Vision Res. Vol. 29, No. 5. pp. 553-561, 1989 0042~6989189 13.00 + 0.00 Printed in Great Britain. All rights reserved Copyright 0 1989 Pergamon Press pk IS THERE A CONSTANCY FOR VELOCITY? SUZANNE P. MCKEE and LESLIE WELCH Smith-Kettlewell Eye Research Institute, 2232 Webster St, San Francisco, CA 94115, U.S.A. zyxwvutsrqponmlkjihg (Received 22 March 1988; in revised form 12 September 1988) Abstract-Human observers are unable to use disparity information to transform the angular velocity signal into a precise object-based code. The Weber fraction for discriminating changes in objective velocity (cm/set) is about twice the Weber fraction for discriminating changes in angular velocity (deg/sec), and is substantially higher than predicted from a combination of the errors in judging disparity and angular velocity. By comparison, judgments of the distance traversed by the moving target show excellent size constancy. The di~~mination of changes in objective size (cm) is as precise as the disc~mination of changes in angular size (deg). The angular velocity signal is useful without transformation into an object-centered signal; it guides eye and body movements, and is the basis of motion parallax judgments. The need to retain this angular signal may explain why there is no efficient mechanism for velocity constancy. Motion Velocity discrimination Size discrimination Size constancy Velocity constancy INTRODUffION The retinal velocity produced by an object moving at a given physical velocity depends on its distance from the eye. Human observers are generally more interested in the physical dimen- sions of objects than in the retinal stimuli associated with these dimensions, so it is widely assumed that some compensatory mechanism automatically adjusts angular dimensions by a factor related to perceived distance (Helmholtz, 1868; Woodworth, 1938; Epstein, 1973). If an observer had perfect knowledge about the dis- tance between his head and a moving object, then presumably its perceived velocity would correspond perfectly to the actual physical vel~ity~onstancy would prevail. In this study, we will examine the influence of this presumed compensatory mechanism on velocity discrimination. Typically, cons~ncy studies use matching or magnitude estimation to assess what the observer perceives under various experimental manipulations. In a matching study, there is no way for an observer to be wrong; he is the ultimate arbiter of what he perceives. But in a discrimination study, the experimenter defines what is correct based on the physical character- istics of the stimulus. For example, an observer can be asked to choose the larger of two objects independent of their relative distances, and the experimenter can score the judgments on the basis of the physical size of the objects. If the observer is told about the correctness of his choices (“given feedback”), then the precision of his judgments reveals how well size constancy operates for the tested range of distances. Dis- crimination judgments do not really tell us what the observer perceives, because an observer may perceive one thing, but respond with another in order to satisfy the experimenter’s definition of “correct”. Nevertheless, the relative precision of angular and objective judgments can supply some information about how sensory signals are combined to estimate the properties of objects. Consider two traditional models of con- stancy. In the first, the “Helmholtz” model of Fig. 1, the observer has access to two indepen- dent signals: the retinal signal coded in angular units, and a depth signal. In any plausible biological system, both of these signals are subject to error-they are noisy. The observer achieves constancy by correcting the perceived retinal signal by his estimate of perceived dis- tance, so there are two sources of error in his estimate of the physical dimensions of objects, the retinal error and the depth error. It hardly matters whether the correction is a conscious or “unconscious inference”; the discrimination of objective dimensions is necessarily less precise than the discrimination of angular dimensions. The important assumption of this model is that the observer has access to a signal coded in angular co-ordinates. In the “Gestalt” model of constancy, the observer has access only to constancy-corrected signals-signals which are already adjusted by a 553