A Survey on Shape Correspondence

TLDR

Shape correspondence is a challenging yet essential problem in geometry processing, motivated by recent advances in space–time registration and semantic shape analysis that require understanding both local and global structure of shapes. This survey reviews methods for computing correspondences between geometric shapes—triangular meshes, contours, or point sets—by examining the problem’s various formulations and summarizing the principal solution approaches. The authors classify correspondence methods by input/output representation, objective function, and solution strategy, and discuss each category’s representative techniques.

Abstract

Abstract We review methods designed to compute correspondences between geometric shapes represented by triangle meshes, contours or point sets. This survey is motivated in part by recent developments in space–time registration, where one seeks a correspondence between non‐rigid and time‐varying surfaces, and semantic shape analysis, which underlines a recent trend to incorporate shape understanding into the analysis pipeline. Establishing a meaningful correspondence between shapes is often difficult because it generally requires an understanding of the structure of the shapes at both the local and global levels, and sometimes the functionality of the shape parts as well. Despite its inherent complexity, shape correspondence is a recurrent problem and an essential component of numerous geometry processing applications. In this survey, we discuss the different forms of the correspondence problem and review the main solution methods, aided by several classification criteria arising from the problem definition. The main categories of classification are defined in terms of the input and output representation, objective function and solution approach. We conclude the survey by discussing open problems and future perspectives.