We address the problem of segmenting an image into a previously unknown number of segments from the perspective of graph partitioning. Specifically, we consider minimum multicuts of superpixel affinity graphs in which all affinities between non-adjacent superpixels are negative. We propose a relaxation by Lagrangian decomposition and a constrained set of re-parameterizations for which we can optimize exactly and efficiently. Our contribution is to show how the planarity of the adjacency graph can be exploited if the affinity graph is non-planar. We demonstrate the effectiveness of this approach in user-assisted image segmentation and show that the solution of the relaxed problem is fast and the relaxation is tight in practice.