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It is worth starting off with a description of the most recent and most relevant developments. The following few paragraphs summarise and highlight some of the main principles which describe the methods used in the existing systems. These are the systems that surely need to be extended and their understanding is the most crucial.
Smith's work follows the work of Davies in an obvious sense, but it explores a different domain with slightly different aims. Davies repeatedly performed a reparameterisation over a given series of shapes, or rather their defining points. All these points were shifted in accordance with displacements, as orchestrated by a monotonically increasing curve. This reparameterisation was applied to all examples in the training set to evaluate an optimal choice of point spreads, or more precisely, the favourable reparameterisations that act upon these points.
In current group-wise registration work, the elements that such reparameterisation affects are the points which control the warps applied to the data44. These chosen warps are then applied to all the examples (or data instances) and measures are used to describe how ``similar'' the data is collectively. Different measures of similarity are used as well as different types of warps. Another way of explaining this process is to say that warps are being found that make data lie in similar positions in the imaginary image grid. 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. 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 search45, 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 oppose to the pair-wise measures using beforehand. This construction of a model can in this way guide the search for good warps. MI and MSD are utilised to check local, small-scale changes only. 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 appearance models for the whole data. For example, in the case of these specific experiments, all the bumps are warped to become quite similar so the model created from them has a low determinant.