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

6

)

%(PMNABHATTACHARYYA DISTANCE

Fig.results7.ANMPastechniqueobtainedGammawiththewithafunction3-stagetheparametricoftheBhattacharyyadistanceBforsegmentationstrategyonstatisticalapproachandtheproposedrealizationsandNonparametricandPoissonstatisticalthesegmentationGLPDs.Eachapproach.isANMPtheimageofFig.2awithGaussian,(b)performedhasbeenParametricwithestimatedon20noisestatistical

thelevelapproach.

setsnake.(a)(a)(b)(c)(d)

Fig.line)8.(a)Syntheticimages(115×83pixels)obtainedandproposedwithGammaGaussian(second(b)line)andnoisesGammawith(c)Bperturbed=0.29.SegmentationwithGaussianresults( rstusedandapproachtheinitialwithcontourthe3is-stagetheonestrategyofFig.(d).models2b.

TheforlevelthesetGLPDssnakehasandbeentheFirst,letusconsiderthecaseofgraylevelsintheimagesthatthatarepurposedistributedoneconsidersaccordingdifferenttotheexponentialnoisyversionsfamily.ofFortheimagebutions.ofTheFig.2aevolutionwithGaussian,oftheANMPGammaasorafunctionPoissonofdistri-theBhattacharyyadistanceBisshowninFig.7.20realizationsofdifferentthescenevalueswereofgeneratedB.Theobtainedforeachimagesnoisehavemodelbeenandseg-formentedeitherwiththeparametricstatisticalapproachorwiththeofthe3-stageproposedstrategy.approachFig.7areillustratessimilarthatforthethethreeperformancestypesofpdf.nonparametricMoreoverstatisticaltheparametricapproachstatisticalofthispaperapproachleadtoandsimilarthevaluesoftheANMPwhenB≥0.3.IfB<0.3theproposedapproachapproachprovidesthatalsoworseleadstoresultsdegradedthantheperformance.

parametricstatisticalClearly,ournonparametricmethoddoesnotrelyonagivenmodel.thatcanThisproduceisaverymajorbadadvantageresultsiftheoverparametricparametricmodelmethodsdoesnoteffectcorrespondandcomparestothebothnoiseapproachinthedata.onaFig.synthetic8illustratesimagewiththisdifferentnoisedistributions.

paperInconclusion,withthe3-stagethenonparametricstrategyleadsapproachtosatisfactoryproposedresultinthisincomparisontotheonesobtainedwithaparametricmodeladaptedrobustness.

tothegraylevel uctuationsbutwithastrongerIEEETRANSACTIONSONIMAGEPROCESSING,VOL.??.NO.??,

????

E.Realimages

amplesWeproposeobtainedtowithshowtheinproposedthissubsectionnonparametricsegmentationstatisticalex-techniqueandthe3-stagestrategyondifferenttypesofrealimages.IntelXeonThe2.segmentations8GHZ(Linuxhave2.4,beengcc2performed.96)with900withMoaPCofRAMandthecomputationaltimesareprovidedinthecaptionsofthe gures.

tion.WeIn rstFig.show9ctheresults nalobtainedcontourobtainedwiththelevelonasetrealimplementa-SARimagecorruptedwithspecklenoiseisrepresented.Thesegmentationresultnoise[37]onaislasershownilluminatedinFig.9f.imageInFig.perturbed10,onewithcanspeckleseethesegmentationFig.10atheresultresultonobtainedavideowhentexturedthetechniqueimage.Weisshowappliedinontheimage.Onecanseeinthatcasethatthetechniqueisinef cientnonhomogenoussincetheregions.presenceHowever,ofshadowsifoneintheconsidersimagetheleadsnewtoimagefde nedbyf(x,y)=|FVFVandFHaretheRoberts s lters(x,y)[38]|2+|FHde ned s(x,withy)|2wherea3×3pixelneighborhoodsand istheconvolutionoperator,oneobtainsanimagewithtworegionsmorehomogenous.Indeed,continuousthevariationgradientoperatorofthegrayallowslevels.onetoThesuppresssegmentationlinearresultisshownonthisinpreprocessedFig.10dandimageonewithcantheseeproposedinFig.technique10bandFig.10cthatparametricstatisticalapproachesdonotleadtosatisfactoryacquiredwithsegmentations.aCCDcameraAnalogousisshownresultinFig.ona11RGBwhereimagetheconsideredpreprocessingnowsimplyconsistsinextractingthesegmentationhuecomponentexampleintheobtainedHSVrepresentationonthehuecomponent[39].AnotherofaRGBimageisshowninFig.12.

WeshowinFig.13segmentationresultsobtainedwithapolygonalcomponentsnakeintheadaptedHSVrepresentationtotworegions.areResultsshownoninFig.theHue13bandonaFig.gray13f.levelInimageFig.13d,whichthesegmentationhasbeenpreprocessedhasbeenobtainedinordertoobtainanewimagegde nedbyg(x,y)=s(x,y) s(x+1,y+1)inwhichthedifferentregionsaremorehomogenous.WeshowinFig.14segmentationresultsobtainedwithaSegmentationpolygonalsnakeresultsadaptedhaverespectivelyto3regionsbeenonobtainedRGBimages.ontheHueonthecomponentsaturationincomponenttheHSVrepresentationintheHSVrepresentationinFig.14bandinFig.14d.TheimageinFig.14cisextractedfromtheBerkeleyDatasetofnaturalimages[40].

Theseresultsshowthattheproposedapproachallowsonetodealwithverydifferenttypesofimages.

IV.CONCLUSION

Wehaveproposedanonparametricstatisticalsnakebasedonthethegrayminimizationleveldistributionsoftheofstochastictheobjectcomplexityandofthebackgroundandwhereareapproximatedbystepfunctionswhoseparametersarees-timatedtominimizeduringathecriterionsegmentationwithoutprocess.freeparameterThisapproachtobetuned

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