AbstractÐWe propose a flexible new technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled. The proposed procedure consists of a closed-form solution, followed by a nonlinear refinement based on the maximum likelihood criterion. Both Our current research is focused on a desktop vision system (DVS) since the potential for using DVSs is large. Cameras are becoming inexpensive and ubiquitous. A DVS aims at the general public who are not experts in computer vision. A typical computer user will perform vision tasks only from time to time, so they will not be willing to invest money for expensive equipment. Therefore, flexibility, robustness, and low cost are important. The camera calibration technique described in this paper was developed with these considerations in mind. The proposed technique only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. The pattern can be printed on a laser printer and attached to a ªreasonableº planar surface (e.g., a hard book cover). Either the camera or the planar pattern can be moved by hand. The motion need not be known. The proposed approach, which uses 2D metric information, lies between the photogrammetric calibration, which uses explicit 3D model, and self-calibration, which uses motion rigidity or equivalently implicit 3D information. Both computer simulation and real data have been used to test the proposed technique and very good results have been obtained. Compared with classical techniques, the proposed technique is considerably more flexible: Anyone can make a calibration pattern by him/herself and the setup is very easy. Compared with self-calibration, it gains a considerable degree of robustness. We believe the new technique advances 3D computer vision one step from laboratory environments to the real world. Note that Triggs [22] recently developed a self-calibration technique from at least five views of a planar scene. His technique is more flexible than ours, but has difficulty to initialize. Liebowitz and Zisserman [13] described a technique of metric rectification for perspective images of planes using metric information, such as a known angle, two equal though unknown angles, and a known length ratio. They also mentioned that calibration of the internal camera parameters is possible provided at least three such rectified planes, although no experimental results were shown. During the revision of this paper, we notice the publication of an independent but similar work by Sturm and Maybank [21] .They use a simplified camera model (image axes are orthogonal to each other) and have studied the degenerate configurations exhaustively for the case of one and two planes, which are very important in practice if only one or two views are used for camera calibration. The paper is organized as follows: Section 2 describes the basic constraints from observing a single plane. Section 3 describes the calibration procedure. We start with a closed-form solution, followed by nonlinear optimization. Radial lens distortion is also modeled. Section 4 provides the experimental results. Both computer simulation and real data are used to validate the proposed technique. In the Appendix, we provides a number of details, including the techniques for estimating the homography between the model plane and its image. We examine the constraints on the camera's intrinsic parameters provided by observing a single plane. We start with the notation used in this paper.
Zhang REF proposed a simple camera calibration technique to determine radial distortion by observing a planar pattern shown at a few different orientations.
A flexible new technique for camera calibration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Science