The Elastic Ratio: Introducing Curvature into Ratio-based Globally Optimal Image Segmentation

In this paper we present the first globally optimal ratio-based image segmentation method allowing to impose curvature regularity of the region boundary. The proposed method is fully unsupervised and compares favorably to other such approaches. To identify the optimal foreground region in the image, the algorithm minimizes the ratio of flux over a weighted sum of length and curvature regularity of the region boundary. The key concept is to find cycles in a product graph where each node corresponds to a pair of image locations. Furthermore our results allow to draw conclusions about certain global optima of a reformulated snakes functional which is independent of parameterization: the proposed algorithm allows to find parameter sets where the modified snakes functional has a meaningful solution and simultaneously provides the corresponding global solution.