IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL.. NO., 1 Nonparam(7)

Abstract — We propose a nonparametric statistical snake technique that is based on the minimization of the stochastic complexity (minimum description length principle). The probability distributions of the gray levels in the different regions of the image

(a)(b)(c)

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(e)

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Fig.by(b)the9.ERS-(a)1SARimage(120×108pixels)ofanagriculturalareaobtained(computationInitialcontour.satellite(distributedbytheESAandprovidedbytheCNES).pixels).time:15(c)Finalcontourobtainedwiththe3-stagestrategy(computation(e)Initialseconds).(d)Sceneilluminatedbyalaser(41×34bettervisualization,timecontour.:(f)Finalcontourobtainedwiththe3-stagestrategythe0.4contrastseconds).ofThethelevelimagessethassnakebeenhasincreased.

beenused.Fora(a)(b)(c)(d)

Fig.camera.10.technique(a)SegmentationSegmentationofresultanimageobtained(86×with60pixels)theproposedacquirednonparametricwithaCCDcessedaversionwithofthe(a)3-stageobtainedstrategy.with:Results(b)aGaussianofthesegmentationmodelfortheonGLPDs,aprepro-techniqueGammamodelfortheGLPDs,(d)theproposednonparametricstatistical(c)kindofinitializationwiththe3-stagethaninstrategyFig.9b(computationhasbeenusedtimefor:4theseconds).levelsetThesnake.

samebytheuserandcanbeimplementedwithdifferentcontourdescriptorsWehaveillustratedsuchaslevelthesetresultssnakeonorpolygonalSAR,videocontour(color)model.andtexturedimages.Moreover,uptolowcontrastvalues,wehaveshownexponentialthatwhenfamily,thethegrayproposedlevelpdfapproachoftheimageprovidebelongsegmen-tothetationstatisticalresultsapproachequivalent.Oftocourse,thoseobtainedthemainwithadvantageaparametricoftheproposednonparametricstatisticaltechniqueisitsrobustnesssincewithoutitadaptsrequiringtotheapriori uctuationinformation.

distributionsofthegraylevelsThereexistsdifferentperspectivestothiswork.Itwouldbeinterestingtogeneralizethistechniquetoothermultiregionapproachesintoaccountbasedpossibleforexamplespatialcorrelationsonlevelsetistechniques.alsoachallengingTakingproblem.

ACKNOWLEDGMENTS

TheauthorsaregratefultoConseilR´egionalPACAfortakingpartinthe nancingofthePhDofPascalMartin.

REFERENCES

[1]M.Kass,[2]models,”I.contourC.GregInt.A.andJ.Witkin,J.ofComput.andD.Vis.Terzopoulos,,vol.1,pp.321–331,“Snakes:1988.

Activecontour

Trans.ImagemodelProcessing(nns-snake)N.Hwang,,vol.for“Acontourneural4,pp.1407–1416, ndingnetwork-basedofdistinctstochasticactive

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features,”IEEE7

Y

0.2

HISTOGRAM (68 BINS)STEP FUNCTION (q=26)

CN(a)(b)

EUQE 0.1

OBJECT

RF 0(c)

(d)

BINS’ INDEX

Fig.pixels11.Exampleoflevelsnakeimageandinitialcontour.(b)Segmentationsegmentation.result(a)RGBobtainedimageonwith227×174huethecomponentwithaGaussianmodelfortheGLPDs.Segmentationobtainedthegrayonleveltheseconds).proposednonparametricintheHSVrepresentationstatisticaltechniquewith:(c)(computationaGaussiantimemodel,(d)objectinthe(e)Histogramhuecomponent.

(solidline)andestimatedGLPDs(dottedline):of21the.4(a)(b)

Fig.and12.(a)RGBimageacquiredwithaCCDcamera(inwithHSVinitialrepresentationcontour.(b)Segmentationresultsobtainedonthe320hue×240componentpixels)timethe:753-stageseconds).

strategywithandthetheproposedlevelsetnonparametricsnakeimplementationstatistical(computationtechnique(a)(b)(c)(d)

(e)(f)

Fig.RGB13.Examplesofsegmentationobtaineddisplayedimageonwiththehue214component×278pixelsoftheandHSVinitialwithrepresentationcontour.thepolygonal(computation(b)Finalsnake.contour(a)time:8.8seconds).(c)Graylevelsimagewith159×138pixelsandinitialcontour.(d)timeFinalbeen:2.2contourseconds).obtainedForabetteronavisualization,preprocessedtheversionof(c)(computationSegmentationincreased.(e)RGBimagewith492×283pixelscontrastandinitialoftheimageshas(computationresultstime:10obtainedseconds).

onthehuecomponentHinHSVrepresentationcontour.(f)