Metamerisms in Structure-from-motion Perception

Abstract

As a three-dimensional object is moving through our world, we generally obtain a vivid impression of both its structure and its motion through space. The time-course of two-dimensional projections of the scene (optic flow) is important in conveying this three-dimensional information to us. The extent to which we can solve this specific inverse problem, i.e. infer a three-dimensional scene from two-dimensional flow, depends on the accuracy with which the required flow characteristics are processed by our visual system. In adequate two-dimensional processing can lead to incomplete representations of the three-dimensional world (three-dimensional metric information is lost). Then the motion and structure of objects can no longer be recovered uniquely. Consequently, metameric classes of three-dimensional representations arise (e.g. only affine properties are conserved). this study investigates under what conditions we find metameric combinations of the perceived attitude and perceived rotation of a plane. Our subjects are presented with stimuli consisting of two horizontally separated planar patches rotating back and forth in depth about vertical axes. Subjects are required to match both the attitude and the rotation magnitude of these two patches. We vary the attitude from 15 to 60 deg vertical slant, and the rotation magnitude from 28 to 98 deg. We find that the matched slant and rotation settings vary widely. For high slant values and for small rotations, attitude and rotation settings become highly correlated, suggesting metamery. For low slant values and for large rotations, the correlation almost disappears, suggesting that both quantities are estimated independently and uniquely. Our paradigm reveals that with one task and one type of stimulus a gradual transition occurs from unique settings (metric representations) to metameric classes of settings (e.g. affine representations).

Cross-modal slant and curvature matching of stereo- and motion-induced surfaces

“…Two points are worth mentioning here: (I) the dependence of slant on the tum is independent of the particular choice of pair A and B as long as these pairs are in the same plane, and (2) the relation between slant and tum is approximately inverse. This predicted relation is supported by psychophysical evidence (van Veen & Werkhoven, 1994).…”

“…Several researchers (Bennett, Hoffinan, Nicola, & Prakash, 1989;Koenderink & Van Doom, 1991;Kontsevich, 1993) have demonstrated how a one-parameter family of solutions can be found from two parallel views. Because the quantitative difference between parallel projection and perspective is negligible in many cases (small objects at about arm's length or farther away) and is often even objectively zero in typical laboratory setups (e.g., on discrete raster displays under the same viewing conditions), one cannot expect the visual system to do any better than to arrive at such a set of solutions (see also van Veen & Werkhoven, 1994). To arrive at a unique solution, extra assumptions have to be made about the specific surface transformation between projections or additional information has to be derived from other sources (e.g., from accommodation, familiar size, etc.).…”

The role of perspective effects and accelerations in perceived three-dimensional structure-from-motion.

“…Van Veen and Werkhoven (1996) asked participants to match two SFM stimuli consisting of small orthographic projections of horizontally slanted planes rotating about a vertical axis, by adjusting the simulated slant and simulated rotation angle of one of the stimuli. They found that adjusted slant and adjusted rotation angle were highly correlated for large slants and small rotation angles, but less so for large rotation angles and small slants.…”

“…Another indication that accelerations are used in SFM comes from experiments performed by Van Veen and Werkhoven (1996), in which participants matched SFM stimuli depicting slanted planes by simultaneously adjusting the slant and rotation angle of one of the simulated planes. The authors argued that the settings in the slant and the rotation should be highly correlated if only first-order information is processed.…”

Locating the singular point in first-order optical flow fields.

“…Such a cloud has several characteristics, which we investigated separately. A similar method of data analysis was used by Van Veen and Werkhoven (1996).…”