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Submitted by pscully on Tue, 10/27/2009 - 09:25.
10/30/2009 - 14:10
10/30/2009 - 15:30
STA/BST 290: Vic Patrangenaru (Florida State U)
Tests for Mean P-Quaternion Objects and Glaucomatous Change Detection from Stereoscopic images of the Eye Fundus.
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 . 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.
 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.