A simple fast algorithm for minimization of the elastica energy combining binary and level set representations

For curves or general interfaces, Euler's elastica energy has a wide range of applications in computer vision and image processing. It is however difficult to minimize the functionals related to the elastica energy due to its non-convexity, nonlinearity and higher order with derivatives. In this paper, we propose a very simple way to combine level set and binary representations for interfaces and then use a fast algorithm to minimize the functionals involving the elastica energy. The proposed algorithm essentially just needs to solve a total variation type minimization problem and a re-distance problem. Nowadays, there are many fast algorithms to solve these two problems and thus the overall efficiency of the proposed algorithm is very high. We then apply the new Euler's elastica minimization algorithm to image segmentation, image inpainting and illusory shape reconstruction problems. Extensive experimental results are finally conducted to validate the effectiveness of the proposed algorithm.