It is becoming increasingly clear that mitochondria play an important role in neural function. Recent studies show mitochondrial morphology to be crucial to cellular physiology and synaptic function and a link between mitochondrial defects and neuro-degenerative diseases is strongly suspected. EM microscopy, with its very high resolution in all three directions, is one of the key tools to look more closely into these issues but the huge amounts of data it produces make automated analysis necessary. State-of-the-art computer vision algorithms designed to operate on natural 2D images tend to perform poorly when applied to EM data for a number of reasons. First, the sheer size of a typical EM volume renders most modern segmentation schemes intractable. Furthermore, most approaches ignore important shape cues, relying only on local statistics that easily become confused when confronted with noise and textures inherent in the data. Finally, the conventional assumption that strong image gradients always correspond to object boundaries is violated by the clutter of distracting membranes. In this work, we propose an automated graph partitioning scheme that addresses these issues. It reduces the computational complexity by operating on supervoxels instead of voxels, incorporates shape features capable of describing the 3D shape of the target objects, and learns to recognize the distinctive appearance of true boundaries. Our experiments demonstrate that our approach is able to segment mitochondria at a performance level close to that of a human annotator, and outperforms a state-of-the-art 3D segmentation technique.