Parallel distributed relaxation labeling

A parallel distributed relaxation labeling (RL) method, called the Lagrange-Hopfield (LH) method, is presented. RL is treated as a constrained optimization problem. The LH method solves the problem using the augmented Lagrangian multiplier technique and the graded Hopfield network. The LH method effectively overcomes instabilities that are inherent in the penalty method (e.g. Hopfield network) or the Lagrange multiplier method in constrained optimization. Due to the use of Lagrangian multipliers, the normalization operation in traditional RL methods is dispensed with. This makes the LH algorithm fully parallel and distributed and is suitable for analog implementation. Experiments also show that the method is able to produce good solutions in terms of the optimized objective values.