Morphological PDE and dilation/erosion semigroups on length spaces
International audience 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...
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Other Authors: | , , , |
Format: | Conference Object |
Language: | English |
Published: |
HAL CCSD
2015
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Subjects: | |
Online Access: | https://minesparis-psl.hal.science/hal-01108145 https://minesparis-psl.hal.science/hal-01108145v3/document https://minesparis-psl.hal.science/hal-01108145v3/file/HamiltonJacobiSemigroupMetricSpaces_ISMM15_final.pdf https://doi.org/10.1007/978-3-319-18720-4_43 |
Summary: | International audience 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. |
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