Bi-invariant Two-Sample Tests in Lie Groups for Shape Analysis

  • We propose generalizations of the T²-statistics of Hotelling and the Bhattacharayya distance for data taking values in Lie groups. A key feature of the derived measures is that they are compatible with the group structure even for manifolds that do not admit any bi-invariant metric. This property, e.g., assures analysis that does not depend on the reference shape, thus, preventing bias due to arbitrary choices thereof. Furthermore, the generalizations agree with the common definitions for the special case of flat vector spaces guaranteeing consistency. Employing a permutation test setup, we further obtain nonparametric, two-sample testing procedures that themselves are bi-invariant and consistent. We validate our method in group tests revealing significant differences in hippocampal shape between individuals with mild cognitive impairment and normal controls.
Metadaten
Author:Martin HanikORCiD, Hans-Christian HegeORCiDGND, Christoph von TycowiczORCiD
Document Type:In Proceedings
Parent Title (English):Shape in Medical Imaging
First Page:44
Last Page:54
Publisher:Springer International Publishing
Place of publication:Cham
Year of first publication:2020
Page Number:11
ArXiv Id:http://arxiv.org/abs/2008.12195
DOI:https://doi.org/10.1007/978-3-030-61056-2_4