Stereo from uncalibrated cameras

Hartley, Richard; Gupta, Rajiv; Chang, Tian-Sheuan

doi:10.1109/cvpr.1992.223179

Cited by 307 publications

(192 citation statements)

References 3 publications

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“…For compactness we denote the reconstruction by the pair ({M i }, {x j }). Without further restriction on the M i or x j , such a reconstruction is called a projective reconstruction, because the points x j may differ by an arbitrary 3D projective transformation from the true reconstruction ( [3,5]). A reconstruction that is known to differ from the true reconstruction by at most a 3D affine transformation is called an affine reconstruction, and one that differs by a Euclidean transformation from the true reconstruction is called a Euclidean reconstruction.…”

Section: The Euclidean Reconstruction Problemmentioning

confidence: 99%

“…Various methods of projective reconstruction from two or more views have been given previously ( [3,5,14]). The method given in [5] is a straight-forward non-iterative construction method from two views.…”

Section: Projective Reconstructionmentioning

confidence: 99%

“…The basic fact about projective reconstruction is the theorem ( [3,5]) that any two reconstructions of a scene from a set of (sufficiently many) image correspondences in images taken with uncalibrated cameras differ by a 3D projective transformation. In particular a solution in which all the cameras have the same calibration must differ by a projective transformation from any other solution in which the cameras are possibly different.…”

Section: Projective Reconstructionmentioning

confidence: 99%

“…The method given in [5] is a straight-forward non-iterative construction method from two views. Where high precision is required, it should be followed by iterative refinement.…”

Section: Projective Reconstructionmentioning

confidence: 99%

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Euclidean reconstruction from uncalibrated views

Hartley¹

1994

Lecture Notes in Computer Science

215

183

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The possibility of calibrating a camera from image data alone, based on matched points identified in a series of images by a moving camera was suggested by Mayband and Faugeras. This result implies the possibility of Euclidean reconstruction from a series of images with a moving camera, or equivalently, Euclidean structure-from-motion from an uncalibrated camera. No tractable algorithm for implementing their methods for more than three images have been previously reported. This paper gives a practical algorithm for Euclidean reconstruction from several views with the same camera. The algorithm is demonstrated on synthetic and real data and is shown to behave very robustly in the presence of noise giving excellent calbration and reconstruction results.

show abstract

Section: The Euclidean Reconstruction Problemmentioning

confidence: 99%

Section: Projective Reconstructionmentioning

confidence: 99%

Section: Projective Reconstructionmentioning

confidence: 99%

“…The method given in [5] is a straight-forward non-iterative construction method from two views. Where high precision is required, it should be followed by iterative refinement.…”

Section: Projective Reconstructionmentioning

confidence: 99%

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Euclidean reconstruction from uncalibrated views

Hartley¹

1994

Lecture Notes in Computer Science

215

183

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show abstract

“…The minimal data required for projective reconstruction is well-known [8,12,28,30]. For two views, seven points are needed and Sturm's method [31] (reintroduced into computer vision in [8,9,22]) can be used, giving at most three real solutions.…”

Section: Introductionmentioning

confidence: 99%

Some Results on Minimal Euclidean Reconstruction from Four Points

2006

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Abstract. Methods for reconstruction and camera estimation from miminal data are often used to boot-strap robust (RANSAC and LMS) and optimal (bundle adjustment) structure and motion estimates. Minimal methods are known for projective reconstruction from two or more uncalibrated images, and for "5 point" relative orientation and Euclidean reconstruction from two calibrated parameters, but we know of no efficient minimal method for three or more calibrated cameras except the uniqueness proof by Holt and Netravali. We reformulate the problem of Euclidean reconstruction from minimal data of four points in three or more calibrated images, and develop a random rational simulation method to show some new results on this problem. In addition to an alternative proof of the uniqueness of the solutions in general cases, we further show that unknown coplanar configurations are not singular, but the true solution is a double root. The solution from a known coplanar configuration is also generally unique. Some especially symmetric point-camera configurations lead to multiple solutions, but only symmetry of points or the cameras gives a unique solution.

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A factorization method for multiple perspective views via iterative depth estimation

Ueshiba¹,

Tomita²

2000

Syst. Comp. Jpn.

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This paper proposes a factorization method that reconstructs camera motion and scene shape based on the matching of multiple images under the condition that the camera captures a perspective view. Starting from the affine projection camera model, the projection depth is iteratively estimated until the measurement matrix has rank 4. Then, the obtained measurement matrix is factorized to restore the three-dimensional information of the scene in the projection space. This approach eliminates noise sensitive processes, such as the calculation of the fundamental matrix, that are required in the factorization for the conventional perspective projection image, and a stable reconstruction is realized. Furthermore, the metric constraint in the conventional affine model is extended, and the metric constraint in the perspective projection condition is derived. It is shown that the reconstruction in Euclidean space is realized if the internal parameters of the camera are given. © 2000 Scripta Technica, Syst Comp Jpn, 31(13): 8795, 2000

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Stereo from uncalibrated cameras

Cited by 307 publications

References 3 publications

Euclidean reconstruction from uncalibrated views

Euclidean reconstruction from uncalibrated views

Some Results on Minimal Euclidean Reconstruction from Four Points

A factorization method for multiple perspective views via iterative depth estimation

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