Statistical morphology

Alan L. Yuille, Luc M. Vincent, Davi Geiger

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

Abstract

Basic morphological operations can be incorporated within a statistical physics formulation as a limit when the temperature of the system tends to zero. These operations can then be expressed in terms of finding minimum variance estimators of probability distributions. It enables one to relate these operations to alternative Bayesian or Markovian approaches to image analysis. It is shown how to derive elementary dilations (winner-take-all) and erosions (loser-take-all). These operations, referred to as statistical dilations and erosion, depend on a temperature parameter β = 1/T. They become purely morphological as β goes to infinity and purely linear averages as β goes to 0. Experimental results are given for a range of intermediate values of β. Concatenations of elementary operations can be naturally expressed by stringing together conditional probability distributions, each corresponding to the original operations, thus yielding statistical openings and closings. Techniques are given for computing the minimal variance estimators.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
PublisherPubl by Int Soc for Optical Engineering
Pages271-282
Number of pages12
Volume1568
ISBN (Print)0819406961
StatePublished - 1991
EventImage Algebra and Morphological Image Processing II - San Diego, CA, USA
Duration: Jul 23 1991Jul 24 1991

Other

OtherImage Algebra and Morphological Image Processing II
CitySan Diego, CA, USA
Period7/23/917/24/91

Fingerprint

Probability distributions
Erosion
Image analysis
Physics
estimators
Temperature
erosion
closing
image analysis
infinity
formulations
physics
temperature

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Yuille, A. L., Vincent, L. M., & Geiger, D. (1991). Statistical morphology. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 1568, pp. 271-282). Publ by Int Soc for Optical Engineering.

Statistical morphology. / Yuille, Alan L.; Vincent, Luc M.; Geiger, Davi.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 1568 Publ by Int Soc for Optical Engineering, 1991. p. 271-282.

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

Yuille, AL, Vincent, LM & Geiger, D 1991, Statistical morphology. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 1568, Publ by Int Soc for Optical Engineering, pp. 271-282, Image Algebra and Morphological Image Processing II, San Diego, CA, USA, 7/23/91.
Yuille AL, Vincent LM, Geiger D. Statistical morphology. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 1568. Publ by Int Soc for Optical Engineering. 1991. p. 271-282
Yuille, Alan L. ; Vincent, Luc M. ; Geiger, Davi. / Statistical morphology. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 1568 Publ by Int Soc for Optical Engineering, 1991. pp. 271-282
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