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The previous sections covered methods for registering 1-D data and also presented a few challenges that are posed. The outputs of these registrations are warp fields - also to be treated as ``shapes'' - which define one-to-one correspondences of points embedded in the image data (``intensity''). For illustrative purposes, in Figure fig-examples-miua each curve at the centre represents a warp/transformation (``shape'') applied to bump images in order to make all of them be alike. For the images considered in this case, these transformations - each corresponding to one image - produce the full alignment of images. They produce correspondences.
Having obtained these correspondences, models can be built directly as described in Chapter cha:Active-Appearance-Models. Because the correspondence is dense, there is no limit in principle on the number of sample points from which the shape, appearance, and combined models are constructed.
