Originally, mathematical morphology was a theory of signal transformations which are invariant under Euclidean translations. An interest in the extension of mathematical morphology to spatially-variant (SV) operators has emerged due to the requirements imposed by numerous applications in adaptive signal (image) processing. This paper presents a general theory of spatially-variant mathematical m...

-Fuzzy set theory has found a promising field of application in the domain of digital image processing, since fuzziness is an intrinsic property of images. For dealing with spatial information in this framework from the signal level to the highest decision level, several attempts have been made to define mathematical morphology on fuzzy sets. The purpose of this paper is to present and discuss ...

The defect morphology is an essential aspect of the evolution crystals' microstructure and its response to stress. Existing methods either only report concentration or characterize some morphologies. need for efficient comprehensive algorithm study defects becoming more evident with increase in amount simulation data improvements data-driven algorithms. We present a method defect's precisely by...

Mathematical morphology has traditionally been grounded in lattice theory. For non-scalar data lattices often prove too restrictive, however. In this paper we present a more general alternative, sponges, that still allows useful definitions of various properties and concepts from morphological theory. It turns out that some of the existing work on “pseudo-morphology” for non-scalar data can in ...

Abstraet--A new approach to digital implementation of continuous-scale mathematical morphology is presented. The approach is based on discretization of evolution equations associated with continuous multiscale morphological operations. Those equations, and their corresponding numerical implementation, can be derived either directly from mathematical morphology definitions or from curve evolutio...

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.