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Statistics and Computing

, Volume 27, Issue 4, pp 1129–1143

First Online: 01 July 2016Received: 23 December 2015Accepted: 07 June 2016DOI: 10.1007-s11222-016-9675-9

Cite this article as: Taylor, S.L., Eckley, I.A. & Nunes, M.A. Stat Comput 2017 27: 1129. doi:10.1007-s11222-016-9675-9


In this article we propose a novel framework for the modelling of non-stationary multivariate lattice processes. Our approach extends the locally stationary wavelet paradigm into the multivariate two-dimensional setting. As such the framework we develop permits the estimation of a spatially localised spectrum within a channel of interest and, more importantly, a localised cross-covariance which describes the localised coherence between channels. Associated estimation theory is also established which demonstrates that this multivariate spatial framework is properly defined and has suitable convergence properties. We also demonstrate how this model-based approach can be successfully used to classify a range of colour textures provided by an industrial collaborator, yielding superior results when compared against current state-of-the-art statistical image processing methods.

KeywordsRandom field Local spectrum Local coherence Colour texture Wavelets Electronic supplementary materialThe online version of this article doi:10.1007-s11222-016-9675-9 contains supplementary material, which is available to authorized users.

Autor: Sarah L. Taylor - Idris A. Eckley - Matthew A. Nunes


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