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A Relaxed Problem of Registration Based on the Saint Venant-Kirchhoff Material Stored Energy for the Mapping of Mouse Brain Gene Expression Data to a Neuroanatomical Mouse Atlas

In this paper, we address the issue of designing a theoretically well-motivated registration model capable of handling large deformations. Motivated by the fine properties of the Saint Venant--Kirchhoff material, we propose a variational model combining a measure of dissimilarity and a regularizer based on the stored energy of such a material. We prove the existence of generalized solutions of this problem. We then describe and analyze a numerical method of resolution based on the introduction of an associated decoupled problem in which an auxiliary variable simulates the Jacobian matrix of the deformation field. A theoretical result is established, and we investigate the efficiency of the proposed matching model for the registration of mouse brain gene expression data to a neuroanatomical mouse atlas.