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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Bayesian estimation of the multifractality parameter for image texture using a whittle approximation.

Sébastien Combrexelle, Herwig Wendt, Nicolas Dobigeon

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    |April 28, 2015
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    Summary
    This summary is machine-generated.

    Accurately estimating multifractal parameters in image textures is challenging. This study introduces a novel Bayesian approach using wavelet leaders, significantly improving estimation performance, especially for small image sizes.

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    Area of Science:

    • Signal and Image Processing
    • Statistical Modeling
    • Computational Mathematics

    Background:

    • Accurate multifractal parameter estimation for image textures is crucial for various applications.
    • Current methods using wavelet transforms face limitations due to computable frequency scales and complex process structures.
    • The non-Gaussian nature and intricate dependence of multifractal processes complicate parameter estimation.

    Purpose of the Study:

    • To propose a novel Bayesian procedure for accurately estimating multifractality parameters in image textures.
    • To address the challenges posed by limited frequency scales and complex multifractal process structures.
    • To develop a robust method for analyzing image texture multifractality, particularly for small image patches.

    Main Methods:

    • Development of a generic semiparametric statistical model for the logarithm of wavelet leaders.
    • Formulation of Bayesian estimators aligned with the statistical model and multifractal theory.
    • Utilization of a Whittle approximation for efficient posterior distribution evaluation within the Bayesian framework.

    Main Results:

    • The proposed Bayesian procedure demonstrates significant improvements over existing benchmark estimators.
    • Enhanced performance in estimating multifractality parameters and discriminating between common multifractal process models.
    • Successful analysis of small image patches (as small as 64x64 pixels), a first for this type of analysis.

    Conclusions:

    • The novel Bayesian procedure offers a robust and effective solution for multifractal parameter estimation in image textures.
    • This method overcomes limitations of previous techniques, particularly for small image datasets.
    • The approach enables more precise texture characterization and analysis in diverse image processing applications.