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June 2013 Bayesian alignment of similarity shapes
Kanti V. Mardia, Christopher J. Fallaize, Stuart Barber, Richard M. Jackson, Douglas L. Theobald
Ann. Appl. Stat. 7(2): 989-1009 (June 2013). DOI: 10.1214/12-AOAS615

Abstract

We develop a Bayesian model for the alignment of two point configurations under the full similarity transformations of rotation, translation and scaling. Other work in this area has concentrated on rigid body transformations, where scale information is preserved, motivated by problems involving molecular data; this is known as form analysis. We concentrate on a Bayesian formulation for statistical shape analysis. We generalize the model introduced by Green and Mardia [Biometrika 93 (2006) 235–254] for the pairwise alignment of two unlabeled configurations to full similarity transformations by introducing a scaling factor to the model. The generalization is not straightforward, since the model needs to be reformulated to give good performance when scaling is included. We illustrate our method on the alignment of rat growth profiles and a novel application to the alignment of protein domains. Here, scaling is applied to secondary structure elements when comparing protein folds; additionally, we find that one global scaling factor is not in general sufficient to model these data and, hence, we develop a model in which multiple scale factors can be included to handle different scalings of shape components.

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Kanti V. Mardia. Christopher J. Fallaize. Stuart Barber. Richard M. Jackson. Douglas L. Theobald. "Bayesian alignment of similarity shapes." Ann. Appl. Stat. 7 (2) 989 - 1009, June 2013. https://doi.org/10.1214/12-AOAS615

Information

Published: June 2013
First available in Project Euclid: 27 June 2013

zbMATH: 06279862
MathSciNet: MR3113498
Digital Object Identifier: 10.1214/12-AOAS615

Keywords: morphometrics , protein bioinformatics , similarity transformations , statistical shape analysis , unlabeled shape analysis

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.7 • No. 2 • June 2013
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