Vision pyramids that do not grow too high

In irregular pyramids, their vertical structure is not determined beforehand as in regular pyramids. We present three methods, all based on maximal independent sets from graph theory, with the aim to simulate the major sampling properties of the regular counterparts: good coverage of the higher resolution level, not too large sampling gaps and, most importantly, the resulting height, e.g. the number of levels to reach the apex. We show both theoretically and experimentally that the number of vertices can be reduced by a factor of 2.0 at each level. The plausibility of log (diameter) pyramids is supported by psychological and psychophysical considerations. Their technical relevance is demonstrated by enhancing appearance-based object recognition. An irregular pyramid hypothesis generation for robust PCA through top-down attention mechanisms achieves higher speed and quality than regular pyramids and non-pyramidal approaches.