Regularization using the MDL principle: estimation of regularization parameters for regions containing discontinuities

Abstract

Regularization is widely utilized as an effective means of solving ill-posed problems, where the solution cannot be uniquely determined from the observed data alone. In most past studies, regularization is applied by setting the regularization parameter as a constant over the entire given image plane. The objective of this to derive an adequate solution adapted to the local properties of the object. A method is proposed in which the regularization parameter is determined for each local area of an image by the MDL (minimum description length) principle. More precisely, the following method is proposed. The description length, which represents the adequateness of the solution derived from the penalty functional and the stabilization functional, and the description length of the regularization parameter distribution on the image, are calculated. Then, the regularization parameter is estimated for each local area based on the MDL principle so that the sum of those description lengths is minimized. As a result, the regularization parameter is determined for each discontinuous area and each smooth area of the object. Lastly, the proposed method is applied to optical flow estimation, and its effectiveness is demonstrated by the results of experiments. © 1999 Scripta Technica, Syst Comp Jpn, 30(8): 61–71, 1999