Bayes risk weighted tree-structured vector quantization with posterior estimation

The authors investigate a method that combines compression and low-level classification of images by designing codes that contain implicit information regarding classification. The design consists of a tree-structured vector quantizer (TSVQ) that incorporates a Bayes risk term into the distortion measure used in the quantizer design algorithm in order to permit a tradeoff of mean squared error and classification error. Once designed, the quantizer can operate to minimize the Bayes risk weighted distortion measure by incorporating the posterior probabilities into the encoding process. A completely nonparametric design algorithm is constructed by estimating these posterior distributions using a TSVQ that incorporates the classification error into the splitting criterion. This approach is used to analyze simulated data and to identify tumors in CT lung images. Comparisons are made with other vector quantizer based classifiers, including Kohonen´s “learning vector quantizer.” For the examples considered, their method provided a classification that was superior to the other methods while simultaneously providing close to or superior compression performance