The algebraic basis of mathematical morphology

Mathematical morphology on bipolar fuzzy sets: general algebraic framework

Article history: Available online 29 May 2012

Fuzzy Bipolar Mathematical Morphology: A General Algebraic Setting

Bipolar information is an important component in information processing, to handle both positive information (e.g. preferences) and negative information (e.g. constraints) in an asymmetric way. In this paper, a general algebraic framework is proposed to handle such information using mathematical morphology operators, leading to results that apply to any partial ordering.

Mathematical Morphology

Aspects of Mathematical Morphology

In this paper we review the basic concepts of integral-geometry-based morphological image analysis. This approach yields an objective, numerical characterization of twoand threedimensional patterns in terms of geometrical and topological descriptors called Minkowski functionals. We review its mathematical foundation and show that it is easy to put the theory into practice by presenting simple c...

Analytical Morphology: Mathematical Morphology of Decision Tables

We propose a method called analytical morphology for data ltering. The method was created on the basis of some ideas of rough set theory and mathematical morphology. Mathematical morphology makes an essential use of geometric structure of objects while the aim of our method is to provide tools for data ltering when there is no directly available geometric structure in the data set.