Markovian analysis of adaptive reconstructive multiparameter τ-openings

Yidong Chen, Edward R. Dougherty

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A classical single-parameter τ-opening is a union of openings in which each structuring element is scaled by the same parameter. Multiparameter binary τ-openings generalize the model in two ways: first, parameters for each opening are individually defined; second, a structuring element can be parameterized relative to its overall shape, not merely sized. The reconstructive filter corresponding to an opening is defined by fully passing any grain (connected component) that is not fully eliminated by the opening and deleting all other grains. Adaptive design results from treating the parameter vector of a reconstructive multiparameter τ-opening as the state space of a Markov chain. Signal and noise are modeled as unions of randomly parameterized and randomly translated primary grains, and the parameter vector is transitioned depending on whether an observed grain is correctly or incorrectly passed. Various adaptive models are considered, transition probabilities are discussed, the state-probability increment equations are deduced from the appropriate Chapman-Kolmogorov equations, and convergence of the adaptation is characterized by the steady-state distribution relating to the Markov chain.

Original languageEnglish (US)
Pages (from-to)253-267
Number of pages15
JournalJournal of Mathematical Imaging and Vision
Volume10
Issue number3
DOIs
StatePublished - 1999
Externally publishedYes

Fingerprint

Markov processes
unions
Markov chain
Markov chains
Union
Adaptive Design
Kolmogorov Equation
Steady-state Distribution
Transition Probability
Connected Components
Increment
State Space
Filter
Binary
transition probabilities
Generalise
Model
filters

ASJC Scopus subject areas

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

Cite this

Markovian analysis of adaptive reconstructive multiparameter τ-openings. / Chen, Yidong; Dougherty, Edward R.

In: Journal of Mathematical Imaging and Vision, Vol. 10, No. 3, 1999, p. 253-267.

Research output: Contribution to journalArticle

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