Restricted ability to recover three-dimensional global motion from one-dimensional local signals: Theoretical observations

Recovering 3D information from a 2D time-varying image is a vital task which human observers face daily. Numerous models exist which compute global 3D structure and motion on the basis of 2D local motion measurements of point-like elements. On the other hand, both experimental and computational research of early visual motion mechanisms emphasize the role of oriented (1D) detectors. Therefore, it is important to find out whether indeed 1D motion signals can serve as primary cues for 3D global motion computation. We have addressed this question by combining mathematical results and perceptual observations. We show that given the 2D-projected 1D instantaneous velocity field, it is mathematically impossible to discriminate rigid rotations from non-rigid transformations and/or to recover the rotation parameters. We relate this fact to existing results in cases where localized (point-like) cues are present, and to our own experiments on human performance in global motion perception when only 1D cues are given. Taken together, the data suggest a necessary role for localized information in early motion mechanisms and call for further physiological and psychophysical research in that direction.