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Analysis of Texture Anisotropy Based on Some Gaussian Fields with Spectral Density

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Mathematical Image Processing

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 5))

Abstract

In this paper, we describe a statistical framework for the analysis of anisotropy of image texture. This framework is based on the modeling of the image by two kinds of non-stationary anisotropic Gaussian field with stationary increments and spectral density: the extended fractional Brownian field (EFBF) and a specific Gaussian operator scaling field (GOSF), which both correspond to a generalization of the fractional Brownian field. In this framework, we tackle anisotropy analysis using some directional processes that are either defined as a restriction of the image on an oriented line or as a projection of the image along a direction. In the context of EFBF and GOSF, we specify links between the regularity of line and projection processes and model parameters, and explain how field anisotropy can be apprehended from the analysis of process regularity. Adapting generalized quadratic variations, we also define some estimators of the regularity of line and projection processes, and study their convergence to field model parameters. Estimators are also evaluated on simulated data, and applied for illustration to medical images of the breast and the bone.

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Author information

Authors and Affiliations

  1. Laboratory MAP5 (CNRS UMR 8145), University Paris Descartes, 45 rue des Saints Pères, 75270, Paris Cedex 06, France

    Hermine Biermé & Frédéric J. P. Richard

Authors
  1. Hermine Biermé
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  2. Frédéric J. P. Richard
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Corresponding author

Correspondence to Frédéric J. P. Richard .

Editor information

Editors and Affiliations

  1. , UMR 6628-MAPMO, Université d'Orléans, Orléans Cedex 2, 45067, France

    Maïtine Bergounioux

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Biermé, H., Richard, F.J.P. (2011). Analysis of Texture Anisotropy Based on Some Gaussian Fields with Spectral Density. In: Bergounioux, M. (eds) Mathematical Image Processing. Springer Proceedings in Mathematics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19604-1_3

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