FUZZY IMAGE SEGMENTATION USING LOCATION AND INTENSITY INFORMATION

Size: px

Start display at page:

Download "FUZZY IMAGE SEGMENTATION USING LOCATION AND INTENSITY INFORMATION"

Bonnie Ryan
6 years ago
Views:

1 FUZZY AGE SEGENTATON USNG OCATON AND NTENSTY NFOATON Ameer Al, aurece S Dooley ad Gour C Karmakar Gppslad School of Computg & formato Techology, oash Uversty, Australa Emal: {AmeerAl, aurecedooley ad GourKarmakar}@fotechmoasheduau Abstract The segmetato results of ay clusterg algorthm are very sestve to the features used the smlarty measure ad the obect types, whch reduce the geeralzato capablty of the algorthm The prevously developed algorthm called mage segmetato usg fuzzy clusterg corporatg spatal formato (FCS merged the depedetly segmeted results geerated by fuzzy clusterg-based o pxel testy ad pxel locato The ma dsadvatages of ths algorthm are that a perceptually selected threshold does ot cosder ay sematc formato ad also produces upredctable segmetato results for obects (regos coverg the etre mage Ths paper drectly addresses these ssues by troducg a ew algorthm called fuzzy mage segmetato usg locato ad testy (FS by modfyg the orgal FCS algorthm t cosders the topologcal feature amely, coectvty ad the smlarty based o pxel testy ad surface varato Qualtatve ad uattatve results cofrm the cosderable mprovemets acheved usg the FS algorthm compared wth FCS ad the fuzzy c-meas (FC algorthm for all three alteratves, amely clusterg usg oly pxel testy, pxel locato ad a combato of the two, for a rage of sample of mages Keywords mage Segmetato, Fuzzy Clusterg, Coectvty, ocato troducto mage segmetato s a very mportat research area because t plays a fudametal role mage aalyss, uderstadg ad codg [] t ca be formally defed as the process of separatg mutually exclusve regos (obects of terest from other regos (obects a mage However, t s the most challegg task because there are ofte a ordate umber of obects ad huge varatos betwee them that make t almost mpossble to approxmate all the obects usg a geeral frame ost real-world mages possess a certa amout of ambguty ad hece the segmetato produces fuzzy regos Fuzzy mage segmetato techues are much more adept at processg such ucertaty tha classcal techues ad ths cotext fuzzy clusterg algorthms are the most popular ad extesvely used mage segmetato techues [] Clusterg methods [3], [4], [5], [6], [7] use may dfferet feature types, such as brghtess (the pxel testy of a gray scale mage ad geometrcal (the spatal locato of the pxels for measurg the smlarty but the segmeted results are very much depedet o the types of feature used clusterg ad the types of the obects a mage Ths rases the uesto as to whch type of feature s most sutable for whch type of obect so lmtg the geeralzato of a clusterg algorthm [3] For stace, FC caot separate mage regos whch have smlar pxel testes by cosderg oly ther pxel testy, though they may be able to by explotg formato o the locato of pxels or a combato of pxel testy ad locato the same way, clusterg caot segmet adacet regos havg dfferet pxel testes by oly cosderg pxel locato, but may well be able to do so by cosderg respectve pxel testes From the observatos, t was also foud that the most cases, clusterg algorthms usg both features, e a combato of pxel testy ad locato dd ot produce the expected results for the obects of a mage havg the same pxel testy ad surface varatos ad some cases, t also was uable to separate the obects havg dstgushable pxel testes These ssues were addressed by Al et al [8] who troduced a algorthm called mage segmetato usg fuzzy clusterg corporatg spatal formato (FCS The ma drawback of ths algorthm s that t uses a perceptually selected threshold, whch redstrbutes the overlap betwee two regos wthout cosderg ay sematc formato about a obect t also does ot hadle well the stuato where a obect covers almost the etre mage Ths paper troduces a ew algorthm called fuzzy mage segmetato usg locato ad testy formato (FS t cosders the coectvty topologcal feature, ad a obect s smlarty based o pxel testy ad surface varato The orgal FCS algorthm has also bee modfed ad tegrated wth the ew algorthm A

