Shape analysis is of central interest in computer vision and geometry processing. Three major computational and theoretical challenges in shape analysis are the computation of correspondences (shape registration or matching), the definition of similarity measures (metrics in shape space), and the generation of intermediate shapes (shape morphing). While there have been numerous solutions proposed to these challenges over the years, existing approaches suffer from various shortcomings–most importantly the computed solutions often require good initial registrations (with human interaction), have outlier solutions, or the respective algorithms are computationally too demanding which prohibits processing of complex, high-resolution shapes. Moreover, respective methods are often designed for perfect meshes and hardly generalize to other shape representations, for example, to noisy point cloud geometries. The aim of this project is to study the above challenges in the framework of shape interpolation: Given two or more shapes create a family of interpolating shapes. Such an interpolation will invariably entail metrics and correspondences. In particular, we will
devise shape interpolation methods for a variety of different shape representations such as point clouds, meshes, or signed distance functions.