The theory and design of lossy compression systems share many
ideas and techniques with statistical classification and regression
and hence also with image segmentation. These similarities motivate
incorporating a Bayes risk term into a Shannon source coding
formulation in order to model a system combining quantization
with either classification (detection) or regression (estimation).
This provides some new (and old) algorithms for compression,
classification, and regression individually, but more interestingly
it provides an approach to the joint optimization of systems
involving both compression and classification. Examples include
the compression of digital mammograms with built in highlighting
of microcalcifications and the compression of image data while
simultaneously segmenting the image into different local types
for separate rendering or printing. The design of such codes
involves ideas from clustering and tree-structured statistical
methods and it leads to issues involving the combination of
quantization, probability density or mass estimation, and classification
and regression. The resulting codes have as ``extreme points"
universal source codes and classified vector quantizers. This
talk will survey the basic ideas, illustrate them with examples,
and describe some of the algorithms under current study along
with several conjectures about their asymptotic performance.
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