Improving Color Image Segmentation by Spatial-Color Pixel Clustering

Size: px

Start display at page:

Download "Improving Color Image Segmentation by Spatial-Color Pixel Clustering"

Lindsey Sharp
6 years ago
Views:

1 Improving Color Imag Sgmntation by Spatial-Color Pixl Clustring Hnryk Palus and Mariusz Frackiwicz Silsian Univrsity of Tchnology, ul. kadmicka 16, Gliwic, Poland BSTCT Imag sgmntation is on of th most difficult stps in th computr vision procss. Pixl clustring is only on among many tchniqus usd in imag sgmntation. In this papr is proposd a nw sgmntation tchniqu, making clustring in th fiv-dimnsional fatur spac built from thr color componnts and two spatial coordinats. Th advantags of taking into account th information about th imag structur in pixl clustring ar shown. Th proposd 5D k-mans tchniqu rquirs, similarly to othr sgmntation tchniqus, an additional postprocssing to liminat ovrsgmntation. Our approach is valuatd on diffrnt simpl and complx imags. Kywords: imag sgmntation, spatial-color pixl clustring 1. INTODUCTION Color imag sgmntation tchniqus play a fundamntal rol in diffrnt machin vision systms. Imag sgmntation is basd on partitioning of th imag into homognous rgions corrsponding to objcts locatd in th scn. Th rsult of imag sgmntation is a much asir imag (st of labld rgions), which howvr facilitats a furthr analysis. Th rgions sparatd during sgmntation procss mt crtain homognity critria, which may b basd on color, gry lvl, txtur tc. Th growing computational capabilitis of th computr quipmnt mak possibl th us mor sophisticatd sgmntation tchniqus with additional pr-procssing,.g. dnoising filtring, and postprocssing,.g. rgion mrging. Howvr, thr is no univrsal tchniqu for color imag sgmntation. In rcnt yars hav bn publishd th rviw works on color imag sgmntation tchniqus [1 3], as wll as th first books dvotd to this subjct [4, 5]. mong th many imag sgmntation tchniqus w can find diffrnt pixl clustring tchniqus such as k-mans [6], k-harmonic mans [7], man-shift [] and othrs. Ths tchniqus blong to pixl-basd tchniqus and do not us information about th structur of th procssd imag and thus ar calld spatial blind. Th imags dominant colors naturally form clustrs in color spac and clustring tchniqus can b considrd as tools for unsuprvisd classification of hundrds of thousands and somtims millions of imag pixls. Furthr considrations will b limitd to th classic clustring tchniqu namd k-mans (KM ). KM is applid hr for clustring color pixls in thr-dimnsional color spac such GB, CIELB tc. and hnc this tchniqu will b markd as 3DKM. ftr adding two spatial pixl coordinats to th thr color componnts of pixl w can clustr pixls in th fiv-dimnsional spac, hnc th dsignation of this vrsion is 5DKM. Th dtails of such spatial-color pixl clustring ar dscribd blow. 2. SPTIL-COLO PIXEL CLUSTEING Th KM tchniqu is on of th oldst [6], most popular and also fastst clustring tchniqus. This rquirs dtrmining th numbr of clustrs k and choosing thir starting cntrs, which is an important limitation. Th sgmntation rsults using 3DKM tchniqu significantly dpnd on th position of starting cntrs of clustrs. This input data may b randomly slctd from th colors occuring in th imag. Th pixls assignd to on Furthr authors information: Hnryk Palus: Hnryk.Palus@polsl.pl, Tlphon: Mariusz Frackiwicz: Mariusz.Frackiwicz@polsl.pl, Tlphon:

