Smoothness of the velocity field and three-dimensional surface detection from optic flow

Five experiments were conducted to determine the importance of smoothness of the velocity field in detecting 3-D surfaces from optic flow. Subjects were presented with optic flow displays simulating either points positioned on a corrugated 3-D surface or points randomly positioned within a 3-D volume. The subject's task was to indicate whether or not the display appeared to be a 3-D surface. Smoothness of the velocity field was examined by systematically varying the speed of individual velocities in the flow field according to a Gaussian distribution with M = 0 and SD = sigma. Variations in frequency, amplitude, density, and surface complexity were also examined. Detection of the corrugated surfaces systematically declined with an increase in sigma. An increase in frequency of the corrugation for simple (single-frequency corrugation) surfaces resulted in a decrease in surface detection accuracy. Accuracy increased with an increase in density and amplitude for both simple and complex (multiple-frequency corrugation) surfaces. An analysis of the deformation of the displays predicted performance on the basis of human observers, providing further support for the importance of deformation for 3-D surface detection.