Why not use the Levenberg–Marquardt method for fundamental matrix estimation?

Chen, P.

doi:10.1049/iet-cvi.2009.0146

Cited by 11 publications

(9 citation statements)

References 14 publications

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“…where Á jjis the determinant. Formula (17) gives the so called identifiability condition, that is, if the determinant of J T J is zero, or even very small, the parameters p j , for j ¼ 1, 2, ⋯,mþ 1, cannot be determined by using the iterative procedure of Eq. 16.…”

Section: Overview Of the Levenberg-marquardt Methodsmentioning

confidence: 99%

“…In this work, we propose an algorithm for numerical solving an inverse heat conduction problem. The algorithm is based on the Galerkin finite element method and Levenberg-Marquardt algorithm [16][17] in conjunction with the least-squares scheme. It is assumed that no prior information is available on the functional form of the unknown diffusion coefficient in the present study, thus, it is classified as the function estimation in inverse calculation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Numerical Approach to Solving an Inverse Heat Conduction Problem Using the Levenberg-Marquardt Algorithm

Tao¹,

Chen²,

Sun³

et al. 2020

Inverse Heat Conduction and Heat Exchangers

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This chapter is intended to provide a numerical algorithm involving the combined use of the Levenberg-Marquardt algorithm and the Galerkin finite element method for estimating the diffusion coefficient in an inverse heat conduction problem (IHCP). In the present study, the functional form of the diffusion coefficient is an unknown priori. The unknown diffusion coefficient is approximated by the polynomial form and the present numerical algorithm is employed to find the solution. Numerical experiments are presented to show the efficiency of the proposed method.

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Section: Overview Of the Levenberg-marquardt Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Numerical Approach to Solving an Inverse Heat Conduction Problem Using the Levenberg-Marquardt Algorithm

Tao¹,

Chen²,

Sun³

et al. 2020

Inverse Heat Conduction and Heat Exchangers

View full text Add to dashboard Cite

show abstract

“…The parameter is then gradually reduced as the iteration procedure advances to the solution of the parameter estimation problem, and then the Levenberg-Marquardt method tends to the Gauss method given by (15). The following criteria were suggested in literature [13] to stop the iterative procedure of the Levenberg-Marquardt method given by (17):…”

Section: Overview Of the Levenberg-marquardt Methodsmentioning

confidence: 99%

“…In this work, we propose an algorithm for numerical solving of an inverse heat conduction problem. The algorithm is based on the Galerkin finite element method and Levenberg-Marquardt algorithm [16,17] in conjunction with the leