A hierarchical geodesic model for diffeomorphic longitudinal shape analysis

Authors:
Nikhil Singh;Jacob Hinkle;Sarang Joshi;P. Thomas Fletcher
Affiliations:
Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah;Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah;Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah;Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah
Venue:
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Year:
2013

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Abstract

Hierarchical linear models (HLMs) are a standard approach for analyzing data where individuals are measured repeatedly over time. However, such models are only applicable to longitudinal studies of Euclidean data. In this paper, we propose a novel hierarchical geodesic model (HGM), which generalizes HLMs to the manifold setting. Our proposed model explains the longitudinal trends in shapes represented as elements of the group of diffeomorphisms. The individual level geodesics represent the trajectory of shape changes within individuals. The group level geodesic represents the average trajectory of shape changes for the population. We derive the solution of HGMs on diffeomorphisms to estimate individual level geodesics, the group geodesic, and the residual geodesics. We demonstrate the effectiveness of HGMs for longitudinal analysis of synthetically generated shapes and 3D MRI brain scans.