The present disclosure describes a system and method for transforming a two-dimensional image of an object into a three-dimensional representation, or model, that recreates the three-dimensional contour of the object. In one example, three pairs of symmetric points establish an initial relationship between the original image and a virtual image, then additional pairs of symmetric points in the original image are reconstructed. In each pair, a visible point and an occluded point are mapped into 3-space with a single free variable characterizing the mapping for all pairs. A value for the free variable is then selected to maximize compactness of the model, where compactness is defined as a function of the model's volume and its surface area. “Noise” correction derives from enforcing symmetry and selecting best-fitting polyhedra for the model. Alternative embodiments extend this to additional polyhedra, add image segmentation, use perspective, and generalize to asymmetric polyhedra and non-polyhedral objects.