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Multivariate locally stationary 2D wavelet processes with application to colour texture analysis.


ABSTRACT: 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.

SUBMITTER: Taylor SL 

PROVIDER: S-EPMC7089644 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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Multivariate locally stationary 2D wavelet processes with application to colour texture analysis.

Taylor Sarah L SL   Eckley Idris A IA   Nunes Matthew A MA  

Statistics and computing 20160701 4


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 <i>within</i> a channel of interest and, more importantly, a localised cross-covariance which describes the localised coherence <i>between</i> channels. Associated estimation theory is also  ...[more]

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