Relaxation labelling algorithms-a review
Image and Vision Computing
Two stages of curve detection suggest two styles of visual computation
Neural Computation
Relaxation by the Hopfield neural network
Pattern Recognition
Autoassociative learning in relaxation labeling networks
Pattern Recognition Letters
The Dynamics of Nonlinear Relaxation Labeling Processes
Journal of Mathematical Imaging and Vision
On the Foundations of Probabilistic Relaxationwith Product Support
Journal of Mathematical Imaging and Vision
Neural Networks for Optimization and Signal Processing
Neural Networks for Optimization and Signal Processing
Computer Vision
Learning Compatibility Coefficients for Relaxation Labeling Processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
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We study the dynamical properties of two new relaxation labeling schemes described in terms of differential equations, and hence evolving in continuous time. This contrasts with the customary approach to defining relaxation labeling algorithms which prefers discrete time. Continuous-time dynamical systems are particularly attractive because they can be implemented directly in hardware circuitry, and the study of their dynamical properties is simpler and more elegant. They are also more plausible as models of biological visual computation. We prove that the proposed models enjoy exactly the same dynamical properties as the classical relaxation labeling schemes, and show how they are intimately related to Hummel and Zucker's now classical theory of constraint satisfaction. In particular, we prove that, when a certain symmetry condition is met, the dynamical systems' behavior is governed by a Liapunov function which turns out to be (the negative of) a well-known consistency measure. Moreover, we prove that the fundamental dynamical properties of the systems are retained when the symmetry restriction is relaxed. We also analyze the properties of a simple discretization of the proposed dynamics, which is useful in digital computer implementations. Simulation results are presented which show the practical behavior of the models.