The cue for contour-curvature discrimination

Seven potential geometric cues for contour-curvature discrimination were tested: curvature, turning-angle, arc-length, arc-length-divided-by-chord-length, maximum-deviation (sag), mean-deviation and area. Three experiments were performed, each requiring the discrimination of two simultaneously presented, 1-sec-duration, curved-line stimuli, whose chord-lengths ranged from 12 to 48 arcmin visual angle and whose curvatures ranged from 0 to 0.13 arcmin-1. Experiments 1 and 2 determined for each cue the smallest detectable increment (the increment threshold) as a function of cue value, for a set of spatial transformations of the stimulus (one- and two-dimensional scalings) equivalent to changes in viewing distance and direction. In accordance with statistical estimation theory, the "best" cue was defined as the most efficient one, that is, the one which best accounted for the variance in the data. As a control, Expt 3 compared increment-threshold functions for circular and elliptical arcs of constant chord-length and circular arcs of constant arc-length. Over all three experiments, only sag and its linear approximation, mean-deviation, accounted well for the variance in the data; sag provided the best predictor, and its increment-threshold function satisfied Weber's law over almost all of the stimulus range. Additionally, sag has a special theoretical property (shared only with mean-deviation and area): the relationship it defines (in proportional terms) between curved contours in an image of an object or a scene is constant and independent of viewing distance and direction.