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

Abstract

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 of k-ads in 3D has the structure of a 3k-15 dimensional Lie group that is equivariantly embedded in a 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 a 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 the absence of occlusions, the 3D projective shape of a spatial k-ad can be recovered from a stereo pair of images, thus allowing one to test for mean glaucomatous 3D projective shape change detection from standard stereo pair eye images.Lie group 3D projective shape Extrinsic means One sample test statistic on manifolds Nonparametric bootstrap Stereo pairs 3D scene reconstruction from a pair of noncalibrated camera views Medical imaging of the eye