Branch-and-Bound Methods for Euclidean Registration Problems

Olsson, Carl; Kahl, Fredrik; Oskarsson, Magnus

doi:10.1109/tpami.2008.131

Cited by 149 publications

(151 citation statements)

References 19 publications

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“…Olsson et al [13] proposed to minimize the reprojection error in the image space by using branch-and-bound iterations. Their method retrieves the global optimum, irrespective of initialization.…”

Section: Related Workmentioning

confidence: 99%

“…All inliers are used to estimate the camera pose. Since the ground truth camera pose is not easily available, we minimize the reprojection error by using the branch-and-bound method [13] and use the estimated pose as the ground truth, with respect to which the rotation and translation error are evaluated. The branch-and-bound method takes more than two minutes in each of the experiments, thus inappropriate for real-time applications at all.…”

Section: Experiments With Real Datamentioning

confidence: 99%

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ASPnP: An Accurate and Scalable Solution to the Perspective-n-Point Problem

Zheng

Sugimoto

Okutomi

2013

IEICE Trans. Inf. & Syst.

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Yinqiang ZHENG†a) , Nonmember, Shigeki SUGIMOTO †b) , and Masatoshi OKUTOMI †c) , Members SUMMARYWe propose an accurate and scalable solution to the perspective-n-point problem, referred to as ASPnP. Our main idea is to estimate the orientation and position parameters by directly minimizing a properly defined algebraic error. By using a novel quaternion representation of the rotation, our solution is immune to any parametrization degeneracy. To obtain the global optimum, we use the Gröbner basis technique to solve the polynomial system derived from the first-order optimality condition. The main advantages of our proposed solution lie in accuracy and scalability. Extensive experiment results, with both synthetic and real data, demonstrate that our proposed solution has better accuracy than the stateof-the-art noniterative solutions. More importantly, by exploiting vectorization operations, the computational cost of our ASPnP solution is almost constant, independent of the number of point correspondences n in the wide range from 4 to 1000. In our experiment settings, the ASPnP solution takes about 4 milliseconds, thus best suited for real-time applications with a drastically varying number of 3D-to-2D point correspondences * . key words: pose estimation, perspective-n-point, Gröbner basis, global optimum IntroductionThe perspective-n-point problem (PnP) aims to estimate the orientation and position, or rotation and translation, of a calibrated perspective camera by using n known 3D reference points and their corresponding 2D image projections. It has widespread applications in robot localization [1], hand-eye calibration [2], augmented reality [3] and so on. Considering these various application scenarios, a desirable PnP solution should be accurate, efficient and generally applicable, i.e., capable of handling both planar and non-planar cases with either a few or even hundreds of 3D-to-2D correspondences. Related WorksAs the minimal case, P3P (n = 3) has been thoroughly investigated in the literature [4], [5]. However, it has at most four possible solutions, and this multiplicity makes a P3P solver very sensitive to noise. In practice, it is usually used together with some robust estimation methods, like RANSAC [6], to remove outliers.To improve robustness to noise, cases of four and more than four correspondences should be considered. There are some specialized algorithms [7] restricted to the slightly redundant n = 4 (P4P) or n = 5 (P5P) cases only. However, the application of these specialized P4P and P5P solutions is limited, since the number of point correspondences might differ from one frame to the other, even in a specific application scenario. As a result, a large body of existing works have tried to improve flexibility, thus applicable to the general n ≥ 4 cases. Quan and Lan [8] proposed a linear solution by combining all the constraints from three-point subsets, whose computational complexity is O(n 5 ). Ansar and Daniilidis [9] developed linear solutions, but with complexity O(n 8 ), for general PnP ...

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Section: Related Workmentioning

confidence: 99%

Section: Experiments With Real Datamentioning

confidence: 99%

ASPnP: An Accurate and Scalable Solution to the Perspective-n-Point Problem

Zheng

Sugimoto

Okutomi

2013

IEICE Trans. Inf. & Syst.

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“…Standard objective functions are based on geometric (e.g. 2D reprojection) [25] or algebraic errors [21]. Yet, iterative methods suffer from a high computational cost and tend to be sensitive to local minima [8,21].…”

Section: Related Workmentioning

confidence: 99%

Leveraging Feature Uncertainty in the PnP Problem

Ferraz¹,

Binefa²,

Moreno-Noguer³

2014

Proceedings of the British Machine Vision Conference 2014

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We propose a real-time and accurate solution to the Perspective-n-Point (PnP) problem -estimating the pose of a calibrated camera from n 3D-to-2D point correspondencesthat exploits the fact that in practice the 2D position of not all 2D features is estimated with the same accuracy. Assuming a model of such feature uncertainties is known in advance, we reformulate the PnP problem as a maximum likelihood minimization approximated by an unconstrained Sampson error function, which naturally penalizes the most noisy correspondences. The advantages of this approach are thoroughly demonstrated in synthetic experiments where feature uncertainties are exactly known.Pre-estimating the features uncertainties in real experiments is, though, not easy. In this paper we model feature uncertainty as 2D Gaussian distributions representing the sensitivity of the 2D feature detectors to different camera viewpoints. When using these noise models with our PnP formulation we still obtain promising pose estimation results that outperform the most recent approaches.

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“…We introduce novel piecewise linear under-and overestimator for square terms. In terms of relaxation tightness, this piecewise relaxation mechanism is superior over the popular convex and concave relaxations in existing literature, such as [13,5,19].…”

Section: Our Contributionmentioning

confidence: 99%

“…In existing computer vision literature ( [13,5,19]), the mainstream idea is to build convex and concave relaxations for nonconvex terms. In the sense of convexity and concavity, the tightest possible relaxations are the convex and concave envelopes, the bilinear envelopes in [13,5,19] (w). Note that we omit the subscript j of x j in this whole section for simplification.…”

Section: Relaxation For Square Termsmentioning

confidence: 99%