Morphological PDE and dilation-erosion semigroups on length spacesReport as inadecuate

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1 CMM - Centre de Morphologie Mathématique

Abstract : This paper gives a survey of recent research on Hamilton-Jacobi partial dierential equations PDE on length spaces. This theory provides the background to formulate morphological PDEs for processing data and images supported on a length space, without the need of a Riemmanian structure. We first introduce the most general pair of dilation-erosion semigroups on a length space, whose basic ingredients are the metric distance and a convex shape function. The second objective is to show under which conditions the solution of a morphological PDE in the length space framework is equal to the dilation-erosion semigroups.

Keywords : Hamilton-Jacobi PDE length space morphological PDE morphological semigroup Hamilton-Jacobi semigroup

Author: Jesus Angulo -



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