Like many predators, humans have forward-facing eyes that are set a short distance apart so that an extensive region of the visual field is seen from two different points of view. The human visual system can establish a three-dimensional (3D) percept from the projection of images into the left and right eye. How the visual system integrates local motion and binocular depth in order to accomplish 3D motion perception is still under investigation. Here, we propose a geometric-statistical model that combines noisy velocity constraints with a spherical motion prior to solve the aperture problem in 3D. In two psychophysical experiments, it is shown that instantiations of this model can explain how human observers disambiguate 3D line motion direction behind a circular aperture. We discuss the implications of our results for the processing of motion and dynamic depth in the visual system.