On Advances in Statistical Modeling of Natural Images

Authors:
A. Srivastava;A. B. Lee;E. P. Simoncelli;S.-C. Zhu
Affiliations:
Department of Statistics, Florida State University, Tallahassee, FL 32306, USA.anuj@stat.fsu.edu;Division of Applied Mathematics, Brown University, Providence, RI 02912, USA;Courant Institute for Mathematical Sciences, New York University, New York, NY 10003, USA;Department of Computer Science, Ohio State University, Columbus, OH 43210, USA
Venue:
Journal of Mathematical Imaging and Vision
Year:
2003

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Abstract

Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) non-Gaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modeling of natural images that attempt to explain these patterns. Two categories of results are considered: (i) studies of probability models of images or image decompositions (such as Fourier or wavelet decompositions), and (ii) discoveries of underlying image manifolds while restricting to natural images. Applications of these models in areas such as texture analysis, image classification, compression, and denoising are also considered.