A Non-local Topology-Preserving Segmentation-Guided Registration Model

In this paper, we address the issue of designing a theoretically well-motivated segmentation-guided registration method capable of handling large and smooth deformations. The shapes to be matched are viewed as hyperelastic materials and more precisely as Saint Venant–Kirchhoff ones and are implicitly modeled by level set functions. These are driven in order to minimize a functional containing both a nonlinear-elasticity-based regularizer prescribing the nature of the deformation, and a criterion that forces the evolving shape to match intermediate topology-preserving segmentation results. Theoretical results encompassing existence of minimizers, existence of a weak viscosity solution of the related evolution problem and asymptotic results are given. The study is then complemented by the derivation of the discrete counterparts of the asymptotic results provided in the continuous domain. Both a pure quadratic penalization method and an augmented Lagrangian technique (involving a related dual problem) are investigated with convergence results.