This paper considers various aspects of generalizing mathematical morphology towards a fuzzy discipline. Since mathematical morphology and fuzzy theory are both based on a set theory, there are many approaches for defining dilation and erosion operations of a fuzzy morphology. Among those approaches are: the alpha-Morphology; the triangular norm based approach of Bloch; the logical approach of ...

In this paper, fuzzy morpuhological image processing is explained and reviewed. Based on the mathematical morphology rules, fuzzy sets and fuzzy logic theorem fuzzy morphology operations are defined. In general mathematical morphology operation definitions are similar structures set theory and set operations definitions. For this reason fuzzy set theory is easly applied to the mathematical morp...

-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 ...

One of the extensions of binary morphology to greyscale images is given by the classical fuzzy mathematical morphology. Interval-valued fuzzy mathematical morphology further extends the latter theory by now also allowing uncertainty in the grey values of the image. In this paper, the decomposition of the intervalvalued fuzzy morphological operations into their binary counterparts is studied bot...

Based on similarities between fuzzy set theory and mathematical morphology Grabisch proposed a fuzzy morphology based on the Sugeno fuzzy integral [2]. This paper shows how these ideas can be applied to practical problems. Fast implementable definitions for erosion and dilation based on the fuzzy integral are given, their properties are discussed and some application examples are presented.

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical p...

A fuzzy data fusion approach was used for human sperm morphology recognition analysis using 3-CCD camera image data. Fuzzy operators were used to create the relationship between abnormal sperm morphology and normal sperm aberrations after digitizing the images. The approaches have focused on frequencies of sperm with either abnormal morphology in semen analysis samples. In order to establish wh...

In this work we are going to set up a new relationship between the L-fuzzy Concept Analysis and the Fuzzy Mathematical Morphology. Specifically we prove that the problem of finding fuzzy images or signals that remain invariant under a fuzzy morphological opening or under a fuzzy morphological closing, is equal to the problem of finding the L-fuzzy concepts of some L-fuzzy context. Moreover, sin...

Bipolarity has not been much exploited in the spatial domain yet, although it has many features to manage imprecise and incomplete information that could be interesting in this domain. This paper is a first step to address this issue, and we propose to define mathematical morphology operations on bipolar fuzzy sets (or equivalently interval valued fuzzy sets or intuitionistic fuzzy sets).