A LAGRANGIAN FORMULATION FOR STATISTICAL FLUID REGISTRATION

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 0 ^th and 1 ^rst 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.

Keywords: Riemannian metrics; genetics; registration; statistical prior.

Fig. 1

Heritability computed from the ICC. Red: more heritable regions h² = 0.75 - Blue: regions with no genetic influence h² = 0 - Top left: A0 no statistical information - Top right: A1 statistical information on the displacements - Bottom left: A2 statistical information on the deformation matrices - Bottom right: A3 both

Fig. 2

distance: left algorithm with dissipation with measure d1 right: algorithm without any stats with measure d2