Formulating and solving a class of optimization problems for high-performance gray world automatic white balance

This paper provides new insights into methods performing automatic white balance for a digitally captured image. It is shown that automatic white balance may be formulated as an optimization problem with explicit definition of objective function, decision variables, and constraints. Three alternative methods of formulating the optimization problem are proposed. It is also shown that fuzzy inference rules, commonly utilized in existing literatures to evaluate to what degree an image satisfying the gray world assumption, may be incorporated into the objective function of the optimization problem. A two-stage adjustment law with constrained search direction is then proposed to update the decision variables. A gradient descent algorithm is employed to numerically solve the problem, which guarantees the convergence and that optimal white balance effort is achieved for most images. Experimental results and a comparative study justify that the proposed methods are preferable to existing methods with regard to the execution time, the algorithmic complexity, and the performance.