Bayesian iterative binary filter design

Vishnu G. Kamat; Edward R. Dougherty

doi:10.1117/12.424975

8 May 2001 Bayesian iterative binary filter design

Proceedings Volume 4304, Nonlinear Image Processing and Pattern Analysis XII; (2001) https://doi.org/10.1117/12.424975
Event: Photonics West 2001 - Electronic Imaging, 2001, San Jose, CA, United States

Abstract

Optimal translation-invariant binary windowed filters are determined by probabilities of the form P(Y equals 1|x), where x is a vector (template) of observed values in the observation window and Y is the value in the image to be estimated by the filter. The optimal window filter is defined by y(x) equals 1 if P(Y equals 1|x) (greater than) 0.5 and y(x) equals 0 if P(Y equals 1|x) (less than or equal to) 0.5, which is the binary conditional expectation. The fundamental problem of filter design is to estimate P(Y equals 1|x) from data (image realizations), where x ranges over all possible observation vectors in the window. A Bayesian approach to the problem can be employed by assuming, for each x, a prior distribution for P(Y equals 1|x). These prior distributions result from considering a range of model states by which the observed images are obtained from the ideal. Instead of estimating P(Y equals 1|x) directly from observations by its sample mean relative to an image sample, P(Y equals 1|x) is estimated in the Bayesian fashion, its Bayes estimator being the conditional expectation of P(Y equals 1|x) given the data. Recently the authors have shown that, with accurate prior information, the Bayesian multiresolution filter has significant benefits from multiresolution filter design. Further, since the Bayesian filter is trained over a wider range of degradation levels, it inherits the added benefit of filtering a degraded image at different degradation levels in addition permitting iterative filtering. We discuss the necessary conditions that make a binary filter a good iterative filter and show that the Bayesian multiresolution filter is a natural candidate.

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Vishnu G. Kamat and Edward R. Dougherty "Bayesian iterative binary filter design", Proc. SPIE 4304, Nonlinear Image Processing and Pattern Analysis XII, (8 May 2001); https://doi.org/10.1117/12.424975

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KEYWORDS

Image processing

Statistical analysis

Error analysis

Binary data

Image filtering

Field emission displays

Image resolution

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