An implementation for parametric snakes used for object tracking is proposed via generalized deterministic annealing (GDA). Given an arbitrary energy functional that quantifies the quality of the contour solution, GDA computes the snake position by approximating the solution given by stochastic simulated annealing. First, the Markov chain representing the solution space for the snake position is broken into N smaller, local Markov chains representing the position of each discrete snake sample. At each annealing temperature, GDA directly approximates the stationary distribution of the local Markov chains using a mean field approximation for neighboring snake sample positions, and the final distribution reveals the solution. In contrast to the typical implementation via gradient descent, annealing methods can avoid suboptimal local solutions and can be used to compute snakes that are effective in the presence of severe noise and distant initial positions. Unlike simulated annealing, GDA does not utilize random moves to slowly locate a high quality solution and is thus appropriate for time critical applications. In the paper, synthetic experiments (on 231 images) are provided that compare the edge localization performance of snakes computed by GDA, simulated annealing and gradient descent for conditions of varying noise and varying initial snake position. The effectiveness of GDA is also demonstrated in a challenging real-data application (on 910 images) in which white blood cells are tracked from video microscopy.