Stochastic Jump-Diffusion Process for Computing Medial Axes in Markov Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shock Graphs and Shape Matching
International Journal of Computer Vision
Stochastic Computation of Medial Axis in Markov Random Fields
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Skeleton Pruning by Contour Partitioning with Discrete Curve Evolution
IEEE Transactions on Pattern Analysis and Machine Intelligence
Vasculature Segmentation in MRA Images Using Gradient Compensated Geodesic Active Contours
Journal of Signal Processing Systems
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We have been developing a theory of generic 2-D shape based on a reaction-diffusion model from mathematical physics. The description of a shape is derived from the singularities of a curve evolution process driven by the reaction (hyperbolic) term. The diffusion (parabolic) term is related to smoothing and shape simplification. However, the unification of the two is problematic, because the slightest amount of diffusion dominates and prevents the formation of generic first-order shocks. The technical issue is whether it is possible to smooth a shape, in any sense, without destroying the shocks. We now report a constructive solution to this problem, by embedding the smoothing term in a global metric against which a purely hyperbolic evolution is performed from the initial curve. This is a new flow for shape, that extends the advantages of the original one. Specific metrics are developed, which lead to a natural hierarchy of shape features, analogous to the simplification one might perceive when viewing an object from increasing distances. We illustrate our new flow with a variety of examples.