Euclidean reconstruction from constant intrinsic parameters

Heyden, Anders; Åström, Kalle

doi:10.1109/icpr.1996.546045

Cited by 131 publications

(63 citation statements)

References 12 publications

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“…[22,9]) are based implicitly on these constraints, parametrized by K or § and by something equivalent 4 to ¤ or A . All of these methods seem to work well provided the intrinsic degeneracies of the autocalibration problem [18] are avoided.…”

Section: Autocalibration For Non-planar Scenesmentioning

confidence: 99%

“…Hartley [6] has given a particularly simple internal calibration method for the case of a single camera whose translation is known to be negligible compared to the distances of some identifiable (real or synthetic) points in the scene, and Faugeras [2] has elaborated a 'stratification' paradigm for autocalibration based on this. The numerical conditioning of classical autocalibration is historically delicate, although recent algorithms have improved the situation significantly [9,15,22]. The main problem is that classical autocalibration has some restrictive intrinsic degeneracies -classes of motion for which no algorithm can recover a full unique solution.…”

Section: Introductionmentioning

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%

“…Stereo heads can also be autocalibrated [27,11]. Solutions are still -in theory -possible if some of the intrinsic parameters are allowed to vary [9,15]. Hartley [6] has given a particularly simple internal calibration method for the case of a single camera whose translation is known to be negligible compared to the distances of some identifiable (real or synthetic) points in the scene, and Faugeras [2] has elaborated a 'stratification' paradigm for autocalibration based on this.…”

Section: Introductionmentioning

confidence: 99%

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Autocalibration from planar scenes

Triggs

1998

Computer Vision — ECCV'98

254

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%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Autocalibration from planar scenes

Triggs

1998

Computer Vision — ECCV'98

254

169

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“…Direct methods seek to compute a metric reconstruction by estimating the absolute conic. This is encoded conveniently in the dual quadric formulation of autocalibration (Heyden and Åström 1996;Triggs 1997), whereby an eigenvalue decomposition of the estimated dual quadric yields the homography that relates the projective reconstruction to Euclidean. Linear methods (Pollefeys et al 1998) as well as more elaborate SQP based optimization approaches (Triggs 1997) have been proposed to estimate the dual quadric, but perform poorly with noisy data.…”

Section: Previous Workmentioning

confidence: 99%

Globally Optimal Algorithms for Stratified Autocalibration

Chandraker,

Agarwal,

Kriegman

et al. 2009

Int J Comput Vis

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We present practical algorithms for stratified autocalibration with theoretical guarantees of global optimality. Given a projective reconstruction, we first upgrade it to affine by estimating the position of the plane at infinity. The plane at infinity is computed by globally minimizing a least squares formulation of the modulus constraints. In the second stage, this affine reconstruction is upgraded to a metric one by globally minimizing the infinite homography relation to compute the dual image of the absolute conic (DIAC). The positive semidefiniteness of the DIAC is explicitly enforced as part of the optimization process, rather than as a post-processing step.For each stage, we construct and minimize tight convex relaxations of the highly non-convex objective functions in a branch and bound optimization framework. We exploit the inherent problem structure to restrict the search space for the DIAC and the plane at infinity to a small, fixed number of branching dimensions, independent of the number of views. Chirality constraints are incorporated into our convex relaxations to automatically select an initial region which is guaranteed to contain the global minimum. Experimental evidence of the accuracy, speed and scalability of our algorithm is presented on synthetic and real data.

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Reconstruction of 3D contour with an active laser‐vision robotic system

Chang

Nguyen

Chu

2011

Asian Journal of Control

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This paper presents a 3D contour reconstruction approach employing a wheeled mobile robot equipped with an active laser-vision system. With observation from an onboard CCD camera, a laser line projector fixed-mounted below the camera is used for detecting the bottom shape of an object while an actively-controlled upper laser line projector is utilized for 3D contour reconstruction. The mobile robot is driven to move around the object by a visual servoing and localization technique while the 3D contour of the object is being reconstructed based on the 2D image of the projected laser line. Asymptotical convergence of the closed-loop system has been established. The proposed algorithm also has been used experimentally with a Dr Robot X80sv mobile robot upgraded with the low-cost active laser-vision system, thereby demonstrating effective real-time performance. This seemingly novel laser-vision robotic system can be applied further in unknown environments for obstacle avoidance and guidance control tasks.

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Euclidean reconstruction from constant intrinsic parameters

Abstract: Abstract

Cited by 131 publications

References 12 publications

Autocalibration from planar scenes

Autocalibration from planar scenes

Globally Optimal Algorithms for Stratified Autocalibration

Reconstruction of 3D contour with an active laser‐vision robotic system

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