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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