On advances in statistical modeling of natural images

A. Srivastava, A. B. Lee, E. P. Simoncelli, S. C. Zhu

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)17-33
Number of pages17
JournalJournal of Mathematical Imaging and Vision
Volume18
Issue number1
DOIs
StatePublished - Jan 2003

Keywords

  • Bessel K form
  • Generalized Laplacian
  • Image manifold
  • Natural image statistics
  • Non-Gaussian models
  • Scale invariance
  • Statistical image analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics

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