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1、BoundaryExtractioninNaturalImagesUsingUltrametricContourMapsPabloArbelaez´CEREMADE,UMRCNRS7534UniversiteParisDauphine,´PlacedumarechaldeLattredeTassigny,75775Pariscedex16,France´arbelaez@ceremade.dauphine.frAbstractThispaperpresentsalow-levelsystemforboundaryex-tractionandsegmentat
2、ionofnaturalimagesandtheeval-uationofitsperformance.Westudytheproblemintheframeworkofhierarchicalclassification,wherethegeomet-ricstructureofanimagecanberepresentedbyanultra-metriccontourmap,thesoftboundaryimageassociatedtoFigure1.Naturalimageandcompositehumansegmentation.afamilyofn
3、estedsegmentations.Wedefinegenericultra-metricdistancesbyintegratinglocalcontourcuesalongtheregionsboundariesandcombiningthisinformationwithre-ofregionsandscaleareformalizedbythestructureofin-gionattributes.Then,weevaluatequantitativelyourre-dexedhierarchyor,equivalently,bythedefinit
4、ionofanul-sultswithrespecttoground-truthsegmentationdata,prov-trametricdistanceontheimagedomain.Wepresentafor-ingthatoursystemoutperformssignificantlytwowidelymulationoftheproblemintermsofcontoursthatallowstousedhierarchicalsegmentationtechniques,aswellastherepresentanindexedhierarc
5、hyofregionsasasoftboundarystateoftheartinlocaledgedetection.imagecalledultrametriccontourmap.Sincetheearlydaysofcomputervision,thehierarchicalstructureofvisualperceptionhasmotivatedclusteringtech-1.Introductionniquestosegmentation[13],whereconnectedregionsofHierarchicalorganization
6、isoneofthemaincharacteris-theimagedomainareclassifiedaccordingtoaninter-regionticsofhumansegmentation.Ahumansubjectsegmentsadissimilaritymeasure.Weconsiderthetraditionalbottom-naturalimagebyidentifyingphysicalobjectsandmarkingupapproach,alsocalledagglomerativeclustering,wheretheirbo
7、undariesuptoacertainlevelofdetail.Ifwesupposetheregionsofaninitialpartitionareiterativelymerged,andthatdifferentsubjectssegmentingasingleimageperceivewecharacterizethosedissimilaritiesthatareequivalenttothesameobjectsthen,uptovariationsintheexactlocaliza-ultrametricdistances.tionof
8、boundaries,theintersection