2 clustr gnrally blong to diffrnt rgions of sgmntd imag. Clustring may b prformd in th GB color spac with using th Euclidan distanc d GB btwn two pixls: d GB = ( 1 2 ) 2 (G 1 G 2 ) 2 (B 1 B 2 ) 2 (1) whr: 1, G 1, B 1 - color componnts of a pixl with coordinats (X 1, Y 1 ), 2, G 2, B 2 - color componnts of a pixl with coordinats (X 2, Y 2 ) or color componnts in anothr color spac, which is th rsult of convrting th GB spac, for xampl, prcptually uniform CIELB color spac: d LB = (L 1 L 2 ) 2 (a 1 a 2 ) 2 (b 1 b 2 ) 2 (2) whr L is th luminanc, a and b ar th chrominanc componnts of th imag pixl. In ordr to tak into account th pixl coordinats has bn introducd a normalizing spatial wight factor []: M N SW = (3) m whr M N is th spatial rsolution of th imag and m is a paramtr. KM nds an assssmnt of th similarity of imag pixls to clustr cntrs. Simultanous us of color componnts and pixl coordinats in th similarity formula is a problm du to th diffrnt rangs of variability. pplication of SW factor allows to solv this kind of problm: ( ) 2 ( ) 2 d GBXY = ( 1 2 ) 2 (G 1 G 2 ) 2 (B 1 B 2 ) 2 (X1 X 2 ) (Y1 Y 2 ) (4) SW SW ftr simpl transformations w gt: d GBXY = ( 1 2 ) 2 (G 1 G 2 ) 2 (B 1 B 2 ) 2 ( ) 2 ( ) 2 m(x1 X 2 ) m(y1 Y 2 ) (5) M N M N Formula (5) applis to both sgmntation tchniqus; whn m = thn w obtain th formula (1), usful in 3DKM. Th opn qustion rmains, what should b th m paramtr s valu that proprly tak into account both aspcts: color and spatial. 3. POSTPOCESSING Th us of clustring tchniqus in imag sgmntation rquirs in its final phas a rgion labling. Oftn prforms also postprocssing in ordr to rmov ovrsgmntation, which may b th rsult of sgmntation tchniqu, poor slction of its paramtrs or a nois in sgmntd imag. On of th most ffctiv postprocssing mthods is a rmoval of small rgions from th imag by mrging thm to nighboring rgions. This task is simplifid by th arlir labling stp, which usually gnrats a list of formd rgions with information about pixl mmbrship. singl pixl can contribut only on rgion. n ara of rgion is xprssd by th numbr of pixls making up th rgion. Thus, finding rgions with an ara smallr than som thrshold is not a difficult task. 4. QULITY EVLUTION CITEI Evaluation of imag sgmntation rsults lacks both commonly accptd valuation critria and valuation procdurs. Objctiv mthods for th valuation of sgmntation rsults, dscribd in th classical work of Zhang [1], hav bn dividd into analytical and xprimntal. Howvr, sinc thr is no gnral thory of imag sgmntation, th analytical mthods ar poorly dvlopd. Exprimntal mthods ar dominatd by two approachs. Th first approach, namd mpirical goodnss, dos not rquir a rfrnc sgmntd imag and th valuation is carrid out in rspct of original imag. Exampls of goodnss masurs can b homognity of rgions and contrast btwn rgions. In th scond approach,

a discrpancy masur xprssd as a diffrnc btwn th sgmntd and rfrnc imag (ground truth) is computd. Th rfrnc imag is an imag manually sgmntd by th xprt.

Th discrpancy masur may b basd on a numbr of mis-sgmntd pixls, a position of mis-sgmntd pixls tc.

dditionally, in som cass, a final quality indx of vision systm can indicat a quality of sgmntation,.g. a rcognition rat in th cas of objct rcognition systm. Borsotti t al.

