Partial Difference Equations over Graphs: Morphological Processing of Arbitrary Discrete Data

Authors:
Vinh-Thong Ta;Abderrahim Elmoataz;Olivier Lézoray
Affiliations:
University of Caen Basse-Normandie, GREYC CNRS UMR 6072, Image Team, Caen Cedex, France F-14050;University of Caen Basse-Normandie, GREYC CNRS UMR 6072, Image Team, Caen Cedex, France F-14050;University of Caen Basse-Normandie, GREYC CNRS UMR 6072, Image Team, Caen Cedex, France F-14050
Venue:
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Year:
2008

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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.