A unified hyperelastic joint segmentation/registration model based on weighted total variation and nonlocal shape descriptors

Abstract

In this paper, we address the issue of designing a unified variational model for joint segmentation and registration in which the shapes to be matched are viewed as hyperelastic materials, and more precisely, as Saint Venant-Kirchhoff ones. The dissimilarity measure relates local and global (or region-based) information, since relying on weighted total variation and on a nonlocal shape descriptor inspired by the Chan-Vese model for segmentation. Theoretical results emphasizing the mathematical and practical soundness of the model are provided, among which relaxation, existence of minimizers, analysis of two numerical methods of resolution, asymptotic results and a Γ-convergence property.