An Affine Invariant of Parallelograms and Its Application to Camera Calibration and 3D Reconstruction

Fuchao Wu, Fuqing Duan, Zhanyi Hu

Abstract: In this work, a new affine invariant of parallelograms is introduced, and the explicit constraint equations between the intrinsic matrix of a camera and the similar invariants of a parallelogram or a parallelepiped are established using this affine invariant. Camera calibration and 3D reconstruction from parallelograms are systematically studied based on these constraints. The proposed theoretical results and algorithms have wide applicability as parallelograms and parallelepipeds are not rare in man-made scenes. Experimental results on synthetic and real images validate the proposed approaches.