Mean Curvature Is a Good Regularization for Image Processing

Ill-posed problems are very common in many image processing and computer vision tasks. To solve such problems, a regularization must be imposed. In this paper, we argue why mean curvature is a good regularization for these tasks. From a geometry point of view, we show that minimizing mean curvature is to assume that the ground truth is a piece-wise minimal surface. From a statistics point of view, we show that the mean curvature from natural images is sparse. From an optimization point of view, we show that the gradient of mean curvature regularization can be numerically approximated by very simple filters. This fact significantly simplifies the optimization procedure. Thus, the link between these filters and the gradient of mean curvature regularization is established in this paper. In summary, mean curvature is a proper regularization for various ill-posed problems in image processing and computer vision.

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