Approximate topological matching of quadrilateral meshes

We study approximate topological matching of quadrilateral meshes, that is, the problem of finding as large a set as possible of matching portions of two quadrilateral meshes. This study is motivated by applications in graphics that involve shape modeling whose results need to be merged in order to...

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Bibliographic Details
Published in:2008 IEEE International Conference on Shape Modeling and Applications pp. 83 - 92
Main Authors: Eppstein, D., Goodrich, M.T., Kim, E., Tamstorf, R.
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2008
Subjects:
Animation
Biological system modeling
Computer graphics
F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems-Geometrical problems and computations
Finite element methods
Greedy algorithms
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Boundary representations
Performance analysis
Polynomials
Shape
Simultaneous localization and mapping
Software systems
ISBN:9781424422609, 1424422604
Online Access:Get full text
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Summary:We study approximate topological matching of quadrilateral meshes, that is, the problem of finding as large a set as possible of matching portions of two quadrilateral meshes. This study is motivated by applications in graphics that involve shape modeling whose results need to be merged in order to produce a final unified representation of an object. We show that the problem of producing a maximum approximate topological match of two quad meshes in NP-hard. Given this result, which makes an exact solution extremely unlikely, we show that the natural greedy algorithm derived from polynomial-time graph isomorphism can produce poor results, even when it is possible to find matches with only a few non-matching quads. Nevertheless, we provide a "lazy-greedy" algorithm that is guaranteed to find good matches when mis-matching portions of mesh are localized. Finally, we provide empirical evidence that this approach produces good matches between similar quad meshes.
ISBN:9781424422609
1424422604
DOI:10.1109/SMI.2008.4547954