Locally Stationary Wavelet Fields with Application to the Modelling and Analysis of Image Texture
Idris A. Eckley, Guy P. Nason, R. Treloar · Journal of the Royal Statistical Society Series C (Applied Statistics) · 2010
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.