Perception 2003: 23ECVP abstracts

How to make motion parallax stimuli using an inverse Fourier transform

Linqiao Zhang and Michael S. Langer School of Computer Science, McGill University, 3480 University Street, McConnell Engineering Building, Rooms 336 and 329 Montreal, Quebec H3A 2A7, Canada;
e-mail: lzhang15@cs.mcgill.ca, langer@cim.mcgill.ca

Motion parallax is a difference in image velocity that is due to a difference in depth. One interesting example of motion parallax is the motion of falling snowflakes during a snowfall. Snowflakes that are close to the observer fall with a greater image velocity than snowflakes that are far from the observer. This speed/distance effect correlates with a size/distance effect, namely closer objects appear larger. The two effects together suggest a formal relationship between the spatial and temporal frequency components of a motion parallax stimulus such as falling snow. Following the motion plane model of (Watson and Ahumada 1985, Journal of the Optical Society of America A 2 322-342) that w_t = speed * w_y for a vertically moving stimulus, we observe that speed is inversely related to spatial frequency sqrt{w_x^2 + w_y^2} for a motion parallax stimulus, and that the two equations combine to yield a non-planar surface: w_t = w_y / sqrt{w_x^2 + w_y^2} in the 3D frequency. When such a surface is constructed using 1/f amplitudes and random phases, and the inverse Fourier transform is computed, the resulting image sequence produces a motion in depth effect that looks remarkably like falling snow. Besides being an interesting application for computer graphics, this method can also be used to create psychophysical stimuli for studying human motion perception.


MPEG video examples one , two and three .

© 2003 Linqiao Zhang and Michael S. Langer.