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Affine Invariant Geometry for Non-rigid Shapes

Author(s)
Raviv, Dan; Kimmel, Ron
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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Abstract
Shape recognition deals with the study geometric structures. Modern surface processing methods can cope with non-rigidity—by measuring the lack of isometry, deal with similarity or scaling—by multiplying the Euclidean arc-length by the Gaussian curvature, and manage equi-affine transformations—by resorting to the special affine arc-length definition in classical equi-affine differential geometry. Here, we propose a computational framework that is invariant to the full affine group of transformations (similarity and equi-affine). Thus, by construction, it can handle non-rigid shapes. Technically, we add the similarity invariant property to an equi-affine invariant one and establish an affine invariant pseudo-metric. As an example, we show how diffusion geometry can encapsulate the proposed measure to provide robust signatures and other analysis tools for affine invariant surface matching and comparison.
Date issued
2014-06
URI
http://hdl.handle.net/1721.1/103333
Department
Massachusetts Institute of Technology. Media Laboratory
Journal
International Journal of Computer Vision
Publisher
Springer US
Citation
Raviv, Dan, and Ron Kimmel. “Affine Invariant Geometry for Non-Rigid Shapes.” Int J Comput Vis 111, no. 1 (June 14, 2014): 1–11.
Version: Author's final manuscript
ISSN
0920-5691
1573-1405

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