Camera Calibration Combining Images with Two Vanishing Points

Single image calibration is a fundamental task in photogrammetry and computer vision. It is known that camera constant and principal point can be recovered using exclusively the vanishing points of three orthogonal directions. Yet, three reliable and well-distributed vanishing points are not always available. On the other hand, two vanishing points basically allow only estimation of the camera constant (assuming a known principal point location). Here, a camera calibration approach is presented, which exploits the existence of only two vanishing points on several independent images. Using the relation between two vanishing points of orthogonal directions and the camera parameters, the algorithm relies on direct geometric reasoning regarding the loci of the projection centres in the image system (actually a geometric interpretation of the constraint imposed by two orthogonal vanishing points on the ‘image of the absolute conic’). Introducing point measurements on two sets of converging image lines as observations, the interior orientation parameters (including radial lens distortion) are estimated from a minimum of three images. Recovery of image aspect ratio is possible, too, at the expense of an additional image. Apart from line directions in space, full camera calibration is here independent from any exterior metric information (known points, lengths, length ratios etc.). Besides, since the sole requirement is two vanishing points of orthogonal directions on several images, the imaged scenes may simply be planar. Furthermore, calibration with images of 2D objects and/or ‘weak perspectives’ of 3D objects is expected to be more precise than single image approaches using 3D objects. Finally, no feature correspondences among views are required here; hence, images of totally different objects can be used. In this sense, one may still refer to a ‘single-image’ approach. The implemented algorithm has been successfully evaluated with simulated and real data, and its results have been compared to photogrammetric bundle adjustment and plane-based calibration.