Euclidean reconstruction from uncalibrated views

Hartley, Richard

doi:10.1007/3-540-58240-1_13

Cited by 215 publications

(187 citation statements)

References 16 publications

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“…Let x be the fixed image point, F the fundamental matrix between images 1 and 2, e 3 These can be counted as follows: 15 for a 3D projective transformation modulo 7 for a scaled Euclidean one; or 12 for a is a Euclideanizing projectivity. 5 For most other autocalibration methods, this case is ambiguous only if the fixed point is at infinity (rotation about a fixed axis + arbitrary translation). the epipole of image 2 in image 1, and § the constant dual absolute image quadric.…”

Section: Autocalibration For Non-planar Scenesmentioning

confidence: 99%

“…This paper describes a method of autocalibrating a moving projective camera with general, unknown motion and unknown intrinsic parameters, from a single perspective camera with constant but unknown internal parameters moving with a general but unknown motion in a 3D scene, the original Kruppa equation based approach [14] seems to be being displaced by approaches based on the 'rectification' of an intermediate projective reconstruction [5,9,15,22,10]. More specialized methods exist for particular types of motion and simplified calibration models [6,24,1,16].…”

Section: Introductionmentioning

confidence: 99%

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Autocalibration from planar scenes

Triggs

1998

Computer Vision — ECCV'98

258

169

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This paper describes a theory and a practical algorithm for the autocalibration of a moving projective camera, from ¡ £ ¢ ¥ ¤ v iews 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 non-planar 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 inter-image homographies as a projective scene representation.

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Section: Autocalibration For Non-planar Scenesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Autocalibration from planar scenes

Triggs

1998

Computer Vision — ECCV'98

258

169

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“…A method for doing this using sparse techniques to minimize time complexity is given in [1]. In general, minimization of geometric error can be expected to give the best possible results (depending on how realistic the error model is).…”

Section: Geometric Distancementioning

confidence: 99%

Computation of the quadrifocal tensor

Hartley¹

1998

Computer Vision — ECCV'98

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This paper gives a practical and accurate algorithm for the computation of the quadrifocal tensor and extraction of camera matrices from it. Previous methods for using the quadrifocal tensor in projective scene reconstruction have not emphasized accuracy of the algorithm in conditions of noise. Methods given in this paper minimize algebraic error either through a non-iterative linear algorithm, or two alternative iterative algorithms. It is shown by experiments with synthetic data that the iterative methods, though minimizing algebraic, rather than more correctly geometric error measured in the image, give almost optimal results.

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“…This naturally leads to non-linear minimization methods This work has been supported by "Société Aérospatiale" and by DRET. which require some form of initialization [8], [4]. If the initial "guess" is too faraway from the true solution then the minimization process is either very slow or it converges to a wrong solution.…”

Section: Introductionmentioning

confidence: 99%

“…With a calibrated camera one may compute Euclidean shape up to a scale factor using either a perspective model [8], or a linear model [9], [10], [6]. With an uncalibrated camera the recovered shape is defined up to a projective transformation or up to an affine transformation [4]. One can therefore address the problem of either Euclidean, affine, or projective shape reconstruction.…”

Section: Introductionmentioning

confidence: 99%

Euclidean reconstruction: From paraperspective to perspective

Christy

Horaud

1996

Lecture Notes in Computer Science

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Abstract. In this paper we describe a method to perform Euclidean reconstruction with a perspective camera model. It incrementally performs reconstruction with a paraperspective camera in order to converge towards a perspective model. With respect to other methods that compute shape and motion from a sequence of images with a calibrated perspective camera, this method converges in a few iterations, is computationally efficient, and does not suffer from the non linear nature of the problem. Moreover, the behaviour of the algorithm may be simply explained and analysed, which is an advantage over classical non linear optimization approaches. With respect to 3-D reconstruction using an approximated camera model, our method solves for the sign (reversal) ambiguity in a very simple way and provides much more accurate reconstruction results.

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Euclidean reconstruction from uncalibrated views

Cited by 215 publications

References 16 publications

Autocalibration from planar scenes

Autocalibration from planar scenes

Computation of the quadrifocal tensor

Euclidean reconstruction: From paraperspective to perspective

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