Graph cut optimization is one of the standard workhorses of image segmentation since for binary random field representations of the image, it gives globally optimal results and there are efficient polynomial time implementations. Often, the random field is applied over a flat partitioning of the image into non-intersecting elements, such as pixels or super-pixels. In the paper we show that if, instead of a flat partitioning, the image is represented by a hierarchical segmentation tree, then the resulting energy combining unary and boundary terms can still be optimized using graph cut (with all the corresponding benefits of global optimality and efficiency). As a result of such inference, the image gets partitioned into a set of segments that may come from different layers of the tree. We apply this formulation, which we call the pylon model, to the task of semantic segmentation where the goal is to separate an image into areas belonging to different semantic classes. The experiments highlight the advantage of inference on a segmentation tree (over a flat partitioning) and demonstrate that the optimization in the pylon model is able to flexibly choose the level of segmentation across the image. Overall, the proposed system has superior segmentation accuracy on several datasets (Graz-02, Stanford background) compared to previously suggested approaches.