ON THE RECOVERY OF MOTION AND STRUCTURE WHEN CAMERAS ARE NOT CALIBRATED

Abstract

This paper addresses the problem of computing the camera motion and the Euclidean 3D structure of an observed scene using uncalibrated images. Given at least two images with pixel correspondences, the motion of the camera (translation and rotation) and the 3D structure of the scene are calculated simultaneously. We do not assume the knowledge of the intrinsic parameters of the camera. However, an approximation of these parameters is required. Such an approximation is all the time available, either from the camera manufacturer's data or from former experiments. Classical methods based on the essential matrix are highly sensitive to image noise. This sensitivity is amplified when the intrinsic parameters of the cameras contain errors. To overcome such instability, we propose here a method where a particular choice of a 3D Euclidean coordinate system with a different parameterization of the motion/structure problem allowed us to reduce significantly the total number of unknowns. In addition, the simultaneous calculation of the camera motion and the 3D structure has made the computation of the motion and structure less sensitive to the errors in the values of the intrinsic parameters of the camera. All steps of our method are linear. However, a final nonlinear optimal step might be added to improve the accuracy of the results and to allow the orthogonality of the rotation matrix to be taken into account. Experiments with real images validated our method and showed that a good quality motion/structure can be recovered from a pair of uncalibrated images. Intensive experiments with simulated images have shown the relationship between the errors on the intrinsic parameters and the accuracy of the recovered 3D structure.