2 umercal aalyss of FC, FCS ad the proposed FS s performed usg oe of the effcet obectve segmetato evaluato methods, amely dscrepacy based o the umber of msclassfed pxels [9] ths paper all the clusterg results are preseted usg the fuzzy c-meas (FC algorthm [3] for pxel testy oly, pxel locato oly ad a combato of the two The paper s orgazed as follows: Secto, the basc mathematcal prcples of the FC algorthm are outled; whle the theoretcal cocepts of the modfed FCS ad the ew FS algorthms are dscussed Sectos 3 ad 4 respectvely The umercal evaluato of the expermetal results s aalysed Secto 5 Fally, some coclusos are gve Secto 6 Fuzzy C-eas Algorthm (FC FC s the most popular ad oldest fuzzy-based clusterg techue [] t s stll wdely used features aalyss, patter recogto, mage processg, classfer desg ad clusterg [0] The FC algorthm s maly based o the optmzato of the followg obectve fucto ad costrats [], [3]: J (, v = ( µ d c = = µ ( {, K, c} ad {, } 0 µ ; K, ( c = 0 {, K } µ = ;, (3 < = {, K c} µ < ;, (4 where c ad are the umber of clusters ad data respectvely µ s a set of membershp values µ v s a vector cotag the values of cluster ceters v s the fuzzfer < d s the Eucldea dstace betwee a datum x ad the cetre of the th cluster v The obectve fucto ( s teratvely mmzed usg the followg two euatos for µ ad v respectvely: µ = (5 v c k = = = d d k ( µ ( µ = x The cluster ceters are talzed ether radomly or by a approxmato method The membershp values µ ad cluster ceters v are updated through a teratve process (6 utl the maxmum chage µ becomes less or eual to a specfed threshold 3 The odfed FCS Algorthm A detaled descrpto of the orgal mage segmetato usg fuzzy clusterg corporatg spatal formato (FCS algorthm s gve [8] The ma drawback of ths algorthm cocers the perceptually selected threshold used to redstrbute the overlap betwee two regos wthout cosderg ay sematc formato of a obect To address ths ssue, the FCS algorthm has bee modfed to redstrbute the overlap by usg 8- coected obects ad the ormalzed pxel locatos wth a rage from mmum to maxmum gray level pxel testy, thereby elmatg the threshold The modfed FCS algorthm (Algorthm, s embedded the ew FS algorthm, whch s descrbed the ext secto Algorthm : The modfed fuzzy clusterg corporatg spatal formato (FCS algorthm Precodto: tally segmet regos ad utlsg pxel testy ad ormalsed pxel locato or a combato of pxel testy ad ormalsed pxel locato respectvely produced by ay fuzzy clusterg algorthm The umber of segmeted regos ( Postcodto: The fal segmeted regos Determe the smlar (closest regos of to : { P ( x, y Pk ( x y } smlar ( = m, k where P ( x, y ad ( erge smlar regos betwee P k x, y ad k : = { P( x, y P( x, y O P( x, y k } where P ( x, y s the pxel at locato ( y s smlar to k x, ad 3 Calculate the overlap betwee the two merged regos: O = P ( x, y P ( x, y AND P( x, y AND AND, 4 edstrbute the overlap by cosderg 8- coected obects 5 edstrbute aga the overlap usg ormalzed pxel locato ad pxel testy f there are ay more pxels the overlappg rego

