mage segmentaton s a rch research feld nowadays. Dfferent systems were proposed n the lterature, some of them presentng good results, however, often, they do not have fast, accurate and adaptve tranng steps. In ths paper a he computer used for tests was a Pentum 4 wth.66ghz and 5MB of RAM.

8 8 robust and fast Local Adaptve Receptve Feld Selforganzng Map (LARFSOM), was presented to acheve these goals. Moreover the LARFSOM-RBF network features booth color and border segmentaton makng t very sutable for mage processng systems. he maor contrbuton of LARFSOM-RBF among other recent and successful mage segmentaton models, lke the SmAR[5], for example, s the ablty to booth color and border segment mages fully based on unsupervsed learnng, whle other approaches ust perform on type of segmentaton or need supervsed steps. he segmentaton technque s based on a two-stage neural network. For color segmentaton the clusterng characterstcs wth growng number of nodes of LARFSOM s used. For border segmentaton RBF nodes uses prevously learned nformaton of LARFSOM to determne the border pxels, therefore an LARFSOM - RBF two-stage network s proposed for the whole segmentaton process. Four dfferent mages wth hgher segmentaton complextes were tested and successfully color segmented. he acheved results showed that LARFSOM s a very fast learner; ust few tranng teratons were enough for the network to make an approprate understandng of the mages color dstrbuton. It was shown n most of the tme less than % of the mage pxels needed to be randomly presented to LARFSOM n tranng step, for a fne color dstrbuton understandng. he adaptve number of nodes was also a maor feature of LARFSOM, once the number of obects n the mages are pror unknown. he edge detecton algorthm showed to be effectve n segmentng the four mages. he fne-tunng parameters made t possble to adust the edge detecton selectvty as desred. he automatc adustment of edge detecton fne tunng parameters s of ure nterest. he dea s to ncorporate these parameters as network nput for self and adaptve optmum calbraton. [4] G. Dong, M. Xe, "Color Clusterng and Learnng for Image Segmentaton Based on Neural Networks", IEEE ransactons on Neural Networks, Vol.6, No.4, 005. [5] R.C. Gonzalez, R.E. Woods, Dgtal Image Processng, Edgard Blücher, 000. [6] D.S. Broomhead and D. Lowe, Multvarable functonal nterpolaton and adaptatve networks, Complex Systems, Vol., pp , 988. [7] C.V. Jawahar, P.K. Bswas and K. Ray, Investgatons On Fuzzy hresholdng Based On Fuzzy Clusterng, Pattern Recognton, Vol.30, No.0, 997. [8] K. Kananawanshkula, B. Uyyanonvara, "Novel fast color reducton algorthm for tme-constraned applcatons", Journal of Vsual Communcaton & Image Representaton. Vol.6, pp.3 33, 005. [9]. Kohonen, Self-organzng Maps. nd edton, Sprnger-Verlag [0] S. Marsland, J. Shapro, U. Nehmzow, A selforganzng network that grows when requred. Neural Networks, Vol.5 pp , 00. [] S.H. Ong, N.C. Yeo, K.H. Lee, Y.V. Venkatesh, D.M. Cao, Segmentaton of color mages usng a two-stage self-organzng network, Image and Vson Computng, Vol.0, pp.79 89, 00. [] N. Papamarkos, A. E. Atsalaks, C. P. Strouthopoulos, Adaptve color reducton, IEEE ransactons On Systems Man And Cybernetcs Part B-Cybernetcs Vol.3, No., pp.44-56, 00. [3] J.R. Parker, Algorthms for Image Processng and Computer Vson, John Wley and Sons, 997. [4] P.J. ovanen, J. Ansamak, J.P.S. Parkknen, J. Melkanen, "Edge detecton n multspectral mages usng the self-organzng map", Pattern Recognton Letters, Vol.4, pp , 003. [5] N.C. Yeo, K.H. Lee, Y.V. Venkatesh, S.H. Ong, "Colour mage segmentaton usng the selforganzng map and adaptve resonance theory", Image and Vson Computng, Vol.3, pp , 005. References [] CH. Chang, P. Xu, R. Xao, R. S.. Srkanthan, New adaptve color quantzaton method based on self-organzng maps, IEEE ransactons on Neural Networks, Vol.6, No.: pp.37-49, 005. [] H.D. Cheng, X.H. Jang, Y. Sun, J.L. Wang, "Color mage segmentaton: advances and prospects", Pattern Recognton, Vol.34, No., pp.59-8, 00. [3] D. derdder, H. Handels, Image Processng wth Neural Networks A Revew, Pattern Recognton, Vol.35, pp.79 30, 00.