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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]

PMID: 32226238

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Project description:MOTIVATION: Solenoid proteins are emerging as a protein class with properties intermediate between structured and intrinsically unstructured proteins. Containing repeating structural units, solenoid proteins are expected to share sequence similarities. However, in many cases, the sequence similarities are weak and non-detectable. Moreover, solenoids can be degenerated and widely vary in the number of units. So that it is difficult to detect them. Recently, several solenoid repeats detection methods have been proposed, such as self-alignment of the sequence, spectral analysis and discrete Fourier transform of sequence. Although these methods have shown good performance on certain data sets, they often fail to detect repeats with weak similarities. In this article, we propose a new approach to recognize solenoid repeats and non-solenoid proteins using stationary wavelet packet transform (SWPT). Our method associates with three advantages: (i) naturally representing five main factors of protein structure and properties by wavelet analysis technique; (ii) extracting novel wavelet features that can capture hidden components from solenoid sequence similarities and distinguish them from global proteins; (iii) obtaining statistics features that capture repeating motifs of solenoid proteins. RESULTS: Our method analyzes the characteristics of amino acid sequence in both spectral and temporal domains using SWPT. Both global and local information of proteins are captured by SWPT coefficients. We obtain and integrate wavelet-based features and statistics-based features of amino acid sequence to improve the classification task. Our proposed method is evaluated by comparing to state-of-the-art methods such as HHrepID and REPETITA. The experimental results show that our algorithm consistently outperforms them in areas under ROC curve. At the same false positive rate, the sensitivity of our WAVELET method is higher than other methods. AVAILABILITY: http://www.naaan.org/anvo/Software/Software.htm.

Dataset Information

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

Publications

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

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