A landmark-based nonlinear elasticity model for mouse atlas registration

This paper is devoted to the registration of gene expression data to a neuroanatomical mouse atlas in two dimensions. We use a nonlinear elasticity regularization allowing large deformations, guided by an intensity-based data fidelity term and by landmarks. We overcome the difficulty of minimizing the nonlinear elasticity functional by introducing an additional variable v ≃ ∇u, where u is the displacement. Thus, in the obtained Euler-Lagrange equation, the nonlinearity is no longer in the derivatives of the unknown, u. Experimental results show gene expression data mapped to a mouse atlas for a standard L² data fidelity term in the presence of landmarks. We also present comparisons with biharmonic regularization. An advantage of the proposed nonlinear elasticity model is that usually no regridding is necessary, while keeping the data term, regularization term and landmark term in a unified minimization approach.