Morphological image processing has been based traditionally on modeling images as sets or as points in a complete lattice of functions and viewing morphological image transformations as set or lattice operators. Thus, so far, the two classic approaches to analyzing or designing the deterministic systems of mathematical morphology have been (1) geometry, by viewing them as image set transformati...

In the present thesis various aspects concerning discretisation and approximation of images and morphological image operators are systematically investigated. Binary images in the context of morphological image operators, which is considerably presented in the monograph Morphological Image Operators by Henk Heijmans, are modelled as subsets of a basic set. Thus the starting point is the discret...

In this paper, we present a methodology for automatic pattern recognition of binary images objects using morphological operators and genetic programming. The results are expressed in terms of the basic morphological operators and logical operators. Genetic Programming (GP) is based on concepts of genetics and Darwin’s principle of natural selection to genetically breed and evolve computer progr...

Partial Differential Equations (PDEs)-based morphology offers a wide range of continuous operators to address various image processing problems. Most of these operators are formulated as Hamilton–Jacobi equations or curve evolution level set and morphological flows. In our previous works, we have proposed a simple method to solve PDEs on point clouds using the framework of PdEs (Partial differe...

This paper introduces a new and more appropriate ECG signal preprocessing using mediated morphological filters. These filters are based on a particular combination of median operator and classical morphological operators. The proposed method has been applied to adult and fetal ECG signals as an efficient preprocessing task. Accurate numerical descriptions demonstrate better performance quality ...

Multimodal medical images are often of too different a nature to be registered on the basis of the image grey values only. It is the purpose of this chapter to construct operators that extract similar structures from these images that will enable registration by simple grey value based methods, such as optimization of cross-correlation. These operators can be constructed using only basic morpho...

In the framework of structural representations for applications in image understanding, we establish links between similarities, hypergraph theory and mathematical morphology. We propose new similarity measures and pseudo-metrics on lattices of hypergraphs based on morphological operators. New forms of these operators on hypergraphs are introduced as well. Some examples based on various dilatio...

The aim of this paper is to characterize morphological convex geometries (resp., antimatroids). We define these two structures by using closure operators, and kernel operators. We show that these convex geometries are equivalent to poset geometries. 2000 Mathematics Subject Classification. 37F20, 06A07.

In this paper we introduce a class of morphological operators with applications to sharpening digitized grey valued images. We introduce t.he underlying partial differential equation (PDE) that governs this class of operators. For discrete implementations of the operator class! we show that instances utilizing a parabolic structuring function, have special properties that lead to an efficient i...

Please cite this article in press as: J. Angulo, Geom I: Colour quaternions, J. Vis. Commun. (2009), d The definition of morphological operators for colour images requires a total ordering for colour points. A colour can be represented by different algebraic structures, in this paper we focus on real quaternions. The paper presents two main contributions. On the one hand, we have studied differ...