3 a discrpancy masur xprssd as a diffrnc btwn th sgmntd and rfrnc imag (ground truth) is computd. Th rfrnc imag is an imag manually sgmntd by th xprt. Gnration of such rfrnc imags is oftn problmatic, bcaus diffrnt popl crat diffrnt sgmntations for th sam imag. Th discrpancy masur may b basd on a numbr of mis-sgmntd pixls, a position of mis-sgmntd pixls tc. nothr form of valuation of sgmntation rsults is a subjctiv assssmnt carrid out by an xprt or group of xprts. dditionally, in som cass, a final quality indx of vision systm can indicat a quality of sgmntation,.g. a rcognition rat in th cas of objct rcognition systm. Borsotti t al. in th papr [] proposd for sgmntation valuation an mpirical quality function and applid it to clustring-basd sgmntation tchniqus: [ 1 2 ( ) ] 2 = i (i ) (6) 1 (M N) 1 log i i=1 whr I - sgmntd imag, M N - spatial rsolution of th imag, - th numbr of rgions in sgmntd imag, i - th ara of th rgion with indx i, ( i ) - th numbr of rgions with ara qual to i and i - th color rror of rgion with indx i. Th rror in GB color spac is calculatd as th sum of th Euclidan distancs btwn color componnts of rgion pixls and th componnts of avrag color, which is a color attribut of this rgion in sgmntd imag. First trm in (6) is a normalization factor, th scond trm pnalizs th ovrsgmntation (rsults with too many rgions), and th third trm pnalizs sgmntd imag with non-homognous rgions. Bcaus th color rror is gratr for larg rgions, th last trm is scald by th surfac ara. Th main ida of using this kind of function can b formulatd as follows: th smallr th valu of th valuation function, th bttr will b th sgmntation rsult. 5. EXPEIMENTL TESTS To study th proposd sgmntation mthods w slctd two groups of imags. In th first group ar rlativly simpl imags (Fig.1) that show uniformly colord objcts on a uniform background. Th imags wr acquird in our laboratory conditions and thir spatial rsolution is 32x2 pixls. Th scond group (Fig.2) contains complx imags dpicting natural scns and drivd from th Univrsity of Brkly imag databas [] that is frquntly usd in studis on th imag sgmntation. Th spatial rsolution of ths imags is 41x321 pixls. ll tsts wr prformd on thr simpl and thr complx tst imags. i (a) (b) (c) Figur 1. Simpl tst imags: a) Scn1, b) Scn2, c) Scn3 Both tstd 3DKM and 5DKM tchniqus wr initializd randomly by choosing random coordinats of pixls, which color componnts dtrmin th initial clustr cntrs. In th cas of 3DKM wr usd th color componnts only and in th cas of 5DKM additionally th pixl coordinats. andom initialization rquird th sris of drawings; in ach imag sgmntation 1 random drawings for ach clustr ar adoptd. Th numbr of clustrs for simpl imags (k = ) was smallr than numbr of clustrs for complx imags (k = 32). Th us of 5DKM tchniqu rquird also a dfinition of valus of m paramtrs. Fig.3 prsnts a rlationship btwn th valus of valuation function avragd ovr 1 random drawings and th valu of m paramtr in th

(a) (b) (c) Figur 2. Complx tst imags []: a) #3, b) #44, c) #2461. (a) (b) Figur 3. Sgmntation quality vs m paramtr valu: a) simpl imags, b) complx imags. Tabl 1.

from to 15. On th basis of ths tst rsults th authors proposd for simpl imags m = 2 and for complx imags m = 14. In both KM tchniqus was applid th sam numbr of itrations qual to 2.

Th thrshold valu should b slctd according to th scn and cannot b gratr than an ara of rgion corrsponding to th smallst objct that should b sgmntd.

4 (a) (b) (c) Figur 2. Complx tst imags []: a) #3, b) #44, c) #2461. (a) (b) Figur 3. Sgmntation quality vs m paramtr valu: a) simpl imags, b) complx imags. Tabl 1. Valus of critrion for simpl imags (k = ) Simpl imags Scn1 Scn2 Scn3 Q(I 3DKM 5DKM 3DKMPP 5DKMPP rang from to 15. On th basis of ths tst rsults th authors proposd for simpl imags m = 2 and for complx imags m = 14. In both KM tchniqus was applid th sam numbr of itrations qual to 2. Th postprocssing dscribd in th Sction 3 and dpndnt on th thrshold valu (small rgion ara) is usd in ordr to improv th sgmntation rsults. Th thrshold valu should b slctd according to th scn and cannot b gratr than an ara of rgion corrsponding to th smallst objct that should b sgmntd. doptd valus of ar includd in th tabls showing th rsults (Tabl 1 and Tabl 2). 6. CONCLUSION sults of th studis on 5DKM tchniqu hav shown that ovrsgmntation in sgmntd imags is lss than in th cas of 3DKM tchniqu. Similarly, in th cas of 5DKM th valu of valuation funktion is gnrally

