STATISTICS COLLOQUIUM
FRIDAY, October 30th, 2009 at 2.10pm, MSB 1147 (Colloquium Room)
Refreshments: 3.30pm, MSB 4110 (Statistics Lounge)
Speaker: Vic Patrangenaru (Florida State University)
Title: Tests for Mean P-Quaternion Objects and Glaucomatous Change Detection from Stereoscopic images of the Eye Fundus.
Abstract: This is joint work with M. Crane. 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 general position in 3D has a structure of 3k - 15 dimensional Lie group (P-Quaternions) that is equivariantly embedded in an Euclidean space, therefore testing for mean 3D projective shape change amounts to a one sample test for extrinsic mean P-Quaternion Objects. 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 [1]. On the other hand, in absence of occlusions, the 3D projective shape of a spatial configuration can be recovered from a stereo pair of images, thus allowing to test for mean glaucomatous 3D projective shape change detection from standard stereo pairs of eye images.
References:
[1] V. Patrangenaru, X. Liu and S. Sugathadasa (2010). Nonparametric 3D Projective Shape Estimation from Pairs of 2D Images - I, In Memory of W.P. Dayawansa. Journal of Multivariate Analysis. 101, 11-31.
