Affine Invariant Geometry for Non-rigid Shapes
Author(s)Raviv, Dan; Kimmel, Ron
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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.
DepartmentMassachusetts Institute of Technology. Media Laboratory
International Journal of Computer Vision
Raviv, Dan, and Ron Kimmel. “Affine Invariant Geometry for Non-Rigid Shapes.” Int J Comput Vis 111, no. 1 (June 14, 2014): 1–11.
Author's final manuscript