Traditional methods of motion segmentation use powerful geometric constraints to understand motion, but fail to leverage the semantics of high-level image understanding. Modern CNN methods of motion analysis, on the other hand, excel at identifying well-known structures, but may not precisely characterize well-known geometric constraints. In this work, we build a new statistical model of rigid motion flow based on classical perspective projection constraints. We then combine piecewise rigid motions into complex deformable and articulated objects, guided by semantic segmentation from CNNs and a second "object-level" statistical model. This combination of classical geometric knowledge combined with the pattern recognition abilities of CNNs yields excellent performance on a wide range of motion segmentation benchmarks, from complex geometric scenes to camouflaged animals.