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Statistics of Natural Images and Models
"... 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 ..."
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Cited by 198 (5 self)
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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 scaleinvariance 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
Statistics of range images
 CVPR
, 2000
"... 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 ..."
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Cited by 62 (5 self)
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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
Gaussian limits for determinantal random point
 Annals of Probability
, 2002
"... 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—σalgebra of ..."
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Cited by 24 (0 self)
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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—σalgebra of Borel subsets and µ a σfinite 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):=
j huang @ cfm. brown.edu
"... 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. Som ..."
Abstract
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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 scaleinvariance 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
RENORMALIZATION OF WEAK NOISES OF ARBITRARY SHAPE FOR ONE–DIMENSIONAL CRITICAL DYNAMICAL SYSTEMS: ANNOUNCEMENT OF RESULTS AND NUMERICAL EXPLORATIONS
"... Abstract. We study the effect of noise on one–dimensional critical dynamical systems (that is, maps with a renormalization theory). We consider in detail two examples of such dynamical systems: unimodal maps of the interval at the accumulation of period– doubling and smooth homeomorphisms of the cir ..."
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Abstract. We study the effect of noise on one–dimensional critical dynamical systems (that is, maps with a renormalization theory). We consider in detail two examples of such dynamical systems: unimodal maps of the interval at the accumulation of period– doubling and smooth homeomorphisms of the circle with a critical point and with golden mean rotation number. We show that, if we scale the space and the time, several properties of the noise (the cumulants or Wick–ordered moments) satisfy some scaling relations. A consequence of the scaling relations is that a version of the central limit theorem holds. Irrespective of the shape of the initial noise, if the bare noise is weak enough, the effective noise becomes close to Gaussian in several senses that we can make precise. We notice that the conclusions are false for maps with positive Lyapunov exponents. The method of analysis is close in spirit to the study of scaling limits in renormalization theory. We also perform several numerical experiments that confirm the rigorous results and that suggest several conjectures. 1.