Extraction of relief from visual motion.

We quantified the ability of human subjects to discriminate the relative distance of two points from a slanted plane when viewing the projected velocities of this scene (orthographic projection). The relative distance from a plane (called relief) is a 3-D property that is invariant under linear (affine) transformations. As such, relief can in principle be extracted from the instantaneous projected velocity field; a metric representation, which requires the extraction of visual acceleration, is not required. The stimulus consisted of a slanted plane P (specified by three points) and two points Q1 and Q2 that are non-coplanar with P. This configuration of points oscillated rigidly around the vertical axis. We have measured the systematic error and accuracy with which human subjects estimate the relative distance of points Q1 and Q2 from plane P as a function of the slant of P. The systematic error varies with slant: it is low for small slant values, reaches a maximum for medium slant values, and drops again for high slant values. The accuracy covaries with the systematic error and is thus high for small and large slant values and low for medium slant values. These results are successfully modeled by a simple relief-from-motion computation based on local estimates of projected velocities. The data are well predicted by assuming (1) a measurement error in velocity estimation that varies proportionally to velocity (Weber's law) and (2) an eccentricity-dependent underestimation of velocity.