Scaled Euclidean 3D reconstruction based on externally uncalibrated cameras

Abstract

Previous work shows that based on five non-coplanar correspondences of two uncalibrated cameras, 3D reconstruction can be achieved under projectile models, or based on four non-coplanar correspondences of two uncalibrated cameras, 3D reconstruction can be achieved under affine models, with three unknown parameters. In this paper, we show that based on four coplanar correspondences of two externally uncalibrated cameras, 3D reconstruction can be achieved in Euclidean space with only one unknown scaling parameter. Moreover, the unknown scale factor is the physical distance from the camera center to the plane formed by the four points in 3D space. If this distance is known a priori, then the 3D structure can be completely recovered. Both simulated and real data experimental results show that our reconstruction algorithm works reasonably robustly.