The gerrymander problem in vector quantization

In vector quantization (VQ) applied to image coding, the objective is to determine a set of code vectors for the coding of the population vectors of an image. It is clear that each basis vector should represent about the same number of population vectors, and no population vector should be very badly represented. However, various VQ algorithms have a tendency to produce a gerrymander, in which a few code vectors come to be the representative of many or most population vectors, while at the same time some code vectors represent very few of the population. This situation, analogous to a political gerrymander, arises for ill-chosen initial code vectors. We introduce a scheme, to be applied in conjunction with iterative VQ algorithms, that blocks the development of a gerrymander. This new algorithm involves the replacement of non-representative code vectors by those population vectors that are most poorly represented. Experimental data on the VQ of gray-scale images using progressive (hard) c-means show that the scheme is most effective, and marginally improved when applied in conjunction with the deliberate duplication of the most popular code vector