A system processes 2D images of 2D or 3D objects, creating a model of the object that is consistent with the image and as veridical as the perception of the 2D image by humans. Vertices of the object that are hidden in the image are recovered by using planarity and symmetry constraints. The 3D shape is recovered by maximizing 3D compactness of the recovered object and minimizing its surface area. In some embodiments, these two criteria are weighted by using the geometric mean.