Estimates of temporal proximity (sometimes called time-to-collision)from random-dot flow patterns are shown to be based upon retinal speed, rather than upon changes in dot density. Neither the spatial nor the temporal gradient of motion is essential to the task, but estimates can be made from either alone. Performance is unaffected by the addition of rotational motion, suggesting that observers are capable of extracting the radial component of motion, which contains all the relevant information, from complex stimuli.Movement of an observer through the world produces a smooth transformation of the retinal image containing information about the direction of movement and about the three-dimensional layout of surfaces in the world (Clocksin, 1980;Cutting, 1986; J. J. Gibson, Olum, & Rosenblatt, 1955;Harris & Freeman, 1990;Koenderink, 1985Koenderink, , 1986 Koenderink & van Doom, 1975, 1976Lee, 1974;Longuet-Higgins & Prazdny, 1980;Nakayama & Loomis, 1974;Rieger & Lawton, 1985;Waxman & Wohn, 1988). Previous empirical work has established that human observers can make use of these transformations in a wide variety of tasks, including, for example, the recovery of locomotory heading (Warren & Hannon, 1988;Warren, Morris, & Kalish, 1988), three-dimensional surface layout (Harris, Freeman, & Hughes, 1992; Landy, Dosher, Sperling, & Perkins, 1991;Siegel & Andersen, 1988;Treue, Husain, & Andersen, 1991), surface rigidity (de Bruyn & Orban, 1990), and relative depth (Braunstein, 1968;Braunstein & Andersen, 1981;Flock, 1964; E. J. Gibson, J. J. Gibson, Smith, & Flock, 1959;Rogers & Graham, 1979, 1985.In this paper, we concentrate upon the extraction of temporal proximity. (This variable is sometimes called timeto-contact, or time-to-collision, implying that its main use is in the control oflocomotion. However, because it can be computed on a point-by-point basis and relates equally well to directions far from the locomotory heading, we prefer the term temporal proximity because it conveys the wider potential use in providing a time-based map of threedimensional surface layout.) Previous studies (Lee, 1976;Lee, Lishman, & Thomson, 1982;Lee & Reddish, 1981;Lee & Young, 1985;Lee, Young, Reddish, Lough, & Clayton, 1983;McLeod & Ross, 1983;Schiff & Detwiler, 1979; Todd, 1981; Tresilian, 1990) have shown that human observers and some animals can extract temporal proximity from suitable visual displays, but it is not clear from these studies which aspects of the stimulus they used.Translation by the observer, in a straight line at a uniform speed and with a fixed angle of gaze, produces a uniform expansion of the image from a single focus of expansion (FoE) coinciding with the observer's locomotory heading (see, e.g., J. J. Gibson, 1950;Harris, Freeman, & Williams, 1992). The speed of radial image motion increases linearly with distance from the FoE, so the transformation includes a smooth spatial speed gradient along each line of flow. Moreover, as an object gets closer, its image expands progressively faster so that, in addi...
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