Viri~ Res. Vol. 30, No. 2, pp. 273-287, 1990 0042-6989/90 SUM + 0.00 Printed in Great Britain. All rights reserved Copy6gbI Q 1990 Pergamon Prest plc PERCEIVED DIRECTION OF MOVING TWO-DIMENSIONAL PATTERNS VINCENT P. FERRERA+ and HUGH R. WILSON Department of Ophthalmology and Visual Science, and Committcz on Neurobiology, The University of Chicago, 939 E. 57th St. Chicago, IL 60637, U.S.A. (Received 27 December 1988; in revised zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO fotm 24 May 1989) Am-When two drifting cosine gratings arc superimposed, they will, under appropriate conditions, form a coherently moving two-dimensional pattern whose resultant direction of motion may either be between (type I), or outside (type II) the directions of the two components. We have previously shown that type I patterns produce much stronger masking than either of their components, while type II patterna do not. In this study, we measured perceived direction of motion and thresholda for d&rMnation zyxwvutsrqponmlkjihgfe of motion direction. We found that type II patterns had a peraivcd bias of about 7.5 dcg toward the direction of their components, and bad discrimination thresholds around 6.5 dcg, whereas type I pattuns had discrimination thresholds around 1 .O dcg and no significant bii. We conclude that the neural me&a&ms which compute two-dimensional image motion do not strictly implement the inters&ion-of-consMnts construction proposed by Adelson and Movshon (1982). Aperture problem Intersection-of-constraints INTRODUCTION The direction of motion of a one-dimensional pattern such as a drifting cosine grating is ambiguous, and the direction which is actually perceived may vary depending on the shape and orientation of the aperture through which the grating is viewed. This phenomenon was observed by Wallach (1935,1976) and has come to be known as the aperture prohlem or the problem of motion ambiguity. Another way of stating the problem is that the perceived motion of a single drifting grating is consistent with a family of physical motions which are related in that all members have the same magnitude or speed in the direction orthogonal to the orien- tation of the grating. Thus, if each member of this family were represented by a vector in velocity? space, then the heads of all the vectors would fall along a straight line, known as a constraint line (Fennema & Thompson, 1979; Adelson & Movshon, 1982). On the other hand, if two one-dimensional gratings are physically superimposed, the visual system can resolve the motion ambiguity in such l FVcscxlt addras: University of Rochester, Dcpnrtment of phyriology Box 642, Rochester, NY 14642, U.S.A. tin keeping with the d&&ion in physics. we shall use velocity to denote a vector quantity comprised of a magnitude or apeed and a direction of motion. Direction selective Motion Plaid a way that the individual gratings form a two- dimensional pattern which may be perceived to move as a single coherent entity. Adelson and Movshon (1982) noted that the perceived direc- tion of such a two-dimensional pattern might be accounted for by the ambiguity inherent in the motion of its one-dimensional components, and they captured this idea in a geometric construction known as the intersection-of- constraints or velocity-space construction. This construction assumes that the two one- dimensional components are attached to a rigid surface undergoing uniform translation in the frontoparallel plane, and then derives the motion of that surface. The intersection-of-constraints is illustrated in Fig. 1. The stimulw is composed of two cosine gratings with difTerent orientations and drift rates which are physically superimposed. The thin vectors represent the velocity com- ponents of the two gratings, in the direction orthogonal to their orientations. The constraint lines, which are perpendicular to the component motion vectors, represent the range of physical motions which could produce each ‘component. The point where the two constraint lines inter- sect (thick vector) gives the resultant pattern velocity which is consistent with the velocities of both component. This construction has two important features which are of interest in the current study. First, 273