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Robustness of optimal binary filters: analysis and design
Abstract
Optimal binary alters estimates an unobserved ideal aphics. image from an observed image. Optimality is with respect to some error criterion, which is mean absolute error for the binary images. Both the ideal and observed images are random sets and these are governed by parameterized probability laws. The optimal filter is found relative to these laws. Qualitatively, a filter is said to be robust when its performance degradation is acceptable for processes statistically close to the one for which it has been designed. This problem is crucial for practical application since filters will always be applied to image processes that deviate from design processes. The present work treats the general concept of robust binary alters in the Bayesian framework, derives bounds for robustness, provides analytic expressions for measuring filter robustness by first expressing the optimal alter analytically in terms of conditional probabilities of template transitions under the degradation operator transforming the ideal to the observed random set. Robustness surfaces are computed for various text models: independent sparse noise, sparse edge noise, noise under rotation, and restoration of rotation. It is shown that even when the noise is independent of the signal, the signal plays an important role in robustness. By parameterizing the Ideal and Observation random sets the robustness of alter design is examined relative to parameter states. Based on the prior distribution of the states, a measure of robustness is defined for each state and the state possessing maximal robustness is determined. To investigate the problem of designing the most robust filter, concepts of the mean robustness (as opposed to robustness by state) is introduced. Filter design is examined from the perspective of robust states of nature. A simplified model is proposed for determination of robust states from image data and approximation the robustness by estimating model parameters. A global filter is introduced that is applied across all states, particularizes the entire analysis to a sparse noise model in which analytical expressions for robustness are derived. Sufficient conditions are given under which the global filter is uniformly more robust than all state-specific optimal alters.
Description
Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to digital@library.tamu.edu, referencing the URI of the item.Includes bibliographical references (leaves 126-127).
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Citation
Grigoryan, Artyom M (1999). Robustness of optimal binary filters: analysis and design. Master's thesis, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /ETD -TAMU -1999 -THESIS -G75.
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