Statistical morphology and Bayesian reconstruction

Alan Yuille, Luc Vincent, Davi Geiger

Research output: Contribution to journalArticle

Abstract

The aim of this paper is to show that 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 us to relate these operations to alternative Bayesian or Markovian approaches to image analysis. We first show 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 become purely linear averages as β goes to zero. 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 minimum-variance estimators. Finally, we describe simulations comparing statistical morphology and Bayesian methods for image smoothing, edge detection, and noise reduction.

Original languageEnglish (US)
Pages (from-to)223-238
Number of pages16
JournalJournal of Mathematical Imaging and Vision
Volume1
Issue number3
DOIs
StatePublished - Sep 1992

Fingerprint

Probability distributions
Erosion
Edge detection
Noise abatement
Minimum Variance
Image analysis
Variance Estimator
Dilation
Physics
estimators
Probability Distribution
Temperature
erosion
Winner-take-all
Statistical Simulation
Morphological Operations
Concatenation
Noise Reduction
Statistical Physics
Edge Detection

Keywords

  • Bayesian models
  • mean field theory
  • morphology
  • statistical physics

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Systems Engineering
  • Software
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design
  • Artificial Intelligence

Cite this

Statistical morphology and Bayesian reconstruction. / Yuille, Alan; Vincent, Luc; Geiger, Davi.

In: Journal of Mathematical Imaging and Vision, Vol. 1, No. 3, 09.1992, p. 223-238.

Research output: Contribution to journalArticle

Yuille, Alan ; Vincent, Luc ; Geiger, Davi. / Statistical morphology and Bayesian reconstruction. In: Journal of Mathematical Imaging and Vision. 1992 ; Vol. 1, No. 3. pp. 223-238.
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