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1、IEEETRANSACTIONSONPATTERNANALYSISANDMACHINEINTELLIGENCE,VOL.PAMI-8,NO.5,SEPTEMBER1986669ContributiontothePredictionofPerformancesof2)the"one-to-many"(1-to-m)whereforeachfeaturepointintheHoughTransformthepictureplane,severalaccumulatorcellsareincremented(see,
2、forinstance,[10]foradiscussionofthesemethods).HENRIMAITREWeknowthatm-to-mand1-to-Imethodsarealsoavailable,takingadvantageofpartialderivativeinformation,buttheywillnotbeconsideredhere.Abstract-ExactpredictionsoftheperformancesoftheHoughde-II.THEm-to-ICASEPROB
3、LEMSTATEMENTtectionofstraightlinesintwo-dimensionalimagesarepresentedforrectangularandcircularretinas,inCartesianandnormalparameter-LetMbeafeaturepointintheimageplaneand(Rbetheretinaization,inthecaseofnoisysignals.Detectionofcircles,underthesameoftheimage(i.
4、e.,theexistencedomainofM).Wesupposethatassumptions,isdiscussed.Thelimitsofadaptivequantizationtore-thepicturespace8isacontinuousspace;thisassumptiondeservesduceintrinsicnoisearepresented,anditisshownthatasignalpro-specialattention,duetothefiniteresolutionofn
5、umericalimages,cessingapproachisespeciallyconvenienttomeasuretheperformancesbutthediscretecase,nowbeinginvestigatedbyLopez-Krahe[12],ofadetectorbasedontheHoughtransform.isfarmoredifficultandwillnotbepresentedhere.LetAbeanypointintheHough(orparameter)spaceSCa
6、ssociatedwiththeIndexTerms-Circledetection,Houghtransform,performancepre-structurewearelookingfor.diction,straightlinedetection.Theperformancepredictionproblemcanbestatedasbelow."GivenanyprobabilitydensityfunctionofMon(R,isitI.INTRODUCTIONpossibletodetermine
7、theprobabilitydensityfunctionofA?"TheusefulnessoftheHoughtransformforthedetectionofstruc-turesinimagesisprovenbytheabundanceofliteratureinthisfieldLetP(M)betheprobabilitydensityfunctionofMandP(Mi/Mj)(forarecentsurvey,see[1,pp.692-696]and[2]).Thedetectionbeth
8、econditionalprobabilitydensityfunctionofMiwhenMjisofparametricornonparametriccurvesappearstobeoneoftheknown.importantstepstowardsrobotvision,andtheHoughtransformisIfC(A)istheparametriccurveinSas
