Combining information using hard constraints

In this paper we show how the use of hard constraints in solving estimation problems, by allowing multiple sources of information to be taken into account during optimization, increases robustness and improves efficiency over alternative methods such as the statistical combination of separate optimization results. Our argument is based on an empirical evaluation of the technique which uses a model-based optical flow constraint in a deformable model framework for tracking a face. The flow constraint makes the model-to-edge alignment optimization problem easier by projecting away the portion of the search space that optical flow makes unlikely, while a Kalman filter is used to reconcile hard constraints with the uncertainty in the optical flow data. Using these hard constraints, the system converges more quickly at each iteration and avoids local minima in solutions that cause other methods to lose track. We conjecture that this use of constraints will be effective in any integration application where there are disparities in the difficulty of computational problems associated with the we of different information sources.