5 Tabl 2. Valus of critrion for complx imags (k = 32) Complx imags 3DKM 5DKM 3DKMPP 5DKMPP #3 #44 # also smallr. This suggsts that th simultanous inclusion of color and spatial information in th procss of clustring improvs obtaind sgmntation rsults. similar approach using locally fiv-dimnsional fatur spac is currntly bing dvlopd in th form of suprpixl SLIC tchniqu []. Prsntd in th articl, th spatial-color sgmntation tchniqu basd on KM clustring in fiv-dimnsional spac, can b also dvlopd for othr clustring mthods, particularly thos which ar gnralization of KM, as.g. KHM. CKNOWLEDGMENTS This work was supportd by Polish Ministry for Scinc and Highr Education undr intrnal grant BK- 265/u1/214 for Institut of utomatic Control, Silsian Univrsity of Tchnology, Gliwic, Poland. EFEENCES [1] Vantaram, S.. and Sabr, E., Survy of contmporary trnds in color imag sgmntation, Journal of Elctronic Imaging 21(4), (2). [2] Palus, H., Color imag sgmntation: slctd tchniqus, in [Color Imag Procssing: Mthods and pplications], Lukac,. and Plataniotis, K., ds., 13 1, CC Prss, Boca aton, F, US (26). [3] Chng, H., Jiang, X., Sun, Y., and Wang, J., Color imag sgmntation: advancs and prospcts, Pattrn cognition 34(), (21). [4] Zhang, Y.-L., [dvancs in Imag and Vido Sgmntation], IM Prss, Hrshy, P, US (26). [5] Ho /d./, P.-G. P., [Imag Sgmntation], InTch, ijka, Croatia (2). [6] MacQun, J., Som mthods for classification and analysis of multivariat obsrvations, in [Procdings of th 5th Brkly Symposium on Mathmatics, Statistics, and Probabilitis, Brkly C, US], (167). [7] Zhang, B., Hsu, M., and Dayal, U., K-harmonic mans - data clustring algorithm, Tch. p. T HPL- 1-4, Hwltt Packard Labs, Palo lto, C, US (1). [] Comaniciu, D. and Mr, P., Man shift: robust approach toward fatur spac analysis, IEEE Trans. Pattrn nal. Mach. Intll. 24, (May 22). [] Hsu, C.-Y. and Ding, J.-J., Efficint imag sgmntation algorithm using SLIC suprpixls and boundaryfocusd rgion mrging, in [Procdings of th Intrnational Confrnc on Information, Communications and Signal Procssing (ICICS)], 1 5 (Tainan, Taiwan, 213). [1] Zhang, Y. J., survy on valuation mthods for imag sgmntation, Pattrn cognition 2(), (16). [] Borsotti, M., Campadlli, P., and Schttini,., Quantitativ valuation of color imag sgmntation rsults, Pattrn cognition Lttrs 1(), (1). [] Martin, D., Fowlks, C., Tal, D., and Malik, J., databas of human sgmntd natural imags and its application to valuating sgmntation algorithms and masuring cological statistics, in [Procdings of th th Intrnational Confrnc on Computr Vision], (Vancouvr, BC, Canada, 21).

Homotopy perturbation technique

Homotopy perturbation technique Comput. Mthods Appl. Mch. Engrg. 178 (1999) 257±262 www.lsvir.com/locat/cma Homotopy prturbation tchniqu Ji-Huan H 1 Shanghai Univrsity, Shanghai Institut of Applid Mathmatics and Mchanics, Shanghai 272,