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Returning to Shape Models

Davies repeatedly performed a reparameterisation over a given series of shapes, or rather their defining points (although in principle he dealt with continuous curves where points are just implicitly defined). All these points were shifted in accordance with some displacements, as orchestrated by a monotonically increasing curve. This reparameterisation was applied to all examples, one reparameterisation for each example^6.1 in the training set to evaluate an optimal choice of point spreads, or more precisely, the favourable reparameterisations that act upon these points (in principle, that is defined with respect to a curve which will be represented by a finite number of sample points.

In current group-wise registration work, the elements that such reparameterisation affects are the points which control the warps applied to the data^6.2. These chosen warps are then applied to all the examples (or data instances) and measures are used to describe the vague notion of model-ability. One could argue that the model provides a good indicator of how ``similar'' the data is collectively, en masse. Another way of explaining this process is to say that warps are being found that reveal data correspondences. Correspondences are found when points (or imaginary sample points of the curve) lie in analogous regions - that is - regions that are describing the same part of the logically equivalent class of objects. A warp implicitly defines an uneven plane for images to be embedded in and when all images get embedded in that plane, they should then be collectively similar. Interestingly, that similarity can be checked with the use of AAM's (reminiscent work can be found in [,,]). Ways of evaluating an appearance model and ways of drawing conclusions about the data that was used to build it already exist. The algorithms developed for this work use a similarity measure such as MSD or MI to see how similar images become during search^6.3, before a model is created. The model created from all the examples is the entity that defines the 'goodness' of the warps. A model can in some sense describe and measure of similarity across the entire set, as opposed to the pair-wise measures used previously. This construction of a model can in that unprecedented way guide the search for good warps. The system seeks control points that define good warps and it seeks such points using the idea of reparameterisation. The resulting warps must then produce good models for the whole data. For example, in the case of these specific experiments, all the data instances are warped to become quite similar so the model created from them has a low determinant.