  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.
