A nonlinear elastic deformable template for soft structure segmentation. Application to the heart segmentation in MRI

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