Binary, gray-scale, and vector soft mathematical morphology: Extensions, algorithms, and implementations

Publisher Summary This chapter discusses standard morphological operations, their algebraic properties, and fuzzy morphology. Soft morphological filters are a relatively new subclass of nonlinear filters. They were introduced to improve the behavior of standard morphological filters in noisy environments. Soft mathematical morphology and the definitions of vector soft morphological operations, their basic properties, and their use in color impulse noise attenuation are provided in the chapter. Several implementations of soft morphological filters and an implementation of vector morphological filters are analyzed in the chapter. Soft morphological operations are based on weighted order statistics. Algorithms for implementation of soft morphological operations include the well-known mergesort and quicksort algorithms for weighted order statistics computation. Fuzzy soft mathematical morphology applies the concepts of soft morphology to fuzzy sets. The definitions and the algebraic properties are illustrated in the chapter through examples and experimental results.

[1]  Frank Y. Shih,et al.  Analysis of the properties of soft morphological filtering using threshold decomposition , 1995, IEEE Trans. Signal Process..

[2]  Antonios Gasteratos,et al.  A new algorithm for weighted order statistics operations , 1999, IEEE Signal Processing Letters.

[3]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[4]  V. Barnett.  The Ordering of Multivariate Data , 1976 .

[5]  Jaakko Astola,et al.  Soft morphological filters: a robust morphological filtering method , 1994, J. Electronic Imaging.

[6]  B. Ripley,et al.  Pattern Recognition , 1968, Nature.

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

[8]  Peter Grant.  IEE Proceedings - Vision Image and Signal Processing , 1994 .

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

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

[11]  Divyendu Sinha,et al.  Fuzzy mathematical morphology , 1992, J. Vis. Commun. Image Represent..

[12]  Jaakko Astola,et al.  Soft morphological filters , 1991, Optics & Photonics.

[13]  John I. Goutsias,et al.  Mathematical Morphology and its Applications to Image and Signal Processing , 2000, Computational Imaging and Vision.

[14]  Jaakko Astola,et al.  An Introduction to Nonlinear Image Processing , 1994 .

[15]  Edward R. Dougherty,et al.  Morphological methods in image and signal processing , 1988 .

[16]  Xinhua Zhuang,et al.  Image Analysis Using Mathematical Morphology , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[18]  S. Sangwine,et al.  The Colour Image Processing Handbook , 1998, Springer US.

[19]  Antonios Gasteratos,et al.  Realization of rank order filters based on majority gate , 1997, Pattern Recognit..

[20]  Frank Y. Shih,et al.  Threshold Decomposition of Gray-Scale Soft Morphology into Binary Soft Morphology , 1995, CVGIP Graph. Model. Image Process..