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 (US)
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
StatePublished - Jan 1 1996
EventNonlinear Image Processing VII - San Jose, CA, USA
Duration: Jan 29 1996Jan 30 1996

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume2662
ISSN (Print)0277-786X

Other

OtherNonlinear Image Processing VII
CitySan Jose, CA, USA
Period1/29/961/30/96

Fingerprint

gray scale
roots of equations
filters
formulations

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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 (pp. 129-141). (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 2662).
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. 1996. pp. 129-141 (Proceedings of SPIE - The International Society for Optical Engineering).
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Morales, AW & Ko, SJ 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. Proceedings of SPIE - The International Society for Optical Engineering, vol. 2662, pp. 129-141, Nonlinear Image Processing VII, San Jose, CA, USA, 1/29/96.

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. 1996. p. 129-141 (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 2662).

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

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Morales AW, Ko SJ. 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. 1996. p. 129-141. (Proceedings of SPIE - The International Society for Optical Engineering).