The stability and control of discrete processes
The stability and control of discrete processes
Relaxation labelling algorithms-a review
Image and Vision Computing
Nonlinear discriminant functions and associative memories
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Optimisation algorithms in probabilistic relaxation labelling
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Fast Approximate Energy Minimization via Graph Cuts
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Qualitative Scene Interpretation Using Planar Surfaces
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New Measurements and Corner-Guidance for Curve Matching with Probabilistic Relaxation
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Efficiently Computing Weighted Tree Edit Distance Using Relaxation Labeling
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Automated Nomenclature Labeling of the Bronchial Tree in 3D-CT Lung Images
MICCAI '02 Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part II
Computing approximate tree edit distance using relaxation labeling
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Handwriting Matching and Its Application to Handwriting Synthesis
ICDAR '05 Proceedings of the Eighth International Conference on Document Analysis and Recognition
Robust Point Matching for Nonrigid Shapes by Preserving Local Neighborhood Structures
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Discovering Shape Classes using Tree Edit-Distance and Pairwise Clustering
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Dynamical Systems for Discovering Protein Complexes and Functional Modules from Biological Networks
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PKDD 2007 Proceedings of the 11th European conference on Principles and Practice of Knowledge Discovery in Databases
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We present some new results which definitively explain thebehavior of the classical, heuristic nonlinear relaxation labelingalgorithm of Rosenfeld, Hummel, and Zucker in terms of theHummel-Zucker consistency theory and dynamical systems theory. Inparticular, it is shown that, when a certain symmetry condition is met,the algorithm possesses a Liapunov function which turns out to be (thenegative of) a well-known consistency measure. This follows almostimmediately from a powerful result of Baum and Eagon developed in thecontext of Markov chain theory. Moreover, it is seen that most of theessential dynamical properties of the algorithm are retained when thesymmetry restriction is relaxed. These properties are also shown tonaturally generalize to higher-order relaxation schemes. Someapplications and implications of the presented results are finallyoutlined.