Near-optimal regularization parameters for applications in computer vision

Computer vision requires the solution of many ill-posed problems such as optical flow, structure from motion, shape from shading, surface reconstruction, image restoration and edge detection. Regularization is a popular method to solve ill-posed problems, in which the solution is sought by minimization of a sum of two weighted terms, one measuring the error arising from the ill-posed model, the other indicating the distance between the solution and some class of solutions chosen on the basis of prior knowledge (smoothness, or other prior information). One of important issues in regularization is choosing optimal weight (or regularization parameter). Existing methods for choosing regularization parameters either require the prior information on noise in the data, or are heuristic graphical methods. We apply a method for choosing near-optimal regularization parameters by approximately minimizing the distance between the true solution and the family of regularized solutions. We demonstrate the effectiveness of this approach for the regularization on two examples: edge detection and image restoration.