Bayes risk weighted vector quantization with posterior estimation for image compression and classification

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Abstract
Classification and compression play important roles in communicating digital information. Their combination is useful in many applications, including the detection of abnormalities in compressed medical images. In view of the similarities of compression and low-level classification, it is not surprising that there are many similar methods for their design. Because some of these methods are useful for designing vector quantizers, it seems natural that vector quantization (VQ) is explored for the combined goal. We investigate several VQ-based algorithms that seek to minimize both the distortion of compressed images and errors in classifying their pixel blocks. These algorithms are investigated with both full search and tree-structured codes. We emphasize a nonparametric technique that minimizes both error measures simultaneously by incorporating a Bayes risk component into the distortion measure used for the design and encoding. We introduce a tree-structured posterior estimator to produce the class posterior probabilities required for the Bayes risk computation in this design. For two different image sources, we demonstrate that this system provides superior classification while maintaining compression close or superior to that of several other VQ-based designs, including Kohonen's (1992) "learning vector quantizer" and a sequential quantizer/classifier design.

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