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A Low-dimensional Representation for Robust Partial Isometric Correspondences Computation

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons123496

Brunton,  Alan
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45695

Wand,  Michael
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45449

Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons123492

Weinkauf,  Tino
Computer Graphics, MPI for Informatics, Max Planck Society;

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Citation

Brunton, A., Wand, M., Wuhrer, S., Seidel, H.-P., & Weinkauf, T. (2014). A Low-dimensional Representation for Robust Partial Isometric Correspondences Computation. Graphical Models, 76(2), 70-85. doi:10.1016/j.gmod.2013.11.003.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-F6E9-5
Abstract
Intrinsic shape matching has become the standard approach for pose invariant correspondence estimation among deformable shapes. Most existing approaches assume global consistency. While global isometric matching is well understood, only a few heuristic solutions are known for partial matching. Partial matching is particularly important for robustness to topological noise, which is a common problem in real-world scanner data. We introduce a new approach to partial isometric matching based on the observation that isometries are fully determined by local information: a map of a single point and its tangent space fixes an isometry. We develop a new representation for partial isometric maps based on equivalence classes of correspondences between pairs of points and their tangent-spaces. We apply our approach to register partial point clouds and compare it to the state-of-the-art methods, where we obtain significant improvements over global methods for real-world data and stronger guarantees than previous partial matching algorithms.