Random change on a Lie group and mean glaucomatous projective shape change detection from stereo pair images

In this article we develop a nonparametric methodology for estimating the mean change for matched samples on a Lie group. We then notice that for k ≥ 5, a manifold of projective shapes k-ads in 3D has a structure of 3k − 15 dimensional Lie group that is equivariantly embedded in an Euclidean space, therefore testing for mean change amounts to a one sample test for extrinsic means on this Lie group. The Lie group technique leads to a large sample and nonparametric bootstrap test for one population extrinsic mean on a projective shape space, as recently developed by Patrangenaru, Liu and Sughatadasa. On the other hand, in absence of occlusions, the 3D projective shape of a spatial configurations can be recovered from a stereo pair of images, thus allowing to test for mean glaucomatous 3D projective shape change detection from standard stereo pair eye images.