Multiresolution and large window Bayesian and differencing binary filters /
Optimal translation-invariant binary windowed filters are determined by probabilities of the form P(Y =1lx), 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)=1 if P(...
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| Format: | Thesis eBook |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1999.
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| Summary: | Optimal translation-invariant binary windowed filters are determined by probabilities of the form P(Y =1lx), 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)=1 if P(Y=1lx)> 0.5, y(x)=0 if P(Y=1lx)<=0.5, which is the binary conditional expectation. The fundamental problem of filter design is to estimate P(Y=1lx) from data (image realizations) , where x ranges over all possible observation vectors in the window. A Bayesian approach to the problem is employed by assuming, for each x, a prior distribution for P(Y = 1lx). These prior distributions result from considering a range of model states by which the observed images are obtained from the ideal. P(Y = 1lx) is estimated in the Bayesian fashion, its Bayes estimator being the conditional expectation of P(Y =1 lx) given the data. The difficulty is that, with a relatively large window, for many vectors x there are insufficient observations of x to obtain a good estimate of the prior distribution. This research discusses a multiresolution approach to binary filters with an emphasis on Bayesian Design. For each x, the prior distribution for P(Y = 1lx) is designed for windows of increasing sizes. For the purpose of image restoration, each prior is assumed to be a beta distribution and is estimated over a range of degradation levels. The beta prior is obtained only for those templates whose numbers of occurrences are signficant enough to estimate a reliable probability P(Y = 1lx) for each state of nature. Priors are obtained over a range of feasible window sizes. For each x, the filter is computed using the largest window for which a prior distribution has been designed, further moving to a subwindow if a prior is not available. This is repeated until we are able to make a filtering decision at some window size with a known beta prior for P(Y = 1lx). We are guaranteed a decision at some point since we know that for smaller windows we have a greater percentage of templates occurring sufficiently often to reliably estimate a prior distribution. This hierarchical algorithm enables us to reap the benefits of larger windows when we have confidence in a prior distribution and step down to smaller windows otherwise. We compare the performance of this Bayesian multiresolution approach with a multiresolution version of the differencing filter commonly used in digital document processing. We also test the robustness of the Bayesian designed filter over perturbations of the degradation model. Since the Bayesian filter is designed over a wider range of degradation levels, we show its ability to further restore degraded images by iterative filtering. Large window design issues including limited memory and computer hardware limitations are tackled and large window multiresolution filters are designed. We consider edge noise in the experiments, with an emphasis on realistically degraded document images. |
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| Item Description: | Vita. "Major subject: Electrical Engineering". |
| Physical Description: | ix, 50 leaves : illustrations ; 28 cm. Also available online. Issued also on microfiche from Lange Micrographics. |
| Bibliography: | Includes bibliographical references (leaves 48-49). |