We 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 computer simulation and real data have been used to test the proposed technique, and very good results have been obtained. Compared with classical techniques which use expensive equipment such as two or three orthogonal planes, the proposed technique is easy to use and flexible. It advances 3D computer vision one step from laboratory environments to real world use. The corresponding software is available from the author’s Web page.

In this paper the theoretical and practical feasibility of self-calibration in the presence of varying intrinsic camera parameters is under investigation. The paper’s main contribution is to propose a self-calibration method which efficiently deals with all kinds of constraints on the intrinsic camera parameters. Within this framework a practical method is proposed which can retrieve metric reconstruction from image sequences obtained with uncalibrated zooming/focusing cameras. The feasibility of the approach is illustrated on real and synthetic examples. Besides this a theoretical proof is given which shows that the absence of skew in the image plane is sufficient to allow for self-calibration. A counting argument is developed which—depending on the set of constraints—gives the minimum sequence length for self-calibration and a method to detect critical motion sequences is proposed.

We introduce the concept of self-calibration of a 1D projective camera from point correspondences, and describe a method for uniquely determining the two internal parameters of a 1D camera, based on the trifocal tensor of three 1D images. The method requires the estimation of the trifocal tensor which can be achieved linearly with no approximation unlike the trifocal tensor of 2D images and solving for the roots of a cubic polynomial in one variable. Interestingly enough, we prove that a 2D camera undergoing planar motion reduces to a 1D camera. From this observation, we deduce a new method for self-calibrating a 2D camera using planar motions. Both the self-calibration method for a 1D camera and its applications for 2D camera calibration are demonstrated on real image sequences.

Structure from motion algorithms typically do not use external geometric constraints, e.g., the coplanarity of certain points or known orientations associated with such planes, until a final post-processing stage. In this paper, we show how such geometric constraints can be incorporated early on in the reconstruction process, thereby improving the quality of the estimates. The approaches we study include hallucinating extra point matches in planar regions, computing fundamental matrices directly from homographies, and applying coplanarity and other geometric constraints as part of the final bundle adjustment stage. Our experimental results indicate that the quality of the reconstruction can be significantly improved by the judicious use of geometric constraints.

This paper provides a review on techniques for computing a three-dimensional model of a scene from a single moving camera, with unconstrained motion and unknown parameters. In the classical approach, called autocalibration or self-calibration, camera motion and parameters are recovered first, using rigidity; then structure is easily computed. Recently, new methods based on the idea of stratification have been proposed. They upgrade the projective structure, achievable from correspondences only, to the Euclidean structure, by exploiting all the available constraints.

Camera calibration has been studied extensively in computer vision and photogrammetry and the proposed techniques in the literature include those using 3D apparatus (two or three planes orthogonal to each other or a plane undergoing a pure translation, etc.), 2D objects (planar patterns undergoing unknown motions), and 0D features (self-calibration using unknown scene points). Yet, this paper proposes a new calibration technique using 1D objects (points aligned on a line), thus filling the missing dimension in calibration. In particular, we show that camera calibration is not possible with free-moving 1D objects, but can be solved if one point is fixed. A closed-form solution is developed if six or more observations of such a 1D object are made. For higher accuracy, a nonlinear technique based on the maximum likelihood criterion is then used to refine the estimate. Singularities have also been studied. Besides the theoretical aspect, the proposed technique is also important in practice especially when calibrating multiple cameras mounted apart from each other, where the calibration objects are required to be visible simultaneously.

Università degli studi di Verona We address the problem of autocalibration of a moving camera with unknown constant intrinsic parameters. Existing autocalibration techniques use numerical optimization algorithms whose convergence to the correct result cannot be guaranteed, in general. To address this problem, we have developed a method where an interval branchand-bound method is employed for numerical minimization. Thanks to the properties of Interval Analysis this method converges to the global solution with mathematical certainty and arbitrary accuracy, and the only input information it requires from the user are a set of point correspondences and a search box. The cost function is based on the Huang-Faugeras constraint of the fundamental matrix, and a closed form expression for its Jacobian and Hessian matrices is derived through matrix differential calculus. A recently proposed interval extension based on Bernstein polynomial forms has been investigated to speed up the search for the solution. Finally, experimental results on synthetic and real images are presented.

This paper addresses the problem of calibrating a pinhole camera from images of a surface of revolution. Camera calibration is the process of determining the intrinsic or internal parameters (i.e., aspect ratio, focal length and principal point) of a camera, and it is important for both motion estimation and metric reconstruction of 3D models. In this paper a novel and simple calibration technique is introduced, which is based on exploiting the symmetry of images of surfaces of revolution. Traditional techniques for camera calibration involve taking images of some precisely machined calibration pattern (such as a calibration grid). The use of surfaces of revolution, which are commonly found in daily life (e.g., bowls and vases), makes the process easier as a result of the reduced cost and increased accessibility of the calibration objects. In this paper, it is shown that two images of a surface of revolution will provide enough information for determining the aspect ratio, focal length and principal point of a camera with fixed intrinsic parameters. The algorithms presented in this paper have been implemented and tested with both synthetic and real data. Experimental results show that the camera calibration method presented here is both practical and accurate.

In this paper, we present a flexible new technique for single viewpoint omnidirectional camera calibration. The proposed method only requires the camera to observe a planar pattern shown at a few different orientations. Either the camera or the planar pattern can be freely moved. No a priori knowledge of the motion is required, nor a specific model of the omnidirectional sensor. The only assumption is that the image projection function can be described by a Taylor series expansion whose coefficients are estimated by solving a two-step least-squares linear minimization problem. To test the proposed technique, we calibrated a panoramic camera having a field of view greater than 200° in the vertical direction, and we obtained very good results. To investigate the accuracy of the calibration, we also used the estimated omni-camera model in a structure from motion experiment. We obtained a 3D metric reconstruction of a scene from two highly distorted omnidirectional images by using image correspondences only. Compared with classical techniques, which rely on a specific parametric model of the omnidirectional camera, the proposed procedure is independent of the sensor, easy to use, and flexible. 1.

Modeling of 3D objects from image sequences is one of the challenging problems in computer vision and has been a research topic for many years. Important theoretical and algorithmic results were achieved that allow to extract even complex 3D scene models from images. One recent effort has been to reduce the amount of calibration and to avoid restrictions on the camera motion. In this contribution an approach is described which achieves this goal by combining state-of-the-art algorithms for uncalibrated projective reconstruction, self-calibration and dense correspondence matching.