Modeling natural microimage statistics

Abstract

A large collection of digital images of natural scenes provides a database for analyzing and modeling small scene patches (e.g., 2 x 2) referred to as natural microimages. A pivotal ¯nding is the stability of the empirical microimage distribution across scene samples and with respect to scaling. With a view toward potential applications (e.g. classi¯cation, clutter modeling, segmentation), we present a hierarchy of microimage probability models which capture essential local image statistics. Tools from information theory, algebraic geometry and of course statistical hypothesis testing are employed to assess the "match" between candidate models and the empirical distribution. Geometric symmetries play a key role in the model selection process. One central result is that the microimage distribution exhibits reflection and rotation symmetry and is well-represented by a Gibbs law with only pairwise interactions. However, the acceptance of the up-down reflection symmetry hypothesis is borderline and intensity inversion symmetry is rejected. Finally, possible extensions to larger patches via entropy maximization and to patch classification via vector quantization are briefly discussed.