Nonlocal Morphological Levelings by Partial Difference Equations over Weighted Graphs

Vinh Thong Ta (1) , Abderrahim Elmoataz (1) , Olivier Lézoray (1)

1 Equipe Image - Laboratoire GREYC - UMR6072

In this paper, a novel approach to Mathematical Morphology operations is proposed. Morphological operators based on partial differential equations (PDEs) are extended to weighted graphs of the arbitrary topologies by considering partial difference equations. We focus on a general class of morphological filters, the levelings; and propose a novel approach of such filters. Indeed, our methodology recovers classical local PDEs-based levelings in image processing, generalizes them to nonlocal configurations and extends them to process any discrete data that can be represented by a graph. Experimental results show applications and the potential of our levelings to textured image processing, region adjacency graph based multiscale leveling and unorganized data set filtering.

Domaines: Traitement des images [eess.IV]

Vinh Thong Ta, Abderrahim Elmoataz, Olivier Lézoray. Nonlocal Morphological Levelings by Partial Difference Equations over Weighted Graphs. 19th International Conference on Pattern Recognition (ICPR 2008), Dec 2008, Tampa, United States. pp.1 - 4, ⟨10.1109/ICPR.2008.4761413⟩. ⟨hal-00333396⟩