A Closed-form Solution to 3D Reconstruction of Piecewise Planar Objects from Single Images

This paper proposes a new approach to 3D reconstruction of piecewise planar objects based on two image regularities, connectivity and perspective symmetry. First, we formulate the whole shape of the objects in an image as a shape vector consisting of the normals of all the faces of the objects. Then, we impose several linear constraints on the shape vector using connectivity and perspective symmetry of the objects. Finally, we obtain a closed-form solution to the 3D reconstruction problem. We also develop an efficient algorithm to detect a face of perspective symmetry. Experimental results on real images are shown to demonstrate the effectiveness of our approach.