Joint Segmentation/Registration Model by Shape Alignment via Weighted Total Variation Minimization and Nonlinear Elasticity
Solène Ozeré, Christian Gout, Carole Le Guyader · SIAM Journal on Imaging Sciences · 2015
This paper falls within the scope of joint segmentation-registration using nonlinear elasticity principles. Because Saint Venant--Kirchhoff materials are the simplest hyperelastic materials (hyperelasticity being a suitable framework when dealing with large and nonlinear deformations), we propose viewing the shapes to be matched as such materials. Then we 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. Adding a weighted total variation--based criterion enables us to align the edges of the objects even when the modalities are different. We derive a relaxed problem associated to the 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 $\Gamma$-convergence. Applications are illustrated in academic and biological images.