Viewpoint--invariance of contour-curvature discrimination over extended performance levels

A traditional approach to the problem of human object recognition is to assume that the visual system represents an object in terms of invariant quantities. This study considers a generalization of this approach to the problem of visually recognizing differences in shape, specifically between contour markings on a planar surface, as the position of the surface varies in space. For a given 'shape cue', perceived differences in contour may be quantified by threshold values--Weber fractions--at a particular criterion level of performance. A necessary theoretical condition for the Weber fraction to be constant with the relative viewpoint of the observer is that the cue should be a relative invariant under the natural spatial transformations of the image. Some data are reviewed showing how statistically efficient some cues are in explaining the observed discriminability of symmetric curved contours at a fixed criterion performance level of 75%. A new, fuller analysis is presented showing that the efficiency of the most efficient cue satisfying the invariance condition is maintained over a wide range of criterion performance levels, from 53% to 92% correct, corresponding to discrimination index values of 0.1 to 2.0. Over these levels, Weber's law was found empirically to hold almost exactly.