An Alternative Formulation for Five Point Relative Pose Problem

Batra, Dhruv; Nabbe, Bart; Hebert, Martial

doi:10.1109/wmvc.2007.6

Cited by 29 publications

(24 citation statements)

References 9 publications

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“…Batra et al [13] avoid working on a manifold explicitly and instead use a constrained optimisation toolbox to solve a set of polynomials similar to Equation 4, subject to a nonlinear constraint on the parameters. The method is demonstrated to find solutions to the 5-point problem from random starting points, but is not computationally efficient.…”

Section: Gradient-descent Methods For Computing Ementioning

confidence: 99%

Fast RANSAC Hypothesis Generation for Essential Matrix Estimation

Botterill

Mills²,

Green

2011

2011 International Conference on Digital Image Computing: Techniques and Applications

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Abstract-The RANSAC framework is often used to estimate the relative pose of two cameras from outlier-contaminated point correspondences, via the essential matrix, however this is computationally expensive due the cost of computing essential matrices from many sets of five to seven correspondences. The leading contemporary 5-point solver (Nister, 2004) is slow because of the expensive linear algebra decompositions and polynomial solve which are required. To avoid these costs we propose to use Levenberg-Marquardt optimisation on a manifold to find a subset of the compatible essential matrices. The proposed algorithm finds essential matrices at a higher rate than closedform approaches, and reduces the time needed to find relative poses using RANSAC by 25%.The second contribution of this paper is to apply the optimisations used in 5-point solvers to the classic 7-point algorithm. RANSAC using the optimised 7-point algorithm is considerably faster than 5-point RANSAC (unless planar point configurations are common), despite the increased number of iterations necessary.

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Section: Gradient-descent Methods For Computing Ementioning

confidence: 99%

Fast RANSAC Hypothesis Generation for Essential Matrix Estimation

Botterill

Mills²,

Green

2011

2011 International Conference on Digital Image Computing: Techniques and Applications

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“…Batra et al [1] estimated the essential matrix and translation vector simultaneously as a constrained optimization problem. Naroditsky et al [12] introduced the 3-plus-1 algorithm, which uses 3 point correspondences and 1 directional correspondence to solve the relative pose problem.…”

Section: Related Workmentioning

confidence: 99%

“…Although direct solvers offer a closed-form solution, the use of high degree polynomials may lead to ill-conditioning and they are difficult to solve [1]. Iterative solvers, on the other hand, are numerically stable.…”

Section: Introductionmentioning

confidence: 99%

An Iterative 5-pt Algorithm for Fast and Robust Essential Matrix Estimation

Lui¹,

Drummond²

2013

Procedings of the British Machine Vision Conference 2013

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This paper presents a novel algorithm for calculating epipolar geometry from 5 correspondences. The algorithm directly solves for the orientation of each camera relative to the baseline that separates them and is able to impose the half plane constraints that arise from the requirement that visible landmarks must be in front of both cameras. The algorithm is conceptually simple, and provides numerically stable solutions that are used as a hypothesis generator within RANSAC. It is significantly faster than existing methods and is comfortably able to provide frame-rate performance on real data.

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“…Another type of five point algorithm is a non-linear solver (Batra et al, 2007), where translation vector and the four scalar multipliers are solved with non-linear minimization.…”

Section: Introductionmentioning

confidence: 99%

Quasi-five point algorithm with non-linear minimization

Oda¹

2014

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:Five-point algorithm is a powerful tool for relative orientation, because it requires no initial assumption of camera position. This algorithm determines an essential matrix from five point correspondences between two calibrated cameras, but results multiple solutions and some selecting process is required. This paper proposes Quasi-Five-Point Algorithm which is non-linear solver with seed solution of 8 point algorithm. The method tries to calculate the appropriate essential matrix without selecting process among multiple solutions. It is one of non-linear approach, but tries to find an appropriate seed before non-linear calculation. Using correspondences of 3 or more additional points, seed values of the solution is calculated. In this paper relationship between traditional parametric relative orientation and essential matrix is discussed, and after that quasi-five-point algorithm is introduced.

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An Alternative Formulation for Five Point Relative Pose Problem

Cited by 29 publications

References 9 publications

Fast RANSAC Hypothesis Generation for Essential Matrix Estimation

Fast RANSAC Hypothesis Generation for Essential Matrix Estimation

An Iterative 5-pt Algorithm for Fast and Robust Essential Matrix Estimation

Quasi-five point algorithm with non-linear minimization

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