Visual extrapolation of contour geometry
Manish Singh and Jacqueline M. Fulvio
Proceedings of the National Academy of Sciences, 102 (3), 939-944.


Computing the shapes of object boundaries from fragmentary image contours poses a formidable problem for the visual system. We investigated the extrapolation of contour shape by human vision. Measurements of extrapolation position and orientation were taken at six distances from the point of occlusion, thereby yielding a detailed representation of the extrapolated contours. Analyses of these measurements revealed that:

(i) extrapolation curvature increases linearly with the curvature of the inducing contour, although there is individual bias in the slope;

(ii) the precision with which an extrapolated contour is represented is roughly constant, in angular terms, with increasing distance from the point of occlusion;

(iii) there is a substantial cost of curvature, in that the overall precision of an extrapolated contour decreases systematically with curvature;

(iv) the shapes of visually extrapolated contours are characterized by a nonlinear decrease in curvature, asymptoting to zero; and

(v) this decaying pattern of curvature is explained by a Bayesian model in which, with increasing distance from the point of occlusion, the prior tendency to minimize curvature gradually dominates the likelihood tendency to minimize variation in curvature.