In this paper, we describe a particular set of algorithms for
clustering and show how they lead to codes which can be used to compress
images. The approach is called tree-structured vector quantization (TSVQ) and
amounts to a binary tree-structured two-means clustering, very much in the
spirit of CART. This coding is thereafter put into the larger framework of
information theory. Finally, we report the methodology for how image
compression was applied in a clinical setting, where the medical issue was the
measurement of major blood vessels in the chest and the technology was magnetic
resonance (MR) imaging. Measuring the sizes of blood vessels, of other organs
and of tumors is fundamental to evaluating aneurysms, especially prior to
surgery. We argue for digital approaches to imaging in general, two benefits
being improved archiving and transmission, and another improved clinical
usefulness through the application of digital image processing. These goals
seem particularly appropriate for technologies like MR that are inherently
digital. However, even in this modern age, archiving the images of a busy
radiological service is not possible without substantially compressing them.
This means that the codes by which images are stored digitally, whether they
arise from TSVQ or not, need to be "lossy," that is, not invertible. Since
lossy coding necessarily entails the loss of digital information, it behooves
those who recommend it to demonstrate that the quality of medicine practiced is
not diminished thereby. There is a growing literature concerning the impact of
lossy compression upon tasks that involve detection. However, we are not aware
of similar studies of measurement. We feel that the study reported here of 30
scans compressed to 5 different levels, with measurements being made by 3
accomplished radiologists, is consistent with 16:1 lossy compression as we
practice it being acceptable for the problem at hand.