High Accuracy Fundamental Matrix Computation and Its Performance Evaluation

Kanatani, Kenichi; Sugaya, Yasuyuki

doi:10.1093/ietisy/e90-d.2.579

Cited by 15 publications

(17 citation statements)

References 11 publications

(7 reference statements)

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“…In contrast, other problems in geometric computer vision, such as Simultaneous Pose and Correspondence [24,28,31], Fundamental matrix computation [2,14] , ellipse fitting [2,13,15,17], do take into account specific models of uncertainty per observed point. In most these approaches, the uncertainty is modeled by a covariance matrix, and Maximum Likelihood strategies are proposed to minimize the Mahalanobis distances between the noisy and the true locations of the point observations.…”

Section: Related Workmentioning

confidence: 99%

“…As discussed in [3], estimating the global minima for this kind of problems is impractical. A feasible alternative is to minimize approximated Sampson error functions, for instance by means of iterative approaches such as the Fundamental Numerical Scheme (FNS) [2], the Heterocedastic Errors-in-Variables (HEIV) [17] or projective Gauss Newton [14]. These minimization approaches can be considered as a solution refinement and they need to be fed with an initial solution.…”

Section: Related Workmentioning

confidence: 99%

“…As we mentioned in the related work section, there are several techniques to compute x from this equation, e.g [2,14,17]. In this paper, we chose the Fundamental Numerical Scheme (FNS) approach [2], which solves iteratively the following eigenvalue problem,…”

Section: Integration Of Feature Uncertainties In the Linear Formulationmentioning

confidence: 99%

See 2 more Smart Citations

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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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Leveraging Feature Uncertainty in the PnP Problem

Ferraz¹,

Binefa²,

Moreno-Noguer³

2014

Proceedings of the British Machine Vision Conference 2014

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show abstract

“…(7). Indeed, substitutingf f f = f f f k into the expanded update equation (12) reveals that f f f k satisfies the equation set in (9). This equation set defines the necessary conditions for the critical points of the optimization problem of Eq.…”

Section: Derivationmentioning

confidence: 99%

Simple, Fast and Accurate Estimation of the Fundamental Matrix Using the Extended Eight-Point Schemes

Fathy

Hussein

Tolba

2010

Procedings of the British Machine Vision Conference 2010

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The eight-point scheme is the simplest and fastest scheme for estimating the fundamental matrix (FM) from a number of noisy correspondences. As it ignores the fact that the FM must be singular, the resulting FM estimate is often inaccurate. Existing schemes that take the singularity constraint into consideration are several times slower and significantly more difficult to implement and understand. This paper describes extended versions of the eight-point (8P) and the weighted eight-point (W8P) schemes that effectively take the singularity constraint into consideration without sacrificing the efficiency and the simplicity of both schemes. The proposed schemes are respectively called the extended eight-point scheme (E8P) and the extended weighted eight-point scheme (EW8P). The E8P scheme was experimentally found to give exactly the same results as Hartley's algebraic distance minimization scheme while being almost as fast as the simplest scheme (i.e., the 8P scheme). At the expense of extra calculations per iteration, the EW8P scheme permits the use of geometric cost functions and, more importantly, robust weighting functions. It was experimentally found to give near-optimal results while being 8-16 times faster than the more complicated schemes such as Levenberg-Marquardt schemes. The FM estimates obtained by the E8P and the EW8P schemes perfectly satisfy the singularity constraint, eliminating the need to enforce the rank-2 constraint in a post-processing step.

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“…Any such Λ 0 xi is meant to carry the bulk of information about the relative importance of the individual entries of x i (see [6], [7] for the raw covariance matrices of homography estimates and [8], [9] and Section VI for the raw covariance matrices of fundamental matrix estimates). Upon upgrading every Λ 0 xi to a corresponding corrected covariance matrix…”

Section: B Aml Cost Functionmentioning

confidence: 99%

Multi-projective Parameter Estimation for Sets of Homogeneous Matrices

Chojnacki

Hill

Hengel

et al. 2009

2009 Digital Image Computing: Techniques and Applications

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Abstract-A number of problems in computer vision require the estimation of a set of matrices, each of which is defined only up to an individual scale factor and represents the parameters of a separate model, under the assumption that the models are intrinsically interconnected. One example of such a set is a family of fundamental matrices sharing an infinite homography. Here an approach is presented to estimating a general set of interdependent matrices defined to within separate scales. The input data is assumed to consist of individually estimated matrices for particular models, which when considered collectively may fail to satisfy the constraints representing the inter-model relationships. Two cost functions are proposed for upgrading, via optimisation, the data of this sort to a collection of matrices satisfying the intermodel constraints. One of these functions incorporates error covariances. Each function is invariant to any change of scale for the input estimates. The proposed approach is applied to the particular problem of estimating a set of fundamental matrices of the form of the example set above. Experimental results are given which demonstrate the effectiveness of the approach.

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High Accuracy Fundamental Matrix Computation and Its Performance Evaluation

Cited by 15 publications

References 11 publications

Leveraging Feature Uncertainty in the PnP Problem

Leveraging Feature Uncertainty in the PnP Problem

Simple, Fast and Accurate Estimation of the Fundamental Matrix Using the Extended Eight-Point Schemes

Multi-projective Parameter Estimation for Sets of Homogeneous Matrices

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