In this paper, we apply efficient implementations of integer linear programming to the problem of image segmentation. The image is first grouped into superpixels and then local information is extracted for each pair of spatially adjacent superpixels. Given local scores on a map of several hundred superpixels, we use correlation clustering to find the global segmentation that is most consistent with the local evidence. We show that, although correlation clustering is known to be NP-hard, finding the exact global solution is still feasible by breaking the segmentation problem down into subproblems. Each such sub-problem can be viewed as an automatically detected image part. We can further accelerate the process by using the cutting-plane method, which provides a hierarchical structure of the segmentations. The efficiency and improved performance of the proposed method is compared to several state-of-the-art methods and demonstrated on several standard segmentation data sets.