Fast global optimization of curvature

Two challenges in computer vision are to accommodate noisy data and missing data. Many problems in computer vision, such as segmentation, filtering, stereo, reconstruction, inpainting and optical flow seek solutions that match the data while satisfying an additional regularization, such as total variation or boundary length. A regularization which has received less attention is to minimize the curvature of the solution. One reason why this regularization has received less attention is due to the difficulty in finding an optimal solution to this image model, since many existing methods are complicated, slow and/or provide a suboptimal solution. Following the recent progress of Schoenemann et al., we provide a simple formulation of curvature regularization which admits a fast optimization which gives globally optimal solutions in practice. We demonstrate the effectiveness of this method by applying this curvature regularization to image segmentation.