Locally stationary wavelet fields with application
to the modelling and analysis of image texture
Idris A. Eckley, Guy P. Nason and Robert L. Treloar
This article proposes the modelling and analysis of image texture 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 desired 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 and, hence, we
demonstrate superior
performance in texture classification examples. Our method performs nearly
as well as optimal
Fourier techniques on stationary textures and outperforms them in
non-stationary situations. We
illustrate our techniques using data from an industrial application and
simulated tile data.
KEYWORDS: random field; local spectrum; local autocovariance; texture
classification; texture model; nondecimated
wavelets
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