Detection of spatial discontinuities in first-order optical flow fields

Abstract

We investigated the extent to which the human visual system can detect discontinuities in firstorder optical flow fields. Weconstructed two types of spatial discontinuities: a circular split field with a straight edge and a disk with annular surround. Weused two different first-order optical flow components: an expansion and a rotation. Wefound an intriguing difference in the detection thresholds for straight and circular discontinuities. Whereas straight discontinuities yielded thresholds of 10%-500!6 difference in expansion or rotation, circular discontinuities could, at first, only be detected at extreme differences (» 100%). After a learning period, thresholds for such stimuli decreased, but they remained significantly higher than thresholds for the straight edge. Thresholds rose for stimuli that formed a gradual transition between a circular and a straight edge, and they decreased with increasing eccentricity of the circular discontinuity. Results suggest that symmetry in the stimulus, defined by the coincidence of the center of expansion or rotation and the center of the circular discontinuity, was responsible for the difference in thresholds for circular and straight discontinuities.When we move around in the world, the optical flow field provides much information about the world around us and our movement relative to it (Gibson, 1950). In everyday life, we often come across spatial discontinuities in this optical flow. These discontinuities are caused by objects that move separate from their background or by movement relative to transitions between noncoplanar surfaces (such as between a wall and the floor).Mathematically, one can extract information about the slant and tilt of objects and about the movement of the observer relative to these objects from the first-order structure ofthe flow field (Koenderink & van Doom, 1975;Longuet-Higgins & Prazdny, 1980). Information can also be extracted about the difference between first-order optical flow components in two different planes (e.g., a floor and a wall; Koenderink & van Doom, 1976) or at two different times. Ofcourse, this does not mean that the human visual system uses all the information that can be extracted mathematicaIly from the first-order flow field. To investigate whether the visual system is able to detect discontinuities in first-order flow fields, we constructed 2-D first-order optical flow stimuli with discontinuities that were step functions in the spatial domain.To investigate spatial discontinuities, we implemented two different stimuli: one with a circular discontinuity and one with a straight discontinuity. The stimulus with a straight discontinuity consisted ofa split field with the division along a diameter of the circular aperture. The stimulus with a circular discontinuity was a split field consisting of a circular center with an annular surround. As a first-order flow field, we chose either an expanding field or a rotating field. The center of expansion or rotaCorrespondence should be addressed to S. F. te Pas. Helmholtz Institu...