Visual interpolation and segmentation of sampled contours
A sampled contour consists of isolated, visible points that fall on an invisible, smooth contour. In our experiments, observers are asked to interpolate such contours. In initial studies, we determined that observers accurately interpolated parabolic and circular contours (SD < 2 arc min) across 1.5 deg gaps with as few as 7 visible sampled points. I'll describe how we measure the contribution of each visible point to human interpolation performance and what the resulting influence measures tell us. Many obvious interpolation models (e.g. least-squares parabolic fits) predict human interpolation but fail to predict the human influence measures we find. In brief, such models duplicate human performance but are not using visual information in the same way as people are. In addition, I'll describe how to use influence measures to study contour segmentation as well and present data that arguably represents the first objective measure of whether the observer segments a group of points into two `things'. These results are directly relevant to regularization models of human visual interpolation and segmentation including Bayesian models, and represent a possibly quixotic attempt to tackle Gestalt issues quantitatively and objectively.