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...

This paper is intended as a rst introduction into mathematical morphology, and does not require any preliminary knowledge in this eld. The paper discusses the basic morphological operators, such as dilations, erosions, openings, closings, rank operators, skeletons, and reconstruction operators. Furthermore, it introduces the complete lattice framework for morphology. The paper concludes with an...

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.

Mathematical morphology is a well-established discipline whose aim is to provide speciic tools, based originally on Minkowski operators in aane spaces, for feature selection in complex objects, primarily patterns and images. Complexity of morphological operations makes it desirable to propose a theoretical scheme of an approximate morphological calculus within a general paradigm of soft computi...

In this paper, nonlocal mathematical morphology operators are introduced as a natural extension of nonlocal-means in the max-plus algebra. Firstly, we show that nonlocal morphology is a particular case of adaptive morphology. Secondly, we present the necessary properties to have algebraic properties on the associated pair of transformations. Finally, we recommend a sparse version to introduce a...