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Nonlinear Elasticity Registration and Sobolev Gradients

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Biomedical Image Registration (WBIR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6204))

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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 L 2 gradient, we construct a Sobolev H 1 gradient descent method [13] and take advantage of the smoothing quality of the Sobolev operator \((Id-\triangle)^{-1}\). The MR model with Sobolev H 1 gradient descent (SGMR) improves both matching criterion and computational time substantially. We further apply the L 2 and Sobolev gradient to landmark registration for multi-modal mouse brain data, and observe faster convergence and better landmark matching for the MR model with Sobolev H 1 gradient descent.

Work funded by the National Institutes of Health through the NIH Roadmap for Medical Research, Grant U54 RR021813 entitled Center for Computational Biology.

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Lin, T., Dinov, I., Toga, A., Vese, L. (2010). Nonlinear Elasticity Registration and Sobolev Gradients. In: Fischer, B., Dawant, B.M., Lorenz, C. (eds) Biomedical Image Registration. WBIR 2010. Lecture Notes in Computer Science, vol 6204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14366-3_24

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  • DOI: https://doi.org/10.1007/978-3-642-14366-3_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14365-6

  • Online ISBN: 978-3-642-14366-3

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