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 since 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.

Figure 1: Progression of development in shape correspondence methods.

Figure 2: Examples of applications that make use of correspondence methods: (a) a set of scans (to the left) is rigidly aligned to reconstruct the shape of the bunny (to the right), (b) the horse in two different poses (to the left) is non-rigidly aligned (result shown to the right), (c) the teapot is morphed into the cup, (d) the motion defined on the horse (top line) is transferred to the camel (bottom line), (e) an application of partial matching: the suction cups on the tentacles of the octopus are detected as being similar (highlighted in yellow), (f) a set of range scans of an object in motion (shown to the left in blue) provides a single reconstructed model on which the motion is defined (shown to the right in color).

PPT Slides (28MB)

We would like to thank the reviewers for their valuable comments and the authors who granted us permission to use their figures in our work. The models used in our illustrations are from the AIM@SHAPE Repository, the SHREC 2007 Watertight Track, and the Non-rigid World Dataset. This work was supported in part by NSERC Grants (Nos. 611370 and 611393), a MITACS Research Grant (No. 699127), and the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.

@inproceedings{vankaick10correspsurvey, author = {Oliver van Kaick and Hao Zhang and Ghassan Hamarneh and Daniel Cohen-Or}, title = {A Survey on Shape Correspondence}, booktitle = {Proc. of Eurographics State-of-the-art Report}, pages = {1--24}, year = 2010, } @article{vankaick11correspsurvey, author = {Oliver van Kaick and Hao Zhang and Ghassan Hamarneh and Daniel Cohen-Or}, title = {A Survey on Shape Correspondence}, journal = {Computer Graphics Forum}, volume = {30}, number = {6}, pages = {1681--1707}, year = 2011, }