Motion is a fundamental grouping cue in video. Many current approaches to motion segmentation in monocular or stereo image sequences rely on sparse interest points or are dense but computationally demanding. We propose an efficient expectation-maximization (EM) framework for dense 3D segmentation of moving rigid parts in RGB-D video. Our approach segments images into pixel regions that undergo coherent 3D rigid-body motion. Our formulation treats background and foreground objects equally and poses no further assumptions on the motion of the camera or the objects than rigidness. While our EM-formulation is not restricted to a specific image representation, we supplement it with efficient image representation and registration for rapid segmentation of RGB-D video. In experiments, we demonstrate that our approach recovers segmentation and 3D motion at good precision.