Establishing Shape Correspondences: A Survey

Shape correspondence between surfaces in 3D is a central problem in geometry processing, concerned with establishing meaningful relations between surfaces. While all correspondence problems share this goal, specific formulations can differ significantly: Downstream applications require certain properties that correspondences must satisfy, while the type of input data and computational constraints influence the choice of method. In this survey, we provide an overview of different correspondence problems, popular paradigms for generating and refining correspondences, and strategies for evaluating their quality. Further, we discuss topological aspects that are especially important for correspondences between surfaces with higher genus. By offering a structured overview and highlighting open challenges, we aim to support and guide future research in the field.