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Preprint: "SHAH: SHape-Adaptive Haar wavelet transform for images with application to classification", by Timmermans & Fryzlewicz
 
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Piotr Fryzlewicz (p.fryzlewicz@lse.ac.uk)
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PostPosted: Wed Apr 25, 2012 6:07 pm    
Subject: Preprint: "SHAH: SHape-Adaptive Haar wavelet transform for images with application to classification", by Timmermans & Fryzlewicz
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Title:
SHAH: SHape-Adaptive Haar wavelet transform for images with application to classification

Authors:
Catherine Timmermans, Universite Catholique de Louvain, catherine.timmermans@uclouvain.be
Piotr Fryzlewicz, London School of Economics, p.fryzlewicz@lse.ac.uk

Abstract:
We propose the SHAH (SHape-Adaptive Haar) transform for images, which results in an orthonormal,
adaptive decomposition of the image into Haar-like components, arranged hierarchically according to
decreasing importance, whose shapes reflect the features present in the image. The decomposition is as
sparse as it can be for piecewise-constant images. It is performed via an iterative bottom-up algorithm
with quadratic computational complexity; however, nearly-linear variants also exist. SHAH is rapidly
invertible.
We use SHAH to define the BAGIDIS semi-distance between images. It compares both the amplitudes
and the locations of the SHAH components of the images and is flexible enough to account for feature
misalignment. Performance of the SHAH+BAGIDIS methodology is illustrated in regression, classification
and clustering problems and shown to be very encouraging.
A clear asset of the methodology is its very general scope: it can be used with any images or more
generally with any data that can be described as graphs or networks.

Available from:
http://stats.lse.ac.uk/fryzlewicz/shah/shah.pdf
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