This article proposes a hyperelastic 3D deformable template for the segmentation of soft structures. It relies on a template, which is a topological, geometrical and material model of the structure to segment. The template is modeled as an elastic body which is deformed by forces derived from the image. The proposed model is based on the nonlinear three-dimensional elasticity problem with a boundary condition of pure traction. In addition, the applied forces depend on the displacements. For computations, a convergent algorithm is proposed to minimize the global energy of template deformation. A discrete algorithm using the finite element method is presented and illustrated on MR images of mice.
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