# mk:fns99

### Summary

*Fuzzy-Subsethood based Color Image Processing*. Mario Köppen, Christoph Nowack and Gert Roesel. In Fuzzy-Neuro Systems 99, pages 33-40, Leipzig, Germany, 1999.

### Abstract

This paper presents the exploitation of the concept of fuzzy--subsethood for defining a new class of color image processing operations. By considering a color value as a fuzzy set, the calculus of fuzzy-subsethood becomes applicable to color images. From this, a simple color threshold operation can be defined, which gives a grayvalue image from the degrees of subsethood. Also, mathematical morphology can be extended to color images this way. For doing so, the important class of Pareto--Morphologies is introduced, and fuzzy--subsethood is used to define a new ranking scheme for multivariate data. This gives the Fuzzy-- Pareto--Morphology (FPM), which fulfills basic requirements for a generalized morphology. An extension of the difference image to color images and an operation given by an intermediate result of FPM, the M-image, are presented as new operations. Some examples of frameworks, which employs the newly defined operations, are given. It comes out, that fuzzy--subsethood allows for the definition of a new class of comprehensive color image processing operations.

### Bibtex entry

`@INPROCEEDINGS { mk:fns99,`

ABSTRACT = { This paper presents the exploitation of the concept of fuzzy--subsethood for defining a new class of color image processing operations. By considering a color value as a fuzzy set, the calculus of fuzzy-subsethood becomes applicable to color images. From this, a simple color threshold operation can be defined, which gives a grayvalue image from the degrees of subsethood. Also, mathematical morphology can be extended to color images this way. For doing so, the important class of Pareto--Morphologies is introduced, and fuzzy--subsethood is used to define a new ranking scheme for multivariate data. This gives the Fuzzy-- Pareto--Morphology (FPM), which fulfills basic requirements for a generalized morphology. An extension of the difference image to color images and an operation given by an intermediate result of FPM, the M-image, are presented as new operations. Some examples of frameworks, which employs the newly defined operations, are given. It comes out, that fuzzy--subsethood allows for the definition of a new class of comprehensive color image processing operations. },

ADDRESS = { Leipzig, Germany },

AUTHOR = { Mario Köppen and Christoph Nowack and Gert Roesel },

BOOKTITLE = { Fuzzy-Neuro Systems 99 },

MODIFIED = { 2008-02-28 16:29:29 +0900 },

EDITOR = { Gerhard Brewka and Ralf Der and Siegfried Gottwald and Andreas Schierwagen },

HASABSTRACT = { Yes },

PAGES = { 33--40 },

PDF = { fns99.pdf },

TITLE = { Fuzzy-Subsethood based Color Image Processing },

YEAR = { 1999 },

}