The Effect of Curvature on Visual Interpolation

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Abstract
The effect of curvature on visual interpolation in partly occluded figures was examined. In experiments 1 and 2, the shape of a visually interpolated contour was measured by using a partially occluded triangle or a partially occluded circle as the target figure. The targets were cut off at both sides, with varying width from trial to trial. In experiment 1, the peak height, which was supposed to represent the shape of the interpolated contour, was measured for each target for each size of the visible part. A significant effect of curvature, as the difference in the peak height between the targets, was found when the width of the visible part was 10 to 20 min. The effect became stronger linearly with increasing length of the visible contour (the buildup effect). The effective curvature thus appeared to be measured along the visible contour in terms of the change of orientation. In experiment 2, the scale invariance of the buildup effect was examined with varying observation distance. It was found that the effect remained the same across scale if the effect was described in terms of visual angle of the visible arc, but not in terms of the proportion of the visible part to the whole figure. This suggests that the effect is derived from the visible contour, but not from the likelihood of the estimated shape of the partly occluded figure. It has been concluded that the curvature induces curved interpolation and that the curvature of the visible contour is measured along the contour as the change of orientation.

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