3 4 The FS Algorthm As metoed Secto, the segmeted results of a clusterg algorthm deped o the features of the smlarty measure ad the types of obect a mage The orgal FCS algorthm dd ot cosder topologcal formato about a obect ad was sestve to the value of the threshold ths secto a algorthm called fuzzy mage segmetato usg locato ad testy formato (FS s preseted (Algorthm to reduce the aforemetoed lmtatos Algorthm : The fuzzy mage segmetato usg locato ad testy (FS algorthm Precodto: The foregroud of the mage to be segmeted ad the umber of segmeted regos ( Postcodto: The fal segmeted regos Calculate the areas w A ad ( ad the foregroud ( A w A f { P( x, y P( x y } =, { P( x, y P( x y f } =, Segmet the mage w f F ( A A Threshold T f A of the etre mage f respectvely THEN Execute the modfed FCS algorthm (Algorthm usg pxel testy ad a combato of pxel testy ad ormalzed pxel locato for tal segmeted regos ESE Fd the tal regos usg FC wth a combato of pxel testy ad ormalsed pxel locato Determe the area segmeted rego A { P( x, y P( x y } =, where { K,,} F f ( A for each A max A Threshold Tmax THEN The obects to be segmeted are smlar wth respect to pxel testy ad surface varato ad hece perform segmetato usg FC wth ormalsed pxel locato ESE The obects are dssmlar ad hece segmet the mage usg the modfed FCS algorthm (Algorthm usg pxel testy ad ormalsed pxel locato FS segmets the foregroud obects by cosderg sematc formato about these obects ad cosders two types of formato the mage, whch does ot cota cosderable umber of backgroud pxels ad the smlarty of the obects based o pxel testy ad surface varato Frstly, the calculato of the area of the w f whole mage A ad the foregroud A, terms of the umber of the pxels s descrbed Step, Algorthm f the area of the foregroud s approxmately the same as the mage, FC usg oly pxel locatos arbtrarly dvdes the mage wthout cosderg sematc formato about the mage To avod ths scearo, the dfferece betwee the foregroud ad etre mage areas s perceptually thresholded ad the segmetato performed usg the modfed FCS algorthm (Algorthm usg pxel testy ad a combato of pxel testy ad ormalzed pxel locato for tal segmeted regos show Step, Algorthm all other cases, the segmetato s performed by cosderg the smlarty ad dssmlarty based o pxel testy ad surface varato of the obects of a mage usg a perceptually defed threshold T max f FC does ot effectvely separate the obects usg a combato of pxel testy ad ormalsed pxel locatos, the obects are smlar pxel testy ad surface varato ad hece FC wth ormalsed pxel locato s appled segmetato (Step, Algorthm Otherwse the obects are dssmlar ad separated by the modfed FCS algorthm usg pxel testy ad ormalsed pxel locato Whle the two thresholds T ad T max are perceptually determed by a small percetage (% of the foregroud ad the largest segmeted rego respectvely, the ew algorthm s ot very sestve to them 5 Expermetal esults The ew FS, FCS ad fuzzy c-meas (FC [3] algorthms were mplemeted usg atlab 6 (The athworks c For FC, oly the pxel testy, ormalsed pxel locato, ad a combato of both features were used Sce the FS ad FCS algorthms are based o clusterg, the pror umber of clusters c has to be maually chose A represetatve sample of three dfferet types of atural grey-scale mage cosstg of dfferet regos (obects havg smlar ad dssmlar pxel testy ad surface varato, used the expermet, were obtaed from S ad from the teret The backgrouds have bee maually removed from all mages for segmetg the foregroud regos usg ther ormalsed pxel locatos ocato the form of the x, y coordates of a pxel are ormalsed wth the rage [0, 55] order to keep them wth the same rage of pxel testes for 8-bt gray scale mages S s aster Photo Collecto, 895 Fracsco Blvd East, Sa afael, CA , USA

The uattatve aalyss was coducted usg oe of the most effcet segmetato evaluato methods, amely dscrepacy based o the umber of msclassfed pxels [9] The cofuso matrx s a by suare matrx, where represets

(g Fgure : (a Orgal tree mage, (b aually segmeted referece mage of (a Fgures (c (e the segmeted results for the tree mage to two regos usg FC wth pxel locatos oly; pxel testy oly ad both features

