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Hamilton-Jacobi Skeletons

The eikonal equation and variants of it are of significant 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 received little consideration
in computer vision. We have introduced a new algorithm for simulating the
eikonal equation, which offers a number of computational and conceptual
advantages over the earlier methods when it comes to shock tracking. In
parallel we have developed a very efficient algorithm for shock detection,
where the key idea is to measure the net outward flux of a vector field
per unit volume, and to detect locations where a conservation of energy
principle is violated. A representative example of a 3D skeleton obtained
from this framework is shown in Fig. 5.6.
*K. Siddiqi, S. Bouix, A. Tannenbaum (University of Minnesota)*

Figure 5.6: Two views of a (3D) divergence-based skeleton of brain
ventricles, segmented from a 3D MR image.

*Annual Report*

*Mon Jun 26 21:22:20 GMT 2000*