Large calibrated datasets of `random' natural images have recently become available. These make possible precise and intensive statistical studies of the local nature of images. We report results ranging from the simplest single pixel intensity to joint distribution of 3 Haar wavelet responses. Some of these statistics shed light on old issues such as the near scale-invariance of image statistics and some are entirely new. We fit mathematical models to some of the statistics and explain others in terms of local image features. 1

The statistics of range images from natural environments is a largely unexplored eldofresearch. It closely relates to the statistical modeling of the scene geometry in natural environments, and the modeling of optical natural images. We have use d a 3D laser range- nder to collect range images from mixed forest scenes. The images are hereanalyzed with respect to di erent statistics. 1

We prove that, under fairly general conditions, a properly rescaled determinantal random point field converges to a generalized Gaussian random process. 1. Introduction and formulation of results. Let E be a locally compact Hausdorff space satisfying the second axiom of countability, B—σ-algebra of Borel subsets and µ a σ-finite measure on (E, B), such that µ(K) < ∞ for any compact K ⊂ E. We denote by X the space of locally finite configurations of particles in E: X ={ξ = (xi) ∞ i=− ∞ : xi ∈ E ∀i, and for any compact K ⊂ E #K(ξ):=

Large calibrated datasets of 'random ' natural images have recently become available. These make possible precise and intensive statistical studies of the local nature of images. We report results ranging from the simplest single pixel intensity to joint distribution of 3 Haar wavelet responses. Some of these statistics shed light on old issues such as the near scale-invariance of image statistics and some are entirely new. We fit mathematical models to some of the statistics and explain others in terms of local image features. 1