3D shape recovery from a single camera image is an illposed inverse problem which must be solved by using a priori constraints (a.k.a priors). We use symmetry and planarity constraints to recover 3D shapes from a single view. In many ways, symmetry and planarity represent the simplicity of a 3D object, and by applying these constraints we attempt to reconstruct a simple 3D shape that can explain the 2D image. Once we assume that the object to be reconstructed is symmetric, all that is left to do is: (i) estimate the plane of symmetry, and (ii) establish the symmetry correspondence between the various parts of the object. The edge map of the image of an object serves as a representation of its 2D shape; establishing symmetry correspondence means identifying pairs of symmetric curves in the edge map. In this work, we assume that the vanishing point, which establishes the symmetry plane up to a scale factor, is known. In addition, we also assume that the focal length and the direction of gravity are known. We extract long smooth curves from the edge map by solving the shortest (least-cost) path problem, where the cost function penalizes large interpolations and large turning angles. We then find the optimal curve matches that minimize the number of planes required to approximate the final 3D reconstruction. This optimization problem is framed as a binary integer program and solved using the Gurobi solver .
Vijai Jayadevan, Aaron Michaux, Edward Delp, Zygmunt Pizlo, "3D Shape Recovery From Real Images Using a Symmetry Prior" in Proc. IS&T Int’l. Symp. on Electronic Imaging: Computational Imaging XV, 2017, pp 106 - 115, https://doi.org/10.2352/ISSN.2470-1173.2017.17.COIMG-452