Approximate Envelope Minimization for Curvature Regularity

We propose a method for minimizing a non-convex function, which can be split up into a sum of simple functions. The key idea of the method is the approximation of the convex envelopes of the simple functions, which leads to a convex approximation of the original function. A solution is obtained by minimizing this convex approximation. Cost functions, which fulfill such a splitting property are ubiquitous in computer vision, therefore we explain the method based on such a problem, namely the non-convex problem of binary image segmentation based on Euler’s Elastica.