Bispectral analysis and model validation of texture images

Statistical approaches to texture analysis and synthesis have largely relied upon random models that characterize the 2-D process in terms of its first- and second-order statistics, and therefore cannot completely capture phase properties of random fields that are non-Gaussian and/or asymmetric. In...

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Bibliographic Details
Published inIEEE transactions on image processing Vol. 4; no. 7; pp. 996 - 1009
Main Authors Hall, T.E., Giannakis, G.B.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.07.1995
Institute of Electrical and Electronics Engineers
Subjects
Analytical models
Applied sciences
Exact sciences and technology
Gaussian processes
Image analysis
Image processing
Image texture analysis
Information, signal and communications theory
Linearity
Parameter estimation
Performance analysis
Phase estimation
Signal processing
Statistical analysis
Telecommunications and information theory
Testing
Random field
ARMA model
Parameter estimation
Experimental result
Image processing
Spectrum analysis
Statistical methods
Digital image
Markov model
Textures
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Summary:Statistical approaches to texture analysis and synthesis have largely relied upon random models that characterize the 2-D process in terms of its first- and second-order statistics, and therefore cannot completely capture phase properties of random fields that are non-Gaussian and/or asymmetric. In this paper, higher than second-order statistics are used to derive and implement 2-D Gaussianity, linearity, and spatial reversibility tests that validate the respective modeling assumptions. The nonredundant region of the 2-D bispectrum is correctly defined and proven. A consistent parameter estimator for nonminimum phase, asymmetric noncausal, 2-D ARMA models is derived by minimizing a quadratic error polyspectrum matching criterion. Simulations on synthetic data are performed and the results of the bispectral analysis on real textures are reported.< >
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ISSN:1057-7149
1941-0042
DOI:10.1109/83.392340