HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Conference papers

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

Vinh Thong Ta 1 Abderrahim Elmoataz 1 Olivier Lézoray 1
1 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen
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.
Complete list of metadata

Cited literature [18 references]  Display  Hide  Download

Contributor : Yvain Queau Connect in order to contact the contributor
Submitted on : Tuesday, March 31, 2015 - 2:53:33 PM
Last modification on : Tuesday, October 19, 2021 - 11:34:59 PM
Long-term archiving on: : Wednesday, July 1, 2015 - 11:45:20 AM


Files produced by the author(s)



Vinh Thong Ta, Abderrahim Elmoataz, Olivier Lézoray. Partial Difference Equations over Graphs: Morphological Processing of Arbitrary Discrete Data. 10th European Conference on Computer Vision (ECCV 2008), Oct 2008, Marseille, France. pp.668-680, ⟨10.1007/978-3-540-88690-7_50⟩. ⟨hal-00333390⟩



Record views


Files downloads