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Overview

The most basic idea is that shapes can be modeled by applying warps to a given correspondence between them (e.g. landmark points). These warps manipulate the correspondence and can therefore produce better shape models. An optimiser is used to warp the correspondence in a fashion that is constructive.

Figure shows that selecting landmark points arbitrarily (or just selecting points that are equally spaced) leads to a model which is poorer than one where careful manual selection of correspondences was involved (as shown in Figure ).

Figure: first two modes of variation of a model built from the equally-spaced annotated training set. Figure from Rhodri Davies [].

Figure: first two modes of variation of a model built from manually-annotated hand data. The figure shows the effect of independently varying the first two modes of variation. Figure from Rhodri Davies [].

By comparing the two figures, it should become evident that if one selects the wrong correspondences, one will obtain poor models. The model of the hand should ideally be capable of encapsulating something which does not result in distortions of a natural form of a hand, as illustrated by the first mode of variation in Figure (notice how thickness of the fingers varies).

This chapter addresses the need to find good correspondences and explores some previous work. In particular, it considers an approach where establishing correspondence is posed as an optimisation problem, where the aim is to select the correspondences between shapes in the training set that result in the best model.

This correspondence-by-optimisation approach requires 3 things:

1. Method of measuring model quality;
2. Method of manipulating correspondence;
3. Method of optimising.

Each one will be dealt with in turn, but as model quality will be measured in terms that are information theoretic, I begin with an introduction to the subject.