4 The uattatve aalyss was coducted usg oe of the most effcet segmetato evaluato methods, amely dscrepacy based o the umber of msclassfed pxels [9] The cofuso matrx s a by suare matrx, where represets the umber of pxels msclassfed to the th rego from the th rego The two types of error, amely Type, error ad Type, error are defed as follows: = error = 00 (7 = = error = 00 (8 = = = (c (e (a (d (b (f (g Fgure : (a Orgal tree mage, (b aually segmeted referece mage of (a Fgures (c (e the segmeted results for the tree mage to two regos usg FC wth pxel locatos oly; pxel testy oly ad both features respectvely (f Segmetato result usg FCS (g Segmetato result usg FS Type, error s the error percetage of all th rego pxels that are msclassfed the other regos, whle Type, error s the error percetage of all rego pxels that are msclassfed to th rego The maually segmeted referece regos wth ther respectve orgal mage are show Fgures (a-(b, (a-(b, ad 3(a- 3(b Note that the two maually referece ad segmeted regos are preseted by two dfferet gray levels stead of the orgal rego testes, order to provde a better vsual terpretato of the segmeted results Expermets were performed usg the brd mage (Fgure (a havg two regos: the brd ( ad the tree ( ad ts segmeted results produced by FC, the orgal FCS [0] ad FS are show Fgure (c-(g f the results produced by the FS algorthm are compared wth the other results (Fgure (c-(f ad maually segmeted referece regos (Fgure (b, t s show that the FS rego algorthm completely separated the brd ( rego Fgure (c ad (e prove that FC arbtrarly dvdes the foregroud obects for ormalzed pxel locato ad a combato of pxel testy ad ormalzed pxel locato The rego from the tree ( correspodg umercal results for the brd ( show Table cofrm the superorty of the ew FS algorthm to the other aalysed algorthms ad shows that FC usg locato ad locato ad pxel testy produced o Type error e o pxels of the brd ( rego were msclassfed to aother rego, because, as metoed before, FC usg them arbtrarly dvded the mage (Fgure (c ad (e For ths reaso, Type rego as a error was also very hgh for the brd ( large umber of pxels from the tree ( msclassfed to ( rego were rego The FS algorthm reduced the Type error sgfcatly whle slghtly creasg the Type error Overall, the mea error percetage of FS (8% s cosderably lower tha for the other algorthms examed Table : Error percetages for the brd rego ( segmetato Fgure Algorthm Error Type Type ea FC (locato FC (testy FC (locato & testy FCS FS

Aother seres of expermets was performed usg the mage (Fgure (a cotag two cows havg dfferet pxel testes The results show Fgure (c-(g llustrate that the FS almost separated the two cows (Fgure (g, whle

5 Aother seres of expermets was performed usg the mage (Fgure (a cotag two cows havg dfferet pxel testes The results show Fgure (c-(g llustrate that the FS almost separated the two cows (Fgure (g, whle the other algorthms dd ot (Fgure (c-(f The average percetage error (88% show Table for the FS algorthm of ths mage s also otceably lower compared wth the others (09%, 836%, 373% ad 45% Table : Error percetages for the cow rego ( segmetato Fgure Algorthm Error Type Type ea FC (locato FC (testy FC (locato & testy FCS FS (a (b The fal expermet was performed usg the dosaur ad mage (Fgure 3(a havg two regos: the cow ( the dosaur ( Aga the segmeted results produced by the FS algorthm (Fgure 3(g separated the etre cow ( ad the dosaur ( except for a few pxels of the dosaur The segmetato error percetage for the dosaur mage s show Table 3, whch aga cofrms the mprovemet of the FS algorthm havg average error of oly 59%, whereas the average error for the other algorthm was 788%, 03%, 66% ad 597% (c (d (e (f (a (b (g Fgure : (a Orgal cow mage, (b aually segmeted referece mage for (a Fgures (c (e the segmeted results of the cow mage to two regos usg FC wth pxel locatos oly; pxel testy oly ad both features respectvely (f Segmetato result usg FCS (g Segmetato result usg FS (c (d (e (f

6 (g Fgure 3: (a Orgal dosaur mage, (b aually segmeted referece mage for (a Fgures (c (e the segmeted results of the su mage to two regos usg FC wth pxel locatos oly; pxel testy oly ad both features respectvely (f Segmetato result usg FCS (g Segmetato result usg FS Table 3: Error percetages for the dosaur rego ( segmetato Fgure 3 Algorthm Error Type Type ea FC (locato FC (testy FC (locato & testy FCS FS From both the ualtatve ad uattatve aalyss, t ca be cocluded that for all the test mages used (Fgures (- (3, the proposed FS algorthm obtas cosderable mprovemet ts segmetato performace compared wth FC for all three cases, that s usg clusterg based o pxel testy, o pxel locato ad the combato of the two, as well as comparso wth the orgal FCS algorthm 6 Coclusos Ths paper has preseted a ew algorthm called mage segmetato usg locato ad testy formato (FS by applyg coectvty, a topologcal feature ad obect smlarty based o the pxel testy ad surface varato Both ualtatve ad uattatve aalyss of the results produced by all algorthms has exhbted the cosderable mprovemet of the ew algorthm compared wth FC usg oly pxel locatos, oly pxel testy, ad a combato of the two as well as the orgal FCS algorthm The ma advatage of ths algorthm s that t ca separate ay type of obect from a mage, to a certa extet From the expermets, t has also bee show that the proposed FS algorthm s sestve to the values of the thresholds T ad T max Sce the ew algorthm s based o clusterg, t s reured that tally the umber of clusters to be used has to be specfed for ths algorthm efereces [] Gath, ada B Geva, Usupervsed Optmal Fuzzy Clusterg, teratoal Joural of Patter Aalyss ad ache tellgece, (7, 989, [] GC Karmakar, Dooley, ad Syed, evew o fuzzy mage segmetato techues, Desg ad aagemet of ultmeda formato Systems: Opportutes ad Challeges, (USA, dea Group Publshg Copyrght, 00 [3] JC Bezdek, Patter ecogto wth fuzzy obectve fucto algorthm (New York: Pleum Press, 98 [4] Krshapuram ad J Keller, A Possblstc Approach to Clusterg, teratoal Joural of Fuzzy Systems, (, 993, 98-0 [5] Y A Tolas ad Paas, O applyg Spatal Costrats Fuzzy mage Clusterg Usg a Fuzzy ule-based System, EEE ter Co o Sgal Processg etters, 998, 5(0, [6] A W C ew, S H eug ad W H au, Fuzzy mage clusterg corporatg spatal cotuty, EE Proc-Vs o mage Sgal Process, 000, 47(,85-9, [7] Z Ch, H Ya, ad T Pham, Fuzzy Algorthms: Wth Applcatos to mage Processg ad Patter ecogto (Sgapore: World Scetfc Publshg Co Pte td 996 [8] Ameer Al, GC Karmakar ad S Dooley, mage segmetato usg fuzzy clusterg corporatg spatal formato, ASTED ter Co o Computer Graphcs ad magg, accepted for the publcato, 003 [9] GC Karmakar, Dooley, A geerc fuzzy rule based mage segmetato algorthm, Patter ecogto etters, 3, 00, 5-7 [0] Ja Yu, Houkua Huag ad Shegfeg Ta, A Effcet Optmalty Test for the Fuzzy C-eas Algorthm, EEE ter Co o Fuzzy Systems, 00, 98-03

K-Map 1. In contrast, Karnaugh map (K-map) method provides a straightforward procedure for simplifying Boolean functions.

K-Map 1. In contrast, Karnaugh map (K-map) method provides a straightforward procedure for simplifying Boolean functions. K-Map Lesso Objectves: Eve though Boolea expressos ca be smplfed by algebrac mapulato, such a approach lacks clear regular rules for each succeedg step ad t s dffcult to determe whether the smplest expresso