NDLI: Sasaki metrics for analysis of longitudinal data on manifolds

Content Provider	IEEE Xplore Digital Library
Author	Muralidharan, P. Fletcher, P.T.
Copyright Year	2012
Description	Author affiliation: School of Computing, University of Utah (Muralidharan, P.; Fletcher, P.T.)
Abstract	Longitudinal data arises in many applications in which the goal is to understand changes in individual entities over time. In this paper, we present a method for analyzing longitudinal data that take values in a Riemannian manifold. A driving application is to characterize anatomical shape changes and to distinguish between trends in anatomy that are healthy versus those that are due to disease. We present a generative hierarchical model in which each individual is modeled by a geodesic trend, which in turn is considered as a perturbation of the mean geodesic trend for the population. Each geodesic in the model can be uniquely parameterized by a starting point and velocity, i.e., a point in the tangent bundle. Comparison between these parameters is achieved through the Sasaki metric, which provides a natural distance metric on the tangent bundle. We develop a statistical hypothesis test for differences between two groups of longitudinal data by generalizing the Hotelling $T^{2}$ statistic to manifolds. We demonstrate the ability of these methods to distinguish differences in shape changes in a comparison of longitudinal corpus callosum data in subjects with dementia versus healthily aging controls.
Starting Page	1027
Ending Page	1034
File Size	346137
Page Count	8
File Format	PDF
ISBN	9781467312264
ISSN	10636919
e-ISBN	9781467312288
e-ISBN	9781467312271
DOI	10.1109/CVPR.2012.6247780
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-06-16
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Manifolds Vectors Measurement Data models Shape Tensile stress Equations
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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