Sinusoidal motion of elements in a random-dot pattern can elicit a striking percept of a rotating volume, a phenomenon known as structure-from-motion (SFM). We demonstrate that if the dots defining the volume are 2D mirror-symmetric, novel 3D interpretations arise. In addition to the classical rotating cylinder, one can perceive mirror-symmetric, flexible surfaces bending along the path of movement. In three experiments, we measured the perceptual durations of the different interpretations in a voluntary control task. The results suggest that motion signals and symmetry signals are integrated during surface interpolation. Furthermore, the competition between the rotating cylinder percept and the symmetric surfaces percept is resolved at the level of surface perception rather than at the level of individual stimulus elements. Concluding, structure-from-motion is an interactive process that incorporates not only motion cues but also form cues. The neurofunctional implication of this is that surface interpolation is not fully completed in its designated neural "engine," MT/V5, but rather in a higher tier area such as LOC, which receives input from MT/V5 and which is also involved in symmetry detection.