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A common approach to the problem of shape completion is based on the calculus of variations: The optimal interpolating shape is taken to be one that minimizes a given smoothness functional, or energy term.  Two important such functionals used in computational vision are total curvature and variation in curvature. Our studies on the visual extrapolation of contour shape suggest, however, that the variational approach is not appropriate for modeling shape completion by human vision. In particular, a key assumption made by variational approaches---that the same shape constraint applies uniformly along the entire length of an interpolated contour---appears to be invalid for human vision.  I will argue that probabilistic models provide a more general and appropriate class of models for human shape completion.