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Title:Topology Matching for Full Automatic Similarity Estimation of 3D Shapes
Authors: Taku Komura ; Masaki Hilaga ; Yoshihisa Shinagawa ; Tosiyasu Kunii
Date:Aug 2001
Publication Title:Proceedings of the 28th annual conference on Computer Graphics and Interactive Techniques (ACM/SIGGRAPH 2001)
Publication Type:Conference Paper Publication Status:Published
Page Nos:203-212
There is a growing need to be able to accurately and efficiently search visual data sets, and in particular, 3D shape data sets. This paper proposes a novel technique, called Topology Matching, in which similarity between polyhedral models is quickly, accurately, and automatically calculated by comparing Multiresolutional Reeb Graphs (MRGs). The MRG thus operates well as a search key for 3D shape data sets. In particular, the MRG represents the skeletal and topological structure of a 3D shape at various levels of resolution. The MRG is constructed using a continuous function on the 3D shape, which may preferably be a function of geodesic distance because this function is invariant to translation and rotation and is also robust against changes in connectivities caused by a mesh simplification or subdivision. The similarity calculation between 3D shapes is processed using a coarse-to-fine strategy while preserving the consistency of the graph structures, which results in establishing a correspondence between the parts of objects. The similarity calculation is fast and efficient because it is not necessary to determine the particular pose of a 3D shape, such as a rotation, in advance. Topology Matching is particularly useful for interactively searching for a 3D object because the results of the search fit human intuition well.
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Bibtex format
author = { Taku Komura and Masaki Hilaga and Yoshihisa Shinagawa and Tosiyasu Kunii },
title = {Topology Matching for Full Automatic Similarity Estimation of 3D Shapes},
book title = {Proceedings of the 28th annual conference on Computer Graphics and Interactive Techniques (ACM/SIGGRAPH 2001)},
publisher = {ACM},
year = 2001,
month = {Aug},
pages = {203-212},
doi = {},
url = {},

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