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.

We describe how 3D affine measurements may be computed from a single perspective view of a scene given only minimal geometric information determined from the image. This minimal information is typically the vanishing line of a reference plane, and a vanishing point for a direction not parallel to the plane. It is shown that affine scene structure may then be determined from the image, without knowledge of the camera's internal calibration (e.g. focal length), nor of the explicit relation between camera and world (pose). In particular, we show how to (i) compute the distance between planes parallel to the reference plane (up to a common scale factor); (ii) compute area and length ratios on any plane parallel to the reference plane; (iii) determine the camera's (viewer's) location. Simple geometric derivations are given for these results. We also develop an algebraic representation which unifies the three types of measurement and, amongst other advantages, permits a first order error pr...

Abstract. Omnidirectional vision systems can provide panoramic alertness in surveillance, improve navigational capabilities, and produce panoramic images for multimedia. Catadioptric realizations of omnidirectional vision combine reflective surfaces and lenses. A particular class of them, the central panoramic systems, preserve the uniqueness of the projection viewpoint. In fact, every central projection system including the well known perspective projection on a plane falls into this category. In this paper, we provide a unifying theory for all central catadioptric systems. We show that all of them are isomorphic to projective mappings from the sphere to a plane with a projection center on the perpendicular to the plane. Subcases are the stereographic projection equivalent to parabolic projection and the central planar projection equivalent to every conventional camera. We define a duality among projections of points and lines as well as among different mappings. This unification is novel and has a a significant impact on the 3D interpretation of images. We present new invariances inherent in parabolic projections and a unifying calibration scheme from one view. We describe the implied advantages of catadioptric systems and explain why images arising in central catadioptric systems contain more information than images from conventional cameras. One example is that intrinsic calibration from a single view is possible for parabolic catadioptric systems given only three lines. Another example is metric rectification using only affine information about the scene. 1

To appear in Proceedings of CVPR 2000. In this paper we describe a formulation of extrinsic camera calibration that decouples rotation from translation by exploiting properties inherent in urban scenes. We then present an algorithm which uses edge features to robustly and accurately estimate relative rotations among multiple cameras given intrinsic calibration and approximate initial pose. The algorithm is linear both in the number of images and the number of features. We estimate the number and directions of vanishing points (VPs) with respect to each camera using a hybrid approach that combines the robustness of the Hough transform with the accuracy of expectation maximization. Matching and labeling methods identify unique VPs and correspond them across all cameras. Finally, a technique akin to bundle adjustment produces globally optimal estimates of relative camera rotations by bringing all VPs into optimal alignment. Uncertainty is modeled and used at every stage to improve accura...

A man-made environment is characterized by a lot of parallel lines and a lot of orthogonal edges. In this article, a new method for detecting the three mutual orthogonal directions of such an environment is presented. Since realtime performance is not necessary for architectural application, like building reconstruction, a computationally more intensive approach was chosen. On the other hand, our approach is more rigorous than existing techniques, since the information given by the condition of three mutual orthogonal directions in the scene is identified and incorporated. Since knowledge about the camera geometry can be deduced from the vanishing points of three mutual orthogonal directions, we use this knowledge to reject falsely detected vanishing points. Results are presented from interpreting outdoor scenes of buildings. Key words Vanishing points, vanishing lines, geometric constraints, architecture, camera calibration

This paper tackles the problem of selfcalibration of multiple cameras which are very far apart. Given a set of feature correspondences one can determine the camera geometry. The key problem we address is finding such correspondences. Since the camera geometry (location and orientation) and photometric characteristics vary considerably between images one cannot use brightness and/or proximity constraints. Instead we propose a three step approach: first we use moving objects in the scene to determine a rough planar alignment, next we use static features to improve the alignment, finally we use o# plane features to determine the epipolar geometry and the horizon line. We do not assume synchronized cameras and we show that enforcing the geometric constraints enables us to align the tracking data in time. We present results on challenging outdoor scenes using real time tracking data. 1 Introduction Imagine you wish to perform automatic visual surveillance on a site. You want the computer ...

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We present a simple approach to combining scene and auto-calibration constraints for the calibration of cameras from single views and stereo pairs. Calibration constraints are provided by imaged scene structure, such as vanishing points of orthogonal directions, or rectified planes. In addition, constraints are available from the nature of the cameras and the motion between views. We formulate these constraints in terms of the geometry of the imaged absolute conic and its relationship to pole-polar pairs and the imaged circular points of planes. Three significant advantages result: first, constraints from scene features, camera characteristics and auto-calibration constraints provide linear equations in the elements of the image of the absolute conic. This means that constraints may easily be combined, and their solution is straightforward. Second, the degeneracies that occur when constraints are not independent may be easily identified. Lastly, the constraints from scene planes and i...

Abstract. In this paper we describe the theory and practice ofself-calibration ofcameras which are fixed in location and may freely rotate while changing their internal parameters by zooming. The basis ofour approach is to make use ofthe so-called infinite homography constraint which relates the unknown calibration matrices to the computed inter-image homographies. In order for the calibration to be possible some constraints must be placed on the internal parameters ofthe camera. We present various self-calibration methods. First an iterative non-linear method is described which is very versatile in terms ofthe constraints that may be imposed on the camera calibration: each ofthe camera parameters may be assumed to be known, constant throughout the sequence but unknown, or free to vary. Secondly, we describe a fast linear method which works under the minimal assumption of zero camera skew or the more restrictive conditions ofsquare pixels (zero skew and known aspect ratio) or known principal point. We show experimental results on both synthetic and real image sequences (where ground truth data was available) to assess the accuracy and the stability ofthe algorithms and to compare the result ofapplying different constraints on the camera parameters. We also derive an optimal Maximum Likelihood estimator for the calibration and the motion parameters. Prior knowledge about the distribution ofthe estimated parameters (such as the location ofthe principal point) may also be incorporated via Maximum a Posteriori estimation. We then identify some near-ambiguities that arise under rotational motions showing that coupled changes ofcertain parameters are barely observable making them indistinguishable. Finally we study the negative effect ofradial distortion in the self-calibration process and point out some possible solutions to it. 1.

It is demonstrated that grouping together features which satisfy a geometric relationship can be used both for (automatic) detection and estimation of vanishing points and lines. We describe the geometry of three commonly occurring types of geometric grouping and present efficient grouping algorithms which exploit these geometries. The three types of grouping are : (1) a family of equally spaced coplanar parallel lines, (2) a planar pattern obtained by repeating some element by translation in the plane, and (3) a set of elements arranged in a regular planar grid. Examples of automatically computing groupings, together with their vanishing points and lines, are given for a number of real images. Key words: Grouping, Vanishing Point and Line Detection, Repetition. 1 Introduction Suppose a plane in the world is imaged by a perspective camera. Then the line at infinity of the plane is projected to a line in the image, the vanishing line. The objective of this paper is to automatically e...