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Lin T, Guyader CL, Dinov I, et al. Gene Expression Data to Mouse Atlas Registration Using a Nonlinear Elasticity Smoother and Landmark Points Constraints. J Sci Comput. 2012;50(3)doi: 10.1007/s10915-011-9563-6.
Lin, T., Guyader, C. L., Dinov, I., Thompson, P., Toga, A., & Vese, L. (2012). Gene Expression Data to Mouse Atlas Registration Using a Nonlinear Elasticity Smoother and Landmark Points Constraints. Journal of scientific computing, 50(3), . https://doi.org/10.1007/s10915-011-9563-6
Lin, Tungyou, et al. "Gene Expression Data to Mouse Atlas Registration Using a Nonlinear Elasticity Smoother and Landmark Points Constraints." Journal of scientific computing vol. 50,3 (2012). doi: https://doi.org/10.1007/s10915-011-9563-6
Lin T, Guyader CL, Dinov I, Thompson P, Toga A, Vese L. Gene Expression Data to Mouse Atlas Registration Using a Nonlinear Elasticity Smoother and Landmark Points Constraints. J Sci Comput. 2012 Mar;50(3). doi: 10.1007/s10915-011-9563-6. PMID: 24273381; PMCID: PMC3838306.
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J Sci Comput. 2012 Mar;50(3). doi: 10.1007/s10915-011-9563-6.

Gene Expression Data to Mouse Atlas Registration Using a Nonlinear Elasticity Smoother and Landmark Points Constraints.

Journal of scientific computing

Tungyou Lin, Carole Le Guyader, Ivo Dinov, Paul Thompson, Arthur Toga, Luminita Vese

Affiliations

  1. Department of Mathematics, UCLA, Los Angeles, CA, USA.

PMID: 24273381 PMCID: PMC3838306 DOI: 10.1007/s10915-011-9563-6

Abstract

This paper proposes a numerical algorithm for image registration using energy minimization and nonlinear elasticity regularization. Application to the registration of gene expression data to a neuroanatomical mouse atlas in two dimensions is shown. We apply a nonlinear elasticity regularization to allow larger and smoother deformations, and further enforce optimality constraints on the landmark points distance for better feature matching. To overcome the difficulty of minimizing the nonlinear elasticity functional due to the nonlinearity in the derivatives of the displacement vector field, we introduce a matrix variable to approximate the Jacobian matrix and solve for the simplified Euler-Lagrange equations. By comparison with image registration using linear regularization, experimental results show that the proposed nonlinear elasticity model also needs fewer numerical corrections such as regridding steps for binary image registration, it renders better ground truth, and produces larger mutual information; most importantly, the landmark points distance and

Keywords: Calculus of variations; Gene expression data; Image registration; Landmark-based; Mouse atlas; Multi-modal; Nonlinear elasticity; Saint Venant-Kirchhoff material

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