Grey-Scale Morphology Based on Fuzzy Logic

There exist several methods to extend binary morphology to grey-scale images. One of these methods is based on fuzzy logic and fuzzy set theory. Another approach starts from the complete lattice framework for morphology and the theory of adjunctions. In this paper, both approaches are combined. The basic idea is to use (fuzzy) conjunctions and implications which are adjoint in the definition of dilations and erosions, respectively. This gives rise to a large class of morphological operators for grey-scale images. It turns out that this class includes the often used grey-scale Minkowski addition and subtraction.

[1]  Stanley R Sternberg,et al.  Grayscale morphology , 1986 .

[2]  Bernard De Baets,et al.  A Fuzzy Morphology: a Logical Approach , 1998 .

[3]  E. Dougherty,et al.  Fuzzification of set inclusion: theory and applications , 1993 .

[4]  Kristel Michielsen,et al.  Morphological image analysis , 2000 .

[5]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[6]  Pierre Soille,et al.  Morphological Image Analysis: Principles and Applications , 2003 .

[7]  Hung T. Nguyen,et al.  A First Course in Fuzzy Logic , 1996 .

[8]  Isabelle Bloch,et al.  Fuzzy mathematical morphology , 1994, Annals of Mathematics and Artificial Intelligence.

[9]  G. Matheron.  Random Sets and Integral Geometry , 1976 .

[10]  H. Zimmermann,et al.  Fuzzy Set Theory and Its Applications , 1993 .

[11]  Isabelle Bloch,et al.  Fuzzy mathematical morphologies: A comparative study , 1995, Pattern Recognit..

[12]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[13]  Petros Maragos,et al.  Threshold Superposition in Morphological Image Analysis Systems , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Garyfalos Papaschinopoulos,et al.  On the fuzzy difference equation xn+1=A+xn/xn-m , 2002, Fuzzy Sets Syst..

[15]  Vartkes Goetcherian,et al.  From binary to grey tone image processing using fuzzy logic concepts , 1980, Pattern Recognit..

[16]  B. Baets,et al.  The fundamentals of fuzzy mathematical morphology, part 1 : basic concepts , 1995 .

[17]  Christian Ronse,et al.  Why mathematical morphology needs complete lattices , 1990, Signal Process..

[18]  Henk J. A. M. Heijmans,et al.  Theoretical Aspects of Gray-Level Morphology , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Frank Klawonn,et al.  Foundations of fuzzy systems , 1994 .

[20]  Etienne E. Kerre,et al.  Connections between binary, gray-scale and fuzzy mathematical morphologies , 2001, Fuzzy Sets Syst..

[21]  H. Heijmans.  Morphological image operators , 1994 .

[22]  Henk J. A. M. Heijmans.  A note on the umbra transform in gray-scale morphology , 1993, Pattern Recognit. Lett..