Affine Invariant Geometry for Non-rigid Shapes
Name
11263_2014_728_ReferencePDF.pdf
Size
955.22 KB
Format
Adobe PDF
Checksum (MD5)
ba6051fd58d826adba733aa8e1606327
Author(s)
Raviv, Dan
Kimmel, Ron
Date Issued
June 2014
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
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.
MIT Department
Massachusetts Institute of Technology. Media Laboratory
Terms of Use
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.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s11263-014-0728-2
