Self-annealing and self-annihilation: unifying deterministic annealing and relaxation labeling

Deterministic annealing and relaxation labeling algorithms for classification and matching are presented and discussed. A new approach—self annealing—is introduced to bring deterministic annealing and relaxation labeling into accord. Self annealing results in an emergent linear schedule for winner-take-all and linear assignment problems. Self annihilation, a generalization of self annealing is capable of performing the useful function of symmetry breaking. The original relaxation labeling algorithm is then shown to arise from an approximation to either the self annealing energy function or the corresponding dynamical system. With this relationship in place, self annihilation can be introduced into the relaxation labeling framework. Experimental results on synthetic matching and labeling problems clearly demonstrate the three-way relationship between deterministic annealing, relaxation labeling and self annealing.