Nonlinear elasticity registration and sobolev gradients

Authors:
Tungyou Lin;Ivo Dinov;Arthur Toga;Luminita Vese
Affiliations:
University of California, Los Angeles, CA;University of California, Los Angeles, CA;University of California, Los Angeles, CA;University of California, Los Angeles, CA
Venue:
WBIR'10 Proceedings of the 4th international conference on Biomedical image registration
Year:
2010

Citing 7
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Abstract

We propose Mooney-Rivlin (MR) nonlinear elasticity of hyperelastic materials and numerical algorithms for image registration in the presence of landmarks and large deformation. An auxiliary variable is introduced to remove the nonlinearity in the derivatives of Euler-Lagrange equations. Comparing the MR elasticity model with the Saint Venant-Kirchhoff elasticity model (SVK), the results show that the MR model gives better matching in fewer iterations. To accelerate the slow convergence due to the lack of smoothness of the L2 gradient, we construct a Sobolev H1 gradient descent method [13] and take advantage of the smoothing quality of the Sobolev operator (Id-Δ)-1. The MR model with Sobolev H1 gradient descent (SGMR) improves both matching criterion and computational time substantially. We further apply the L2 and Sobolev gradient to landmark registration for multimodal mouse brain data, and observe faster convergence and better landmark matching for the MR model with Sobolev H1 gradient descent.