The gradient of human visual interpolation

Purpose. Hon, Maloney & Landy (1OVS. [abst.J, 1996, 37, S170) examined human performance in visual interpola don of sampled contours. They measured the contribution of each of the.visibli: points to the interpolation judgment by systematically displacing it, and measuring the resulting change in interpolation performance. The ratio of effect magnhude to displacement magnitude (for small displacements) is referred to as the influence of the perturbed point. We test whether the combined influence measures can be interpreted as an estimate of the gradient of human interpolator performance (much as a gradient is, effectively, a vector of directional der vatives). This interpretation holds only if the effects of perturbations obey superposition', the effect of simultaneously perturbing two fixed points must be ne sum of the effects of perturbing each point in isolation, for sufficiently sm ill perturbations. Methods. The stimuli were presented on a spatially-calibrate i projection CRT driven by a CRS board. Eight approximately equally spaced points were sampled from a parabolic contour. A ninth point located about th; center, initially displaced away from the contour, is adjusted by the subject to appear to lie on the contour defined by the other 8 points. Each of two observers : nade 4 settings for; 3 angles of rotation, 4 single point perturbations with 2 directions of perturbation (towards concave or convex side), 6 pairwise perturbations of the 4 perturbable points with 2 directions of perturbation for each of the points, and 6 control trials with no points perturbed. Results. We did net reject superposition for either observer. Conclusions. We are able to measure :he gradient of human visual interpolation performance. We show how this infon nation can be used to develop a model of human sampled-contour interpolation performance.