Finding optimal convex gray-scale structuring elements for morphological multiscale representation

Aldo W. Morales, Sung-Jea Ko

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Recent papers in multiscale morphological filtering, particularly, have renovated the interest in signal representation via multiscale openings. Although most of the analysis was done with flat structuring elements, extensions to grayscale structuring elements (GSE) are certainly possible. In fact, we have shown that opening a signal with convex and symmetric GSE does not introduce additional zero-crossings as the filter moves to a coarser scales. However, the issue of finding an optimal GSE is still an open problem. In this paper, we present a procedure to find an optimal GSE under the least mean square (LMS) algorithm subject to three constraints: The GSE must be convex, symmetric, and non-negative. The use of the basis functions simplifies the problem formulation. In fact, we show that the basis functions for convex and symmetric GSE are concave and symmetric, thus alternative constraints are developed. The results of this algorithm are compared with our previous work.

Original languageEnglish
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsEdward R. Dougherty, Jaakko T. Astola, Harold G. Longbotham
Pages129-141
Number of pages13
Volume2662
Publication statusPublished - 1996 Jan 1
Externally publishedYes
EventNonlinear Image Processing VII - San Jose, CA, USA
Duration: 1996 Jan 291996 Jan 30

Other

OtherNonlinear Image Processing VII
CitySan Jose, CA, USA
Period96/1/2996/1/30

Fingerprint

gray scale
roots of equations
filters
formulations

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Morales, A. W., & Ko, S-J. (1996). Finding optimal convex gray-scale structuring elements for morphological multiscale representation. In E. R. Dougherty, J. T. Astola, & H. G. Longbotham (Eds.), Proceedings of SPIE - The International Society for Optical Engineering (Vol. 2662, pp. 129-141)

Finding optimal convex gray-scale structuring elements for morphological multiscale representation. / Morales, Aldo W.; Ko, Sung-Jea.

Proceedings of SPIE - The International Society for Optical Engineering. ed. / Edward R. Dougherty; Jaakko T. Astola; Harold G. Longbotham. Vol. 2662 1996. p. 129-141.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Morales, AW & Ko, S-J 1996, Finding optimal convex gray-scale structuring elements for morphological multiscale representation. in ER Dougherty, JT Astola & HG Longbotham (eds), Proceedings of SPIE - The International Society for Optical Engineering. vol. 2662, pp. 129-141, Nonlinear Image Processing VII, San Jose, CA, USA, 96/1/29.
Morales AW, Ko S-J. Finding optimal convex gray-scale structuring elements for morphological multiscale representation. In Dougherty ER, Astola JT, Longbotham HG, editors, Proceedings of SPIE - The International Society for Optical Engineering. Vol. 2662. 1996. p. 129-141
Morales, Aldo W. ; Ko, Sung-Jea. / Finding optimal convex gray-scale structuring elements for morphological multiscale representation. Proceedings of SPIE - The International Society for Optical Engineering. editor / Edward R. Dougherty ; Jaakko T. Astola ; Harold G. Longbotham. Vol. 2662 1996. pp. 129-141
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