Last update: Feb. 8, 2004
Publications by Kaleem Siddiqi et al. on shape symmetry elicitation :
BibTeX references.
by K. Siddiqi, S. Bouix, A. R. Tannenbaum & S. W. Zucker.
International Journal of Computer Vision (IJVC), 48(3), 215-231, 2002.
Also appeared in an early version in ICCV'99:
International Conference on Computer Vision (Corfu, Greece), September,
1999.
The eikonal equation and variants of it are of signicant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shape-from-shading and for recent dynamic theories of shape. Its numerical simulation can be delicate, owing to the formation of singularities in the evolving front and is typically based on level set methods. However, there are more classical approaches rooted in Hamiltonian physics which have yet to be widely used by the computer vision community. In this paper we review the Hamiltonian formulation, which offers specic advantages when it comes to the detection of singularities or shocks. We specialize to the case of Blum's grass fire flow and measure the average outward flux of the vector field that underlies the Hamiltonian system. This measure has very different limiting behaviors depending upon whether the region over which it is computed shrinks to a singular point or a non-singular one. Hence, it is an effective way to distinguish between these two cases. We combine the flux measurement with a homotopy preserving thinning process applied in a discrete lattice. This leads to a robust and accurate algorithm for computing skeletons in 2D as well as 3D, which has low computational complexity. We illustrate the approach with several computational examples.
Keywords: eikonal equation, Hamiltonian systems, flux and divergence, 2D and 3D skeletons, shape analysis.
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2004.
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