An Approach Towards Fast Gradient-based Image Segmentation

Abstract—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.