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Locally stationary wavelet fields with application to the modelling and analysis of image texture

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  • Idris A. Eckley
  • Guy P. Nason
  • Robert L. Treloar

Abstract

Summary. The paper proposes the modelling and analysis of image texture by using an extension of a locally stationary wavelet process model into two dimensions for lattice processes. Such a model permits construction of estimates of a spatially localized spectrum and localized autocovariance which can be used to characterize texture in a multiscale and spatially adaptive way. We provide the necessary theoretical support to show that our two‐dimensional extension is properly defined and has the proper statistical convergence properties. Our use of a statistical model permits us to identify, and correct for, a bias in established texture measures based on non‐decimated wavelet techniques. The method proposed performs nearly as well as optimal Fourier techniques on stationary textures and outperforms them in non‐stationary situations. We illustrate our techniques by using pilled fabric data from a fabric care experiment and simulated tile data.

Suggested Citation

  • Idris A. Eckley & Guy P. Nason & Robert L. Treloar, 2010. "Locally stationary wavelet fields with application to the modelling and analysis of image texture," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(4), pages 595-616, August.
    • Handle: RePEc:bla:jorssc:v:59:y:2010:i:4:p:595-616
    DOI: 10.1111/j.1467-9876.2009.00721.x
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    References listed on IDEAS

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    1. Alexandra M. Schmidt & Anthony O'Hagan, 2003. "Bayesian inference for non‐stationary spatial covariance structure via spatial deformations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 743-758, August.
    2. G. P. Nason & R. Von Sachs & G. Kroisandt, 2000. "Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 271-292.
    3. Banerjee, Sudipto & Gelfand, Alan E., 2006. "Bayesian Wombling: Curvilinear Gradient Assessment Under Spatial Process Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1487-1501, December.
    4. Le, Nhu D. & Zidek, James V., 1992. "Interpolation with uncertain spatial covariances: A Bayesian alternative to Kriging," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 351-374, November.
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    Cited by:

    1. Erwan Koch, 2019. "Spatial Risk Measures and Rate of Spatial Diversification," Risks, MDPI, vol. 7(2), pages 1-26, May.
    2. repec:jss:jstsof:43:i03 is not listed on IDEAS

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