A constrained registration problem based on Ciarlet-Geymonat stored energy

Ratiba Derfoul; Carole Le Guyader

doi:10.1117/12.2037004

21 March 2014 A constrained registration problem based on Ciarlet-Geymonat stored energy

Ratiba Derfoul, Carole Le Guyader

Proceedings Volume 9034, Medical Imaging 2014: Image Processing; 90343Q (2014) https://doi.org/10.1117/12.2037004
Event: SPIE Medical Imaging, 2014, San Diego, California, United States

Abstract

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.

Citation Download Citation

Ratiba Derfoul and Carole Le Guyader "A constrained registration problem based on Ciarlet-Geymonat stored energy", Proc. SPIE 9034, Medical Imaging 2014: Image Processing, 90343Q (21 March 2014); https://doi.org/10.1117/12.2037004

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KEYWORDS

Image registration

Brain

Numerical analysis

Data modeling

Distance measurement

Medical imaging

Finite element methods

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