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 highdimensional multivariate unorganized data.

• Type: Conference
• Year: 2008
• Where: ECCV
• Authors: Vinh-Thong Ta, Abderrahim Elmoataz, Olivier Lezoray
• Keywords: Computer Vision, ECCV 2008, Image Processing Context, Image Processing Problems, Multivariate Unorganized Data, Nonlocal Configurations, Partial Difference Equations