An Approach Towards Fast Gradient-based Image Segmentation

In this paper we present and investigate an approach to fast multi-label color image segmentation using convex optimization techniques. The presented model is in some ways related to the well-known Mumford-Shah model, but deviates in certain important aspects. The optimization problem has been designed with two goals in mind: The objective function should represent fundamental concepts of image segmentation, such as incorporation of weighted curve length and variation of intensity in the segmented regions, while allowing transformation into a convex concave saddle point problem that is computationally inexpensive to solve. This paper introduces such a model, the nontrivial transformation of this model into a convex-concave saddle point problem, and the numerical treatment of the problem. We evaluate our approach by applying our algorithm to various images and show that our results are competitive in terms of quality at unprecedentedly low computation times. Our algorithm allows high-quality segmentation of megapixel images in a few seconds and achieves interactive performance for low resolution images.