Hierarchical representations are ubiquitous in morphological image processing and are mathematically modeled as ultrametric spaces. In this talk, morphological operators for functions defined on ultrametric spaces are considered. The notion of ultrametric structuring function is introduced. Then, using as fundamental ingredient the convolution in the (max,min)-algebra, the multi-scale ultrametric dilation and erosion are defined and their semigroup properties are stated.

This presentation is part of Minisymposium “MS48 - Recent Advances in Mathematical Morphology: Algebraic and PDE-based Approaches”
organized by: Martin Welk (Private University for Health Sciences, Medical Informatics and Technology (UMIT)) , Michael Breuss (Brandenburg University of Technology) .

Authors:

Jesús Angulo (Center for Mathematical Morphology, Départ. de Mathématiques et Systèmes, MINES ParisTech)

Keywords:

mathematical morphology, nonlinear image processing, ultrametric space