title: Nonlocal PDEs-based morphology on weighted graphs for image and data processing.
abstract: Mathematical morphology (MM) offers a wide range of operators to address various image processing problems. These operators can be defined in terms of algebraic (discrete) sets or as partial differential equations (PDEs). In this paper, we introduce a nonlocal PDEs-based morphological framework defined on weighted graphs. We present and analyze a set of operators that leads to a family of discretized morphological PDEs on weighted graphs. Our formulation introduces nonlocal patch-based configurations for image processing and extends PDEs-based approach to the processing of arbitrary data such as nonuniform high dimensional data. Finally, we show the potentialities of our methodology in order to process, segment and classify images and arbitrary data.
authors.affiliation: LaBRI, Université de Bordeaux-IPB-CNRS, F-33405 Talence Cedex, France. vinh-thong.ta@labri.fr
authors.forename: Vinh-Thong
authors.initials: VT
authors.lastname: Ta
authors.forename: Abderrahim
authors.initials: A
authors.lastname: Elmoataz
authors.forename: Olivier
authors.initials: O
authors.lastname: Lézoray
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D008962:Models, Theoretical; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity