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Journal of Electronic Imaging

Adaptive reconstructive τ-openings: convergence and the steady-state distribution
Author(s): Yidong Chen; Edward R. Dougherty
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Paper 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.

Paper Details

Date Published: 1 July 1996
PDF: 17 pages
J. Electron. Imaging. 5(3) doi: 10.1117/12.244908
Published in: Journal of Electronic Imaging Volume 5, Issue 3
Show Author Affiliations
Yidong Chen, National Inst. of Health (United States)
Edward R. Dougherty, Rochester Institute of Technology (United States)


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