Bayesian alignment of similarity shapes

Kanti V. Mardia, Christopher J. Fallaize, Stuart Barber, Richard M. Jackson & Douglas L. Theobald
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 (2006) for the pairwise alignment of two unlabelled 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 sufficent 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.

Some key words:
Morphometrics, Protein bioinformatics, Similarity transformations, Statistical shape analysis, Unlabelled shape analysis

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