The previous chapters have been mainly concerned with analysis of labelled landmarks, where there is clear, meaningful correspondence between the landmarks. Matching configurations of points where the correspondence is unknown is an important but challenging problem in many application areas, including in bioinformatics and computer vision.
In this chapter we shall consider Bayesian approaches that have been developed for matching unlabelled point sets. The matching problem, where the sets of points may be of different sizes, is relevant for the comparison of molecules and the comparison of objects from different views in computer vision. For example, if we have two protein surfaces represented by sets of amino acid locations, a question of interest is whether the two surfaces have a region of the same size-and-shape. This region may correspond to a binding site that the proteins have in common; for example they may both bind to the same protein molecule.
Some initial inferential methods to compare unlabelled shape include the MCMC simulation methodology developed by Green and Mardia (2006), Dryden et al. (2007) and Schmidler (2007), which themselves have connections with work stemming from Moss and Hancock (1996), Rangarajan et al. (1997), Chui and Rangarajan (2000, 2003) and Taylor et al. (2003) among others.
Consider the dataset which was described in Section 1.4.9. The active site of protein 1 contains 40 amino acids and the ...