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.