Invariant Statistics and Coding of Natural Microimages

Fort Collins, CO, June, 1999. (Published on Web). Invariant Statistics and Coding of Natural Microimages Donald Geman1 and Alexey Koloydenko2 Abstract We search for universal characteristics of the microstructure of natural images. Our data consist of a very large set of 3 3 patches randomly extracted from indoor and outdoor grey level scenes. The patches are grouped into natural equivalence classes (\patterns") based on photometry, \complexity" and geometry. We analyze the stability of the pattern statistics over image sets, resolutions and grey scale distortions. Important aspects of the probability distribution of the patterns, e.g., the dominant masses, are stable in our experiments. We also compare the statistics of the natural patch world with those of arti cially generated images; the results are consistent with recently proposed \scaling laws" for the sizes of objects in natural images. These results suggest that well-chosen patch labels might serve as elementary features in pattern recognition and other imaging problems in which the ne structure of the grey level con gurations is not essential, and we sketch a computationally e cient way to carry this out using tree-structured vector quantization.