Iglesias, Jose A.Berkels, BenjaminRumpf, MartinScherzer, OtmarMichael Bronstein and Jean Favre and Kai Hormann2014-02-012014-02-012013978-3-905674-51-4https://doi.org/10.2312/PE.VMV.VMV13.089-096Frequently, one aims at the co-registration of geometries described implicitly by images as level sets. This paper proposes a novel shape sensitive approach for the matching of such implicit surfaces. Motivated by physical models of elastic shells a variational approach is proposed, which distinguishes two different types of energy contributions: a membrane energy measuring the rate of tangential distortion when deforming the reference surface into the template surface, and a bending energy reflecting the required amount of bending. The variational model is formulated via a narrow band approach. The built in tangential distortion energy leads to a suitable equidistribution of deformed length and area elements, under the optimal matching deformation, whereas the minimization of the bending energy fosters a proper matching of shape features such as crests, valleys or bumps. In the implementation, a spatial discretization via finite elements, a nonlinear conjugate gradient scheme with a Sobolev metric, and a cascadic multilevel optimization strategy are used. The features of the proposed method are discussed via applications both for synthetic and realistic examples.I.3.5 [Computer Graphics]Computational Geometry and Object ModelingBoundary representationsI.4.3 [Image Processing and Computer Vision]EnhancementRegistration