euler弹性修复模型及其split+bregman快速算法

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1、Abstract1nep锄ajdlfierentialequations(PDE)isoneofthemainstreammethodsofimgepmcessmg·Image却ai毗gmodelsbasedonpartialdifferentialeq嘶011Shavegoodefiectonnon-textureimageinpainting．TheEulerelasticmodelthrou曲thein仃DductionoftheEuler'elasticterm，usethesmoothcurvetoinp豳血＆毗匮chnot011lysolv

2、etheunco皿ectlvltyprincipleofthetraditionalTVandMumford．Shahmodel，butalsomakepossibletobandle1agre-areaimageinpainting．ItmakesthecornpleXityofdi茂renceschemeandleadstohugecalculationandlowefficiencyiflls谊gtraditionaJgradientdescend?ethod，诎charegreatlyhinderedthejrealityoftheimage娜

3、血t吨techmquesj1nep雄财eIaborated出eprincipleofdigitalimageinp砌ingte蛳quesandpartiajdlfferentlaLlequatioIlS，introducedseveraltraditionalmodelsbasedonpartialdi位reIItiaLIequaff0璐andtheirprinciples，statedadvantagesanddisadv趾tagesofeachmodel．a11dmalmyIntroduced出eEulerelasticinpaintingmode

4、landitsmechanismandprinciple．Forme饥挝1tlonal删entdescendalgorithmefficiencyproblem，we蛾南rnltheorig访aJVariationalmodelintoasimpleiterativeoptimizationmodeluSingSplitBre鲫an副gonttlmbymtroduciIlgsomeauxiliaryvariablesandBre舯a11ite枷vep黝n她andsolVe1tⅥaaJtematingminimizationprocedure．Thefi

5、nalequationsareaseriesofsimDIe删er-L鲫geeq删ionoftheprimalvariableandsomegeneralizedsoR慨Sholding士onnuJaSwltIl场ghcomputationefficiency．Throughmultipleexperimentst0verifI，thee牡ectivenessalldcomputationalefficiencyofthe出90ritbIll．Finally，describedtheappllca缸0nsoftheEulerelastictermint

6、heotherareasofima99processingbythecombmatlonofthecurrentstituation，andpointedoutthedirectionof如眦researchbvcombinedingwithproblemsanddefectsintbisarticle。KeyWords：Imageinpainting；Euler'seIasticterm；PDE；SpHtB唧aⅡAlgorithm㈣㈣IIIIIIIIIIIIIIIIIIMIIIIIIIIY2338028目录第一章绪论⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯

7、⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯11．1研究目的与意义⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯11．2国内外研究现状⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯21．3主要工作及章节安排⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯3第二章数字图像修复理论基础⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯52．1数字图像修复原理⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯52．2图像修复原则⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯62．3偏微分方程方法⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯72．4本章小结

8、⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．⋯⋯⋯⋯⋯⋯⋯⋯⋯一9第三章基于PDE的经典修复模型⋯