Contrast invariant image analysis and PDE’s

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1、ContrastinvariantimageanalysisandPDE’sFr´ed´ericGuichardJean-MichelMorelRobertRyan2ContentsIntroduction1I.1Images.................................1I.2Imageprocessing...........................3I.3PDEsandimageprocessing.....................11I.4Notationandbackgroundmaterial.

2、................30I.4.1Aframeworkforsetsandimages..............34ILinearImageAnalysis371TheHeatEquation391.1LinearsmoothingandtheLaplacian................391.2Existenceanduniquenessofsolutionsoftheheatequation....411.3Exercises...............................451.4Commentsand

3、references......................472IteratedLinearFiltersandtheHeatEquation492.1SmoothingandtheLaplacian....................492.2Theconvergencetheorem......................512.3Directionalaveragesanddirectionalheatequations........542.4Exercises..............................

4、.552.5Commentsandreferences......................563LinearScaleSpaceandEdgeDetection593.1Theedgedetectiondoctrine.....................593.1.1Discussionandcritique...................603.2Exercises...............................653.3Commentsandreferences......................

5、664FourAlgorithmstoSmoothaShape674.1Dynamicshape............................674.2Curveevolutionusingtheheatequation..............684.3Restoringlocalityandcausality...................694.3.1Localizingthedynamicshapemethod...........704.3.2Renormalizedheatequationforcurves...

6、........714.4Exercises...............................724.5Commentsandreferences......................73iiiCONTENTSIIContrast-InvariantImageAnalysis755Contrast-InvarianceandLevelSets775.1Fromanimagetoitslevelsetsandback..............785.2Contrastchangesandlevelsets..........

7、.........795.3Exercises...............................845.4Commentsandreferences......................846Specifyingthecontrastofimages856.1Midwayequalization.........................876.2Experimentingmidwayequalizationonimagepairs........896.2.1Movieequalization............

8、..........936.3Commentsandreferences......................937Contrast-InvariantMon