# Correspondences between Salient Points on 3D Shapes

## Abstract

Establishing correspondences between salient points on 3D shapes results in a function mapping similar parts of 3D objects. In this paper, we present a new method for establishing binary correspondences between salient points on 3D shapes. Our algorithm is independent of the shape representation and the object topology. It does not require any prepositioning of the objects. Our method first detects stable salient points that are representative for certain parts of the shape. For each of these salient points it then computes an associated local shape descriptor. We introduce a matching energy between the salient points in two shapes which depends on the similarity of the descriptors and the spatial relationship of the salient points. An iterative optimization scheme determines a correspondence mapping between the salient points which minimizes this energy. The resulting binary correspondences between the salient points can be used for applications like 3D shape retrieval based on similarity estimation, classification of 3D objects, editing, and statistical shape analysis. It is especially useful as an initialization method for approaches relying on prior knowledge about corresponding points like cross parameterization or morphing.

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## Bibtex

@TECHREPORT{cg-2006-3, author = {Wessel, Raoul and Novotni, Marcin and Klein, Reinhard}, title = {Correspondences between Salient Points on 3D Shapes}, number = {CG-2006-3}, year = {2006}, month = jun, institution = {Universit{\"a}t Bonn}, abstract = {Establishing correspondences between salient points on 3D shapes results in a function mapping similar parts of 3D objects. In this paper, we present a new method for establishing binary correspondences between salient points on 3D shapes. Our algorithm is independent of the shape representation and the object topology. It does not require any prepositioning of the objects. Our method first detects stable salient points that are representative for certain parts of the shape. For each of these salient points it then computes an associated local shape descriptor. We introduce a matching energy between the salient points in two shapes which depends on the similarity of the descriptors and the spatial relationship of the salient points. An iterative optimization scheme determines a correspondence mapping between the salient points which minimizes this energy. The resulting binary correspondences between the salient points can be used for applications like 3D shape retrieval based on similarity estimation, classification of 3D objects, editing, and statistical shape analysis. It is especially useful as an initialization method for approaches relying on prior knowledge about corresponding points like cross parameterization or morphing.}, issn = {1610-8892} }