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.
"Medical image compression and vector quantization." Statist. Sci. 13 (1) 30 - 53, February 1998. https://doi.org/10.1214/ss/1028905972