Visual interpolation of sampled contours in three-dimensional space is local

Observers interpolate sampled contours with high accuracy and little bias. Recent results support the claim that the human interpolation mechanism is local: it uses only the nearest points in interpolating across a gap in a sampled contour. We present experiments designed to test this hypothesis directly by measuring the influence of each point on interpolation of sampled parabolic contours in space. Each sampled contour consisted of eight points that fell on an otherwise invisible parabolic contour. The binocularly-presented contour was constrained to be in the fronto-parallel plane or in a plane rotated 70 degrees from the fronto-parallel plane about a vertical axis. It subtended approximately 20 × 5 degrees of visual angle when the contour plane was fronto-parallel. On each trial, observers adjusted a setting point, constrained to lie on an invisible setting plane orthogonal to the contour, until it appeared to lie on the contour. In certain trials, one of the fixed points on the contour was displaced by a small amount (4 min arc when in the fronto-parallel plane) in a direction orthogonal to the contour (either normal to the contour plane or in the contour plane). The influence of each of the eight fixed points was computed as the vector difference between the mean of 8 settings with that point perturbed and the mean of 16 unperturbed settings, divided by the magnitude of perturbation. We found that influence falls to zero very quickly with distance from the adjustable point. These results support the hypothesis that the human interpolation mechanism is local, involving as few as four points. Perturbations in the contour plane did not lead to systematic changes of setting out of the contour plane and vice versa. We show that, with such small magnitudes of perturbation, our influence measures serve as estimates of the Jacobian of the human visual interpolation system. Such measures sharply constrain possible models for human visual completion of contours.