Texture Regimes for Entropy-Based Multiscale Image Analysis

We present an approach to multiscale image analysis. It hinges on an operative definition of texture that involves a “small region”, where some (unknown) statistic is aggregated, and a “large region” within which it is stationary. At each point, multiple small and large regions co-exist at multiple scales, as image structures are pooled by the scaling and quantization process to form “textures” and then transitions between textures define again “structures.” We present a technique to learn and agglomerate sparse bases at multiple scales. To do so efficiently, we propose an analysis of cluster statistics after a clustering step is performed, and a new clustering method with linear-time performance. In both cases, we can infer all the “small” and “large” regions at multiple scale in one shot.