Binary filter design: Optimization, prior information, and robustness
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abstract
The optimal binary window filter is the binary conditional expectation of the pixel value in the ideal image given the set of observations in the window. This filter is typically designed from pairs of ideal and observation images, and the filter used in practice is the resulting estimate of the optimal filter, not the optimal filter itself. For large windows, design is hampered by the exponentially growing number of window observations. This paper discusses two types of prior information that can facilitate design for large windows: design by adapting a given (prior) filter known to work fairly well and Bayesian design resulting from assuming the conditional probabilities determining the optimal filter satisfy prior distributions reflecting the possible states of nature. A second problem is that a filter must be applied in imaging environments different from the one in which it is designed. This results in the robustness problem: how well does a filter designed for one environment perform in a changed environment? This problem is studied by considering the ideal and observed images to be determined by distributions whose parameters are random and possess prior distributions. Then, based on these prior distributions determining the design conditions, we can evaluate filter performance across the various states. Moreover, a global filter can be designed that tends to maintain performance across states, albeit, at the cost of some increase in error relative to specific states.
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Mathematical Modeling and Estimation Techniques in Computer Vision
