Image segmentation is an important first step of many image processing, computer graphics, and computer vision pipelines. Unfortunately, it remains difficult to automatically and robustly segment cluttered scenes, or scenes in which multiple objects have similar color and texture. In these scenarios, light fields offer much richer cues that can be used efficiently to drastically improve the quality and robustness of segmentations. In this paper we introduce a new light field segmentation method that respects texture appearance, depth consistency, as well as occlusion, and creates well-shaped segments that are robust under view point changes. Furthermore, our segmentation is hierarchical, i.e. with a single optimization, a whole hierarchy of segmentations with different numbers of regions is available. All this is achieved with a submodular objective function that allows for efficient greedy optimization. Finally, we introduce a new tree-array type data structure, i.e. a disjoint tree, to efficiently perform submodular optimization on very large graphs. This approach is of interest beyond our specific application of light field segmentation. We demonstrate the efficacy of our method on a number of synthetic and real data sets, and show how the obtained segmentations can be used for applications in image processing and graphics.