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

Authors:
Tungyou Lin;Carole Guyader;Ivo Dinov;Paul Thompson;Arthur Toga;Luminita Vese
Affiliations:
Department of Mathematics, UCLA, Los Angeles, USA;Laboratoire de Mathématiques, INSA Rouen, Sant-Éteènne-du-Rouvray cedex, France;Laboratory of Neuro Imaging, UCLA School of Medicine, Los Angeles, USA;Laboratory of Neuro Imaging, UCLA School of Medicine, Los Angeles, USA;Laboratory of Neuro Imaging, UCLA School of Medicine, Los Angeles, USA;Department of Mathematics, UCLA, Los Angeles, USA
Venue:
Journal of Scientific Computing
Year:
2012

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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 L 2 dissimilarity measure between the gene expression data and corresponding mouse atlas are smaller compared with the registration model with biharmonic regularization.