This paper introduces an affine invariant of trapezia, and the explicit constraint equation between the intrinsic matrix of a camera and the similarity invariants of a trapezium are established using the affine invariant. By this constraint, the inner parameters, motion parameters of the cameras and the similarity invariants of trapezia can be linearly determined using some prior knowledge on the cameras or the trapezia. The proposed algorithms have wide applicability since parallel lines are not rare in many scenes. Experimental results validate the proposed approaches. This work presents a unifying framework based on the parallelism constraint, and the previous methods based on the parallelograms or the parallelepipeds can be integrated into this framework.

Key words: invariant parallelism constraint camera calibration 3D reconstruction