The Complex Statistics of High-Contrast Patches in Natural Images

Ann B. Lee, Kim Pedersen, and David Mumford

Division of Applied Math. Brown University

Recently, there has been a great deal of interest in modeling the non-Gaussian structures of natural images. However, despite the many advances in the direction of sparse coding and multi-resolution analysis, a description of the full probability distribution of pixels in a neighborhood is still missing. In this study, we explore the space of data points representing the values of 3 x 3 high-contrast patches from optical and 3D range images. We find that the distribution of data is extremely ``sparse'' with the majority of the data points concentrated in clusters and non-linear low-dimensional manifolds. Furthermore, a more detailed analysis of probability densities reveals clear differences between optical and range images, which have similar second-order statistics and scaling properties. Our work indicates the importance of studying the complex statistics of natural images, and the need to understand the intrinsic dimensionality of natural data.

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