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74
Autocalibration and the absolute quadric
 in Proc. IEEE Conf. Computer Vision, Pattern Recognition
, 1997
"... We describe a new method for camera autocalibration and scaled Euclidean structure and motion, from three or more views taken by a moving camera with fixed but unknown intrinsic parameters. The motion constancy of these is used to rectify an initial projective reconstruction. Euclidean scene structu ..."
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Cited by 225 (7 self)
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We describe a new method for camera autocalibration and scaled Euclidean structure and motion, from three or more views taken by a moving camera with fixed but unknown intrinsic parameters. The motion constancy of these is used to rectify an initial projective reconstruction. Euclidean scene structure is formulated in terms of the absolute quadric — the singular dual 3D quadric ( rank 3 matrix) giving the Euclidean dotproduct between plane normals. This is equivalent to the traditional absolute conic but simpler to use. It encodes both affine and Euclidean structure, and projects very simply to the dual absolute image conic which encodes camera calibration. Requiring the projection to be constant gives a bilinear constraint between the absolute quadric and image conic, from which both can be recovered nonlinearly from images, or quasilinearly from. Calibration and Euclidean structure follow easily. The nonlinear method is stabler, faster, more accurate and more general than the quasilinear one. It is based on a general constrained optimization technique — sequential quadratic programming — that may well be useful in other vision problems.
Selfcalibration and metric reconstruction in spite of varying and unknown internal camera parameters
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 1999
"... In this paper the theoretical and practical feasibility of selfcalibration in the presence of varying intrinsic camera parameters is under investigation. The paper’s main contribution is to propose a selfcalibration method which efficiently deals with all kinds of constraints on the intrinsic came ..."
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Cited by 166 (13 self)
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In this paper the theoretical and practical feasibility of selfcalibration in the presence of varying intrinsic camera parameters is under investigation. The paper’s main contribution is to propose a selfcalibration 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 selfcalibration. A counting argument is developed which—depending on the set of constraints—gives the minimum sequence length for selfcalibration and a method to detect critical motion sequences is proposed.
Autocalibration from planar scenes
 European Conference on Computer Vision
, 1998
"... This paper describes a theory and a practical algorithm for the autocalibration of a moving projective camera, from views of a planar scene. The unknown camera calibration, and (up to scale) the unknown scene geometry and camera motion are recovered from the hypothesis that the camera’s internal par ..."
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Cited by 130 (2 self)
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This paper describes a theory and a practical algorithm for the autocalibration of a moving projective camera, from views of a planar scene. The unknown camera calibration, and (up to scale) the unknown scene geometry and camera motion are recovered from the hypothesis that the camera’s internal parameters remain constant during the motion. This work extends the various existing methods for nonplanar autocalibration to a practically common situation in which it is not possible to bootstrap the calibration from an intermediate projective reconstruction. It also extends Hartley’s method for the internal calibration of a rotating camera, to allow camera translation and to provide 3D as well as calibration information. The basic constraint is that the projections of orthogonal direction vectors (points at infinity) in the plane must be orthogonal in the calibrated camera frame of each image. Abstractly, since the two circular points of the 3D plane (representing its Euclidean structure) lie on the 3D absolute conic, their projections into each image must lie on the absolute conic’s image (representing the camera calibration). The resulting numerical algorithm optimizes this constraint over all circular points and projective calibration parameters, using the interimage homographies as a projective scene representation.
Euclidean Reconstruction from Image Sequences with Varying and Unknown Focal Length and Principal Point
"... In this paper the special case of reconstruction from image sequences taken by cameras with skew equal to 0 and aspect ratio equal to 1 has been treated. These type of cameras, here called cameras with Euclidean image planes, represent rigid projections where neither the principal point nor the foca ..."
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Cited by 113 (10 self)
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In this paper the special case of reconstruction from image sequences taken by cameras with skew equal to 0 and aspect ratio equal to 1 has been treated. These type of cameras, here called cameras with Euclidean image planes, represent rigid projections where neither the principal point nor the focal length is known. It will be shown that it is possible to reconstruct an unknown object from images taken by a camera with Euclidean image plane up to similarity transformations, i.e., Euclidean transformations plus changes in the global scale. An algorithm, using bundle adjustment techniques, has been implemented. The performance of the algorithm is shown on simulated data.
Critical motion sequences for monocular selfcalibration and uncalibrated euclidean reconstruction
, 1997
"... Abstract. In this paper, sequences of camera motions that lead to inherent ambiguities in uncalibrated Euclidean reconstruction or selfcalibration are studied. Our main contribution is a complete, detailed classification of these critical motion sequences (CMS). The practically important classes ar ..."
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Cited by 108 (5 self)
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Abstract. In this paper, sequences of camera motions that lead to inherent ambiguities in uncalibrated Euclidean reconstruction or selfcalibration are studied. Our main contribution is a complete, detailed classification of these critical motion sequences (CMS). The practically important classes are identified and their degrees of ambiguity are derived. We also discuss some practical issues, especially concerning the reduction of the ambiguity of a reconstruction. 1
Selfcalibration of rotating and zooming cameras
 International Journal of Computer Vision
, 2001
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Uncalibrated Euclidean reconstruction: a review
, 1999
"... This paper provides a review on techniques for computing a threedimensional model of a scene from a single moving camera, with unconstrained motion and unknown parameters. In the classical approach, called autocalibration or selfcalibration, camera motion and parameters are recovered first, using ..."
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Cited by 38 (8 self)
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This paper provides a review on techniques for computing a threedimensional model of a scene from a single moving camera, with unconstrained motion and unknown parameters. In the classical approach, called autocalibration or selfcalibration, 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 pose and calibration from 4 or 5 known 3D points
 In Proc. 7th Int. Conf. on Computer Vision
, 1999
"... We describe two direct quasilinear methods for camera pose (absolute orientation) and calibration from a single image of 4 or 5 known 3D points. They generalize the 6 point ‘Direct Linear Transform ’ method by incorporating partial prior camera knowledge, while still allowing some unknown calibratio ..."
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Cited by 31 (0 self)
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We describe two direct quasilinear methods for camera pose (absolute orientation) and calibration from a single image of 4 or 5 known 3D points. They generalize the 6 point ‘Direct Linear Transform ’ method by incorporating partial prior camera knowledge, while still allowing some unknown calibration parameters to be recovered. Only linear algebra is required, the solution is unique in nondegenerate cases, and additional points can be included for improved stability. Both methods fail for coplanar points, but we give an experimental eigendecomposition based one that handles both planar and nonplanar cases. Our methods use recent polynomial solving technology, and we give a brief summary of this. One of our aims was to try to understand the numerical behaviour of modern polynomial solvers on some relatively simple test cases, with a view to other vision applications.
Plane + Parallax, Tensors and Factorization
 In Proc. of ECCV
, 2000
"... Abstract. We study the special form that the general multiimage tensor formalism takes under the plane + parallax decomposition, including matching tensors and constraints, closure and depth recovery relations, and intertensor consistency constraints. Plane + parallax alignment greatly simplifies ..."
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Cited by 31 (1 self)
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Abstract. We study the special form that the general multiimage tensor formalism takes under the plane + parallax decomposition, including matching tensors and constraints, closure and depth recovery relations, and intertensor consistency constraints. Plane + parallax alignment greatly simplifies the algebra, and uncovers the underlying geometric content. We relate plane + parallax to the geometry of translating, calibrated cameras, and introduce a new parallaxfactorizing projective reconstruction method based on this. Initial plane + parallax alignment reduces the problem to a single rankone factorization of a matrix of rescaled parallaxes into a vector of projection centres and a vector of projective heights above the reference plane. The method extends to 3D lines represented by viapoints and 3D planes represented by homographies.
Flexible Calibration: Minimal Cases for Autocalibration
"... This paper deals with the concept of autocalibration, i.e. methods to calibrate a camera online. In particular, we deal with minimal conditions on the intrinsic parameters needed to make a Euclidean reconstruction, called flexible calibration. The main theoretical results are that it is only neede ..."
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Cited by 29 (3 self)
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This paper deals with the concept of autocalibration, i.e. methods to calibrate a camera online. In particular, we deal with minimal conditions on the intrinsic parameters needed to make a Euclidean reconstruction, called flexible calibration. The main theoretical results are that it is only needed to know that one intrinsic parameter is constant. The method is based on an initial projective reconstruction, which is upgraded to a Euclidean one. The number of images needed increases with the complexity of the constraints, but the number of points needed is only the number needed in order to obtain a projective reconstruction. The theoretical results are exemplified in a number of experiments. An algorithm, based on bundle adjustments and a linear initialization method are presented and experiments are performed on both synthetic and real data.