Journal of Multivariate Analysis
Mean location and sample mean location on manifolds: asymptotics, tests, confidence regions
Journal of Multivariate Analysis
What can be seen in three dimensions with an uncalibrated stereo rig
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
Simultaneous Multiple 3D Motion Estimation via Mode Finding on Lie Groups
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Sharp adaptation for spherical inverse problems with applications to medical imaging
Journal of Multivariate Analysis
The one- and multi-sample problem for functional data with application to projective shape analysis
Journal of Multivariate Analysis
Journal of Multivariate Analysis
A nonparametric approach to 3D shape analysis from digital camera images - I
Journal of Multivariate Analysis
Asymptotic Minimax Bounds for Stochastic Deconvolution Over Groups
IEEE Transactions on Information Theory
Applied Stochastic Models in Business and Industry
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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.