Gene to mouse atlas registration using a landmark-based nonlinear elasticity smoother

Tungyou Lin; Carole Le Guyader; Erh-Fang Lee; Ivo D. Dinov; Paul M. Thompson; Arthur W. Toga; Luminita A. Vese

doi:10.1117/12.812491

27 March 2009 Gene to mouse atlas registration using a landmark-based nonlinear elasticity smoother

Tungyou Lin, Carole Le Guyader, Erh-Fang Lee, Ivo D. Dinov, Paul M. Thompson, Arthur W. Toga, Luminita A. Vese

Proceedings Volume 7259, Medical Imaging 2009: Image Processing; 72592Q (2009) https://doi.org/10.1117/12.812491
Event: SPIE Medical Imaging, 2009, Lake Buena Vista (Orlando Area), Florida, United States

Abstract

We propose a unified variational approach for registration of gene expression data to neuroanatomical mouse atlas in two dimensions. The proposed energy (minimized in the unknown displacement u) is composed of three terms: a standard data fidelity term based on L² similarity measure, a regularizing term based on nonlinear elasticity (allowing larger smooth deformations), and a geometric penalty constraint for landmark matching. We overcome the difficulty of minimizing the nonlinear elasticity functional by introducing an auxiliary variable v that approximates ∇u, the Jacobian of the unknown displacement u. We therefore minimize now the functional with respect to the unknowns u (a vector-valued function of two dimensions) and v (a two-by-two matrix-valued function). An additional quadratic term is added, to insure good agreement between v and ∇u. In this way, the nonlinearity in the derivatives of the unknown u no longer exists in the obtained Euler-Lagrange equations, producing simpler implementations. Several satisfactory experimental results show that gene expression data are mapped to a mouse atlas with good landmark matching and smooth deformation. We also present comparisons with the biharmonic regularization. An advantage of the proposed nonlinear elasticity model is that usually no numerical correction such as regridding is necessary to keep the deformation smooth, while unifying the data fidelity term, regularization term, and landmark constraints in a single minimization approach.

Citation Download Citation

Tungyou Lin, Carole Le Guyader, Erh-Fang Lee, Ivo D. Dinov, Paul M. Thompson, Arthur W. Toga, and Luminita A. Vese "Gene to mouse atlas registration using a landmark-based nonlinear elasticity smoother", Proc. SPIE 7259, Medical Imaging 2009: Image Processing, 72592Q (27 March 2009); https://doi.org/10.1117/12.812491

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