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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Bibliographic Details
Main Author: Angulo, Jesus
Other Authors: Centre de Morphologie Mathématique (CMM), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Springer-Verlag Berlin Heidelberg
Format: Conference Object
Language:English
Published: HAL CCSD 2015
Subjects:
Hamilton > Jacobi PDE
length space
morphological PDE
morphological semigroup
Hamilton > Jacobi semigroup
[INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV]
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Iceland
Online Access:https://hal-mines-paristech.archives-ouvertes.fr/hal-01108145
https://hal-mines-paristech.archives-ouvertes.fr/hal-01108145v3/document
https://hal-mines-paristech.archives-ouvertes.fr/hal-01108145v3/file/HamiltonJacobiSemigroupMetricSpaces_ISMM15_final.pdf
https://doi.org/10.1007/978-3-319-18720-4_43
Description
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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