Partial Difference Equations over Graphs: Morphological Processing of Arbitrary Discrete Data
Abstract
Mathematical Morphology (MM) offers a wide range of operators to address various image processing problems. These processing can be defined in terms of algebraic set or as partial differential equations (PDEs). In this paper, a novel approach is formalized as a framework of partial difference equations (PdEs) on weighted graphs. We introduce and analyze morphological operators in local and nonlocal configurations. Our framework recovers classical local algebraic and PDEs-based morphological methods in image processing context; generalizes them for nonlocal configurations and extends them to the treatment of any arbitrary discrete data that can be represented by a graph. It leads to considering a new field of application of MM processing: the case of high-dimensional multivariate unorganized data.
Cite
Text
Ta et al. "Partial Difference Equations over Graphs: Morphological Processing of Arbitrary Discrete Data." European Conference on Computer Vision, 2008. doi:10.1007/978-3-540-88690-7_50Markdown
[Ta et al. "Partial Difference Equations over Graphs: Morphological Processing of Arbitrary Discrete Data." European Conference on Computer Vision, 2008.](https://mlanthology.org/eccv/2008/ta2008eccv-partial/) doi:10.1007/978-3-540-88690-7_50BibTeX
@inproceedings{ta2008eccv-partial,
title = {{Partial Difference Equations over Graphs: Morphological Processing of Arbitrary Discrete Data}},
author = {Ta, Vinh-Thong and Elmoataz, Abderrahim and Lezoray, Olivier},
booktitle = {European Conference on Computer Vision},
year = {2008},
pages = {668-680},
doi = {10.1007/978-3-540-88690-7_50},
url = {https://mlanthology.org/eccv/2008/ta2008eccv-partial/}
}