Adaptive reconstructive τ-openings: Convergence and the steady-state distribution

Yidong Chen, Edward R. Dougherty

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

A parameterized τ-opening is a filter defined as a union of openings by a collection of compact, convex structuring elements, each scalar multiplied by the parameter. For a reconstructive τ-opening, the filter is modified by fully passing any connected component not completely eliminated. Applied to the signal-union-noise model, in which the reconstructive filter is designed to sieve out clutter while passing the signal, the optimization problem is to find a parameter value that minimizes the MAE between the filtered and ideal image processes. The present study introduces an adaptation procedure for the design of reconstructive τ-openings. The adaptive filter fits into the framework of Markov processes, the adaptive parameter being the state of the process. There exists a stationary distribution governing the parameter in the steady state and convergence is characterized via the steady-state distribution. Key filter properties such as parameter mean, parameter variance, and expected error in the steady state are characterized via the stationary distribution. The Chapman-Kolmogorov equations are developed for various scanning modes and transient behavior is examined.

Original languageEnglish (US)
Pages (from-to)266-282
Number of pages17
JournalJournal of Electronic Imaging
Volume5
Issue number3
StatePublished - 1996
Externally publishedYes

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Adaptive filters
Markov processes
Scanning
filters
unions
sieves
adaptive filters
clutter
scalars
optimization
scanning

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Atomic and Molecular Physics, and Optics
  • Computer Vision and Pattern Recognition

Cite this

Adaptive reconstructive τ-openings : Convergence and the steady-state distribution. / Chen, Yidong; Dougherty, Edward R.

In: Journal of Electronic Imaging, Vol. 5, No. 3, 1996, p. 266-282.

Research output: Contribution to journalArticle

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