Numerical invariantization for morphological PDE schemes

Martin Welk, Pilwon Kim, Peter J. Olver

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


Based on a new, general formulation of the geometric method of moving frames, invariantization of numerical schemes has been established during the last years as a powerful tool to guarantee symmetries for numerical solutions while simultaneously reducing the numerical errors. In this paper, we make the first step to apply this framework to the differential equations of image processing. We focus on the Hamilton-Jacobi equation governing dilation and erosion processes which displays morphological symmetry, i.e. is invariant under strictly monotonically increasing transformations of gray-values. Results demonstrate that invariantization is able to handle the specific needs of differential equations applied in image processing, and thus encourage further research in this direction.

Original languageEnglish (US)
Title of host publicationScale Space and Variational Methods in Computer Vision, First International Conference, SSVM 2007, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783540728221
StatePublished - Jan 1 2007
Event1st International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2007 - Ischia, Italy
Duration: May 30 2007Jun 2 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4485 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other1st International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2007

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