Overlap in adaptive vector quantization

Constantinescu and Storer (1994) introduced an adaptive single-pass vector quantization algorithm (AVQ) that employs variable size and shaped codebook entries that are "learned" as an image is processed (no specific training or prior knowledge of the data is used). The approach allows the tradeoff between compression and fidelity to be continuously adjusted from lossless (with less compression) to highly lossy (with greater compression). Although practical performance compares favorably with the JPEG standard as well as standard trained vector quantization implementations, analysis of its performance appears difficult. A key aspect of AVQ is that matches are allowed to overlap, and it is not necessary to perform some sort of bin packing in order to cover the image with variable size and shape matches. Here we show that the AVQ approach is in some sense optimal asymptotically, module the overlapping factor which is defined to be the average number of times that a pixel is covered. We also present experiments that study the relationship of overlapping to performance.