A constrained registration problem based on Ciarlet-Geymonat stored energy
Ratiba Derfoul, Carole Le Guyader · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2014
In this paper, we address the issue of designing a theoretically well-motivated registration model capable of handling large deformations and including geometrical constraints, namely landmark points to be matched, in a variational framework. The theory of linear elasticity being unsuitable in this case, since assuming small strains and the validity of Hooke’s law, the introduced functional is based on nonlinear elasticity principles. More precisely, the shapes to be matched are viewed as Ciarlet-Geymonat materials. We demonstrate the existence of minimizers of the related functional minimization problem and prove a convergence result when the number of geometric constraints increases. We then describe and analyze a numerical method of resolution based on the introduction of an associated decoupled problem under inequality constraint in which an auxiliary variable simulates the Jacobian matrix of the deformation field. A theoretical result of -convergence is established. We then provide preliminary 2D results of the proposed matching model for the registration of mouse brain gene expression data to a neuroanatomical mouse atlas.