A Lagrangian formulation for statistical fluid registration

Authors:
Caroline C. Brun;Natasha Lepore;Xavier Pennec;Yi-Yu Chou;Agatha D. Lee;Marina Barysheva;Greig I. De Zubicaray;Katie L. McMahon;Margaret J. Wright;Arthur W. Toga;Paul M. Thompson
Affiliations:
Laboratory of Neuro Imaging, Department of Neurology, UCLA, Los Angeles, CA;Laboratory of Neuro Imaging, Department of Neurology, UCLA, Los Angeles, CA;Asclepios Research Project, INRIA, Sophia-Antipolis Cedex, France;Laboratory of Neuro Imaging, Department of Neurology, UCLA, Los Angeles, CA;Laboratory of Neuro Imaging, Department of Neurology, UCLA, Los Angeles, CA;Laboratory of Neuro Imaging, Department of Neurology, UCLA, Los Angeles, CA;Centre for Magnetic Resonance, University of Queensland, Brisbane, Queensland, Australia;Centre for Magnetic Resonance, University of Queensland, Brisbane, Queensland, Australia;Genetic Epidemiology Lab, Queensland Institute of Medical Research, Queensland, Australia;Laboratory of Neuro Imaging, Department of Neurology, UCLA, Los Angeles, CA;Laboratory of Neuro Imaging, Department of Neurology, UCLA, Los Angeles, CA
Venue:
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Year:
2009

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Abstract

We defined a new statistical fluid registration method with Lagrangian mechanics. Although several authors have suggested that empirical statistics on brain variation should be incorporated into the registration problem, few algorithms have included this information and instead use regularizers that guarantee diffeomorphic mappings. Here we combine the advantages of a large-deformation fluid matching approach with empirical statistics on population variability in anatomy. We reformulated the Riemannian fluid algorithm developed in [4], and used a Lagrangian framework to incorporate 0th and 1st order statistics in the regularization process. 92 2D midline corpus callosum traces from a twin MRI database were fluidly registered using the non-statistical version of the algorithm (algorithm 0), giving initial vector fields and deformation tensors. Covariance matrices were computed for both distributions and incorporated either separately (algorithm 1 and algorithm 2) or together (algorithm 3) in the registration. We computed heritability maps and two vector and tensor-based distances to compare the power and the robustness of the algorithms.