Abstract

Optical flow is the process of inferring a vector field of projected velocity information. Projected information changes with dimensionality: points (e.g., crossings and end points) in space project into contours in space/time, contours (e.g., occluding contours) into surfaces; and surfaces (e.g., waterfalls) into volumes. The extent of each kind of structure can be varied as well, from short in both space and time, as is the case for waterfalls, to long in either space or time or both. The Wallach and O'Connell effect, for example, is short in space and long in time, while surface contours can be long in space and time. Using this space/time structural characterization of patterns, we show that previous approaches to measuring sensitivity have only touched (essentially) three points in a much larger space of possibilities. We then conceptualize the optical flow computation as a two- stage process: (1) measurements taken over image sequences; and (2) interpretation of these measurements into a flow field by a cooperative optimization process. We show that (i) the nature of these measurements changes with the dimensionality of the projected objects; and (ii) since small extents of structure require interpolation (filling in of missing information) the interpretation stage smooths over discontinuities for small extents but not for large ones. We support these computational predictions with psychophysical demonstrations.

© 1985 Optical Society of America