Perception, 1983, volume 12, pages 549-558 Visual apparent movement: transformations of size and orientation Claus Bundesen^, Axel Larsen Psychological Laboratory, Copenhagen University, Njalsgade 94, DK-2300 Copenhagen S, Denmark Joyce E Farrell Department of Psychology, Stanford University, Stanford, CA 94305, USA Received 13 October 1982, in revised form 29 March 1983 Abstract. Sequential alternation between same-shaped stimuli differing in size (size ratio s) and orientation (angular difference v) produced a visual illusion of translation in depth and concurrent rotation. The minimum stimulus-onset asynchrony required for the appearance of a rigidly moving object was approximately a linearly increasing function of (s- l)/(s + 1) for simple translation in depth and a linearly increasing function of v for simple rotation. The extrapolated zero intercept was lower for translation than for rotation, but estimated transformation times were additive in combined transformations. The results suggest that (a) the processes of apparent translation in depth and apparent rotation are individually sequential-additive in structure, and (b) apparent translations and rotations are combined by fine-grained alternation of steps of apparent translation and steps of apparent rotation. Similar principles account for recent data on imagined spatial transformations of visual size and orientation. 1 Introduction Apparent movement can be generated by successively flashing a visual stimulus in two spatial locations. Following Korte (1915), a number of workers have investigated the spatiotemporal conditions for this illusion (see references and data in Larsen et al 1983). The results show that, when other parameters are kept constant, the minimum stimulus-onset asynchrony (SOA) required for optimal apparent movement (beta or apparent continuous movement of an object) is an increasing function of the visual angle separating the stimulus presentations. For long-range apparent movement (cf Anstis 1978, 1980; Braddick 1974, 1980; Pantle and Petersik 1980; Pantle and Picciano 1976; Petersik and Pantle 1979) the function is approximately linear. The slope constant increases with viewing distance, suggesting that the threshold for apparent movement depends upon the apparent separation between the stimulus presentations in three-dimensional space (cf Attneave and Block 1973; Corbin 1942). Parametric studies of apparent rotational movement have yielded comparable results. By presenting a pair of perspective views of a three-dimensional object in continuous sequential alternation, Shepard and Judd (1976) created a perceptual illusion of a single object rotating back and forth. The minimum SOA required for apparent rigid rotation was a linearly increasing function of the angular difference in orientation between the two views, and the function was essentially the same for perceived rotations in depth and in the picture plane. In a similar experiment by Farrell et al (1982), variation in the size of the object affected the zero intercept of the SOA function, but the slope of the function was virtually constant. Consider the meaning of linear relations between the minimum SOA required for perception of apparent translation or rigid rotation and the extent of those transformations. In one theoretical interpretation (Shepard 1981; Shepard and Judd 1976), the slope constants of the SOA functions are measures of the maximum speed of visually impleting (Beck et al 1977; Farrell and Shepard 1981) or 'filling in' a ^Author to whom requests for reprints should be sent.