Random change on a Lie group and mean glaucomatous projective shape change detection from stereo pair images |
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Authors: | M CraneV Patrangenaru |
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Institution: | Florida State University, Department of Statistics, United States |
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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. |
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Keywords: | primary 62H11 secondary 62H10 62H35 |
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