基于偏微分方程的图像修补

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1、西安理工大学硕士学位论文Title:PDE-basedImageInpaintingMajor:ComputationalMathematicsAuthorName:Signature:Supervisor:Signature:AbstractImagerestorationisanimportantcontentinimageprocessing.Thepurposeistorepairscratchesanddefectinimages,orremovetheobjectwiththespecifiedtextinim

2、ageusingsomealgorithms,andultimatelyachievespecificgoals.Inrecentyears,imageinpaintingmethodbasedonpartialdifferentialequations(PDE)tobecomeanimportantimageprocessingscienceresearchcomponent.PDE-basedpatchrepairprocessmodelistotransformtheimagerepairprocessintoase

3、riesofpartialdifferentialequationsortheenergyfunctionalmodel,furtheruseofnumericaliterativemethodstorepairingimages.Thesealgorithmscanmaketherepairareaaroundwaitingforvaluableinformationinaccordancewiththeirowninwarddiffusionisophotepatchimage,whilemaintainingthes

4、moothedgesoftheimageunderthepremiseofthenoise.Thispaperfocusesonimagerepairprocessmethodbasedonpartialdifferentialequations.Indefacedregioninitialization,takingintoaccountthecorrelationbetweendefacedregioninformationandmissinginformation,therelevantrandominitializ

5、ationprogramisdesigned.Comparisonwithotherinitializationprograms,theprogramforpatchingeffectscanactivelyimproveandenhancetheefficiencyofrepairimages.Fortotalvariationpatchingmodel,thispaperanalyzeddetailedtheinfluenceoftheimagegradientandcurvatureofthelevelsettoth

6、econductioncoefficient.ThemorenaturalrepaireffectisobtainedbymodifiedCDDmodel.Meanwhile,takingintoaccountthediffusionalongthetangentialandnormalofisophotes,aunifiedrepairmodelisproposedbycombinationthemodels.Experimentalresultsshowthatthemodelcaneffectivelyimprove

7、thepatchrepairresults.Keywords：partialdifferentialequation;imageinpainting;imagedenoising;curvevolution2目录目录1绪论............................................................................................................................11.1研究目的与意义..................

8、............................................................................11.2偏微分方程图像处理研究进展...........................................................