On advances in statistical modeling of natural images

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

doi:10.1023/A:1021889010444

On advances in statistical modeling of natural images

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

Neural Science

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	17-33
Number of pages	17
Journal	Journal of Mathematical Imaging and Vision
Volume	18
Issue number	1
DOIs	https://doi.org/10.1023/A:1021889010444
State	Published - 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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title = "On advances in statistical modeling of natural images",

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.",

keywords = "Bessel K form, Generalized Laplacian, Image manifold, Natural image statistics, Non-Gaussian models, Scale invariance, Statistical image analysis",

author = "A. Srivastava and Lee, {A. B.} and Simoncelli, {E. P.} and Zhu, {S. C.}",

note = "Funding Information: We thank the creators of van Hateren database for making their database available to public. We express gratitude to our collaborators Ulf Grenander, Kim S. Pedersen and David Mumford for their help in this research. Many thanks to Hamid Krim for his invitation and support in writing this paper. AS has been supported in part by the grants NSF DMS-0101429, ARO DAAD19-99-1-0267, and NMA 201-01-2010. EPS was supported in part by NSF CAREER grant MIP-9796040, the Alfred P. Sloan Foundation, and the Howard Hughes Medical Institute.",

year = "2003",

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doi = "10.1023/A:1021889010444",

language = "English (US)",

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AU - Lee, A. B.

AU - Simoncelli, E. P.

AU - Zhu, S. C.

N1 - Funding Information: We thank the creators of van Hateren database for making their database available to public. We express gratitude to our collaborators Ulf Grenander, Kim S. Pedersen and David Mumford for their help in this research. Many thanks to Hamid Krim for his invitation and support in writing this paper. AS has been supported in part by the grants NSF DMS-0101429, ARO DAAD19-99-1-0267, and NMA 201-01-2010. EPS was supported in part by NSF CAREER grant MIP-9796040, the Alfred P. Sloan Foundation, and the Howard Hughes Medical Institute.

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N2 - 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.

AB - 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.

KW - Bessel K form

KW - Generalized Laplacian

KW - Image manifold

KW - Natural image statistics

KW - Non-Gaussian models

KW - Scale invariance

KW - Statistical image analysis

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JF - Journal of Mathematical Imaging and Vision

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On advances in statistical modeling of natural images

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Keywords

ASJC Scopus subject areas

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