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

M. Crane and V. Patrangenaru

Journal of Multivariate Analysis, 2011, vol. 102, issue 2, 225-237

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.

Keywords: 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 (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00186-7
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:102:y:2011:i:2:p:225-237

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().