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The Euclidean (edge-to-edge) distances around geodesic rings tend to correlate quite well with the identity of a person, which following some further refinements show a recognition rate flirting with 90%, based on this overnight experiment. Further improvements can and will be made. Combining this with GMDS can give much higher recognition rates.
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The reason why rotation helps is implementation related. Geodesics are intrinsic measures. The Euclidean distances are measured along axes in three dimensions and by rotating around the axes we can conveniently measure more separable distances. The next step will be taking a sample of 60 Euclidean distances and modeling them, encoding each face as a parameterised model with PCA, then comparing faces in Eigenspace, measuring the distances between them in a clever high-dimensional way.
