Determining The Optimal Weights In Multiple Objective Function Optimization

An important problem in computer vision is the determination of weights for multiple objective function optimization. This problem arises naturally in many reconstruction problems, where one wishes to reconstruct a function belonging to a constrained class of signals based upon noisy observed data. A common approach is to combine the objective functions into a single total cost function. The problem then is to determine appropriate weights for the objective functions. In this paper we propose techniques for automatically determining the weights, and discuss their properties. The Min{Max Principle, which avoids the problems of extremely low or high weights, is introduced. Expressions are derived relating the optimal weights, objective function values, and total cost.