Statistical morphology

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

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


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
Number of pages12
ISBN (Print)0819406961
StatePublished - 1991
EventImage Algebra and Morphological Image Processing II - San Diego, CA, USA
Duration: Jul 23 1991Jul 24 1991

Publication series

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


OtherImage Algebra and Morphological Image Processing II
CitySan Diego, CA, USA

ASJC Scopus subject areas

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


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