What does the Occluding Contour Tell us about Quantitative Shape?

The local shape of the occluding contour of an object is known to constrain the local shape of the object surface [1], however, these known constraints are qualitative. Here we posit here that in addition to these qualitative constraints, typical regularities of common objects and rules of projection induce dependencies that can be used to derive statistical estimates of quantitative solid shape from the occluding contour. To explore this conjecture, we partition the problem into two parts: 1) Estimation of the 3D rim from the 2D occluding contour, and 2) Estimation of the visible surface shape from the estimated 3D rim. We train and evaluate a number of statistical models on two distinct 3D object datasets and demonstrate that capturing these statistical regularities leads to better estimates of 3D shape than existing methods.