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Extending the range of dilation has not helped in getting better results, despite the fact that conceptually the approach made some sense and surely would have worked to some degree for geodesic distances (although this has not been verified empirically). Surely there should be some way to exploit the descriptors for the sake of face-to-face comparison, but maybe the similarity in topology of faces weakens what is being measured (mainly around the nose tip). The two different approach which were tested could not exceed 80% recognition rate.
We will therefore try dilation at areas further away from the nose.
Expansion of the dilation range well beyond the nose (and accounting for the entire face in comparing images) leads to performance that is only slightly better than a random classifier. The problem as a whole is, we do not have the ground-truth correspondence in images, and being able to compare one image to another at the level of Eigen-decomposition requires this correspondence. Without some edge detection (photometric), it would be hard to obtain. As a geodesic distance alternative for Riemannian surfaces, this new method generally failed to work well enough in just about any experiment that had been set up (there were many). Maybe building a framework around a new Hausdorff distance-based measure will yield something that can usefully be applied to face recognition. Another option would be to revert back to geodesic distances that gave us the best performance so far (with FMM, not exact geodesics). A comprehensive search on the Web does not reveal many surface distance implementations written in Matlab syntax (ones we have not explored already).
While working on 3-D data in isolation we still require at the very least some point of correspondence such as the nose tip. ICP can help get an approximation of other correspondences, but these are never accurate enough. Perhaps there are other known methods of accurately finding more correspondences (from 3-D only), so I will look for some. With more correspondences, far better performance can be assured. Faces would not just 'float' around a single point.