科研训练总结报告

科研训练总结报告

Choosingappropriatedistancemeasurementin

digitalimagesegmentation

Andr´asHajdu1,J´anosKormos2,BenedekNagy3,andZolt´anZ¨org o41

2

3

4InstituteofInformatics,UniversityofDebrecen,H-4010hajdua@inf.unideb.huInstituteofInformatics,UniversityofDebrecen,H-4010kormos@inf.unideb.huInstituteofInformatics,UniversityofDebrecen,H-4010nbenedek@inf.unideb.huInstituteofInformatics,UniversityofDebrecen,H-4010

zorgoz@inf.unideb.huDebrecenPOBox12.DebrecenPOBox12.DebrecenPOBox12.DebrecenPOBox12.

Abstract.Inthispaperweshowhowwecantakeadvantageofusingdi erentdistancefunctionsinimageprocessingapplications.Thepro-posedmethodsarebasedonwell-knownalgorithmsthatusedistancemeasurement.Wefocusonmultidimensionalimageindexingandseg-mentationprocedures,andalsoshowexamplesfortheextractionofsuchfeaturevectorsthatcanbeusedinimageretrieval.Asaspecialfami-ly,weperformadetailedanalysisusingdistancefunctionsgeneratedbyneighbourhoodsequences.Theapplicationofsuchdistancefunctionsisquitenaturalanddescriptiveforimages,sincee.g.thecolourcoordinatesofthepixelsarenon-negativeintegers.Anadditionalinterestingprop-ertyofneighbourhoodsequencesisthattheydonotgeneratemetricsingeneral,sowecanobtainmanydistancefunctionsinthisway.Our nalpurposeisto nddistancefunctionsthatprovidethe”best”resultsforagivenproblem,sowepresentsometoolsthathelpwith ndingthem.1Introduction

Extractingrelevantdatafrommultidimensional(e.g.colour)imagesareimpor-tantoperationswithgrowinginterest[17].Iftheproblemisto ndobjectsontheimagesthentheseoperationsareknownassegmentationmethodsintheliteratureofdigitalimageprocessing.Arichfamilyoftheseproceduresmakeuseofthefactthatobjectsareusuallyde nedbyagroupofneighbouringimagepixelswithsimilarcolourvalues.Asanaturalconsequence,thesealgorithmsneedsomekindofdistancemeasurementtocomparethecoloursofthepixels.Traditionallythemostoftheseimagesegmentationtechniquesarebasedonclas-sical(e.g.Euclidean)metrics.Insomecasesothermetricsmayprovidebetterresults[6],butveryfewsuggestionscanbefoundintheliteraturehowtochoosethem.Especially,ifthedomainoftheproblemisadiscretesetlikemanycolourrepresantionsindigitalimageprocessingintegervalueddistancefunctionsarealsomightbeworthconsidering.Besidethesimplerhandlingofdigitaldistance

科研训练总结报告

2Andr´asHajdu,J´anosKormos,BenedekNagyandZolt´anZ¨org o

functionstheyoftenhavemoreillustrativebehaviourthanclassicmetrics.An-otherimportantpointisthatthesesegmentationtechniquesarebasedononlydistancemeasurementandthesatisfactionoftriangleinequalityisnotanaturalrequirementtohold.Inotherwordssuchdistancefunctionsalsomaybehavewellthatareactuallynotmetrics.

http://www.77cn.com.cnly,ourapproachisbasedondistancefunctiongeneratedbyneighbourhoodsequences,astoeveryneighbourhoodsequenceadistancefunctioncanbeassignedinanaturalway.Theusefulnessofspecialneighbour-hoodsequencesinimageprocessingapplicationswasalreadynotedinthevery rstfundamentalpapersofdigitalimageprocessing,e.g.in[18].Theprecisemathematicalbackgroundofneighbourhoodsequenceswillberecalledinthefollowingsection.Themainadvantagesofthesetypesoffunctionsthattheycanbeintroducedinarbitrary nitedimensionandalsoondi erenttypesofgrid.Moreover,wecanalsotakeadvantagethefactthatthesedistancefunctionsarenotmetricsingeneral.

Weobservethreeclassicalimageprocessingapplicationsthatarebasedondistancemeasurement,namelythede nitionofcolourranges,segmentingob-jectsbyregiongrowingandclassy ngimagepixelsbythetoolsofclusteranal-ysis.Someoftheseproceduresuseparametersandtohelpwiththeirselectionweproposesometools,namelysomehistogramscomposedfromthedi http://www.77cn.com.cningthesetoolsweillustratethebehaviourofclassicalmetricsanddistancefunctionsbasedonneighbourhoodsequences,andalsotheadvantagesofthelatterfamily.Moreover,weshowhowourproposedtoolshelpwithchoosingparameterstoobtainmoreoptimalresults.Asaverygeneraldomaininourinvestigationswefocusonthe3DRed-Gree-Blue(RGB)colourdomain.

Thestructureofthepaperisasfollows.InSection2werecallsomeconceptsandresultsfromthetheoryofneighbourhoodsequencesthatweneedinourfur-theranalysis.Section3explainstheapplicationofneighbourhoodsequencesintheRGB-domainforimagesegmentationpurposes.InSection4wepresentcon-cretetechniquesforcolorimagesegmentationusingdi erentdistancefunctions.Finally,inSection5wesummarizeourresultsandindicatesomecorrespondingopenproblems.

2Neighbourhoodsequences

Inthissectionwerecallsomebasicconceptsandresultsofthetheoryofneigh-bourhoodsequencesbasedon[4,7,18].ThoughwewillconsidertheRGBimagerepresentationindetails,wegivethenotionsforarbitrarydimension,sinceourprocedurescanbeappliedtoarbitrarydimensionalintegerimagerepresenta-tions.Inthetwodimensionalgridthetwopossibleneighbourhoodrelationswerede nedin[18]ascityblockandchessboardmotions.Basedonthesemotionsdis-tanceswerede nedasthelengthofashortestpathbetweenpointsbuildingfrom

科研训练总结报告

http://www.77cn.com.cnterthehigherdimensionalspaceswerealsoinvolvedindigitalgeometry.Letnbeanarbitrarypositiveinteger.LetqandrbetwopointsinZZn.Thei-thcoordinateofthepointqisindicatedbyPri(q).Letmbeanintegerwith1≤m≤n.Thepointsqandrarem-neighbours,ifthefollowingtwoconditionshold:

|Pri(q) Pri(r)|≤1(1≤i≤n),

n |Pri(p) Pri(q)|≤m.

i=1

Withtheconceptoftheneighbourhoodsequencesonecanvarytheusedneighbourhoodcriteriainapathinthefollowingway.Inthendimensionaldig-italspacethesequenceA=(A(i))∞N,i=1,whereA(i)∈{1,...,n}foralli∈Iiscalledann-dimensional(shortlynD)neighbourhoodsequence.Ifforsomel∈IN,A(i+l)=A(i)(i∈IN),thenAisperiodicwithperiodl.Inthiscasewebrie ywriteA={A(1)A(2)...A(l)}.Forexample,wewrite{12}fortheneighbourhoodsequence1,2,1,2,1,2,....Notethattheperiodicneigh-bourhoodsequenceswereintroducedandinvestigatedin[4,5,3,13],whilethegeneral,notneccesaryperiodicneighbourhoodsequencesareusedin[7,11,14,16].Apointsequenceq=q0,q1,...,qm=r,whereqi 1andqiareA(i)-neighboursinZZn(1≤i≤ …… 此处隐藏：21179字，全部文档内容请下载后查看。喜欢就下载吧 ……