A joint segmentation-registration framework based on weighted total variation and nonlinear elasticity principles

In this paper, we address the issue of designing a theoretically well-motivated joint segmentation-registration method capable of handling large deformations. Motivated by the fine properties of Saint Venant-Kirchhoff materials, we propose to view the shapes to be matched as such materials and introduce a variational model combining a measure of dissimilarity based on weighted total variation and a regularizer based on the stored energy function of a Saint Venant-Kirchhoff material. We derive a relaxed problem associated to this initial one for which we are able to provide a result of existence of minimizers. A description and analysis of a numerical method of resolution based on a decoupling principle is then provided including a theoretical result of Γ-convergence. Applications on biological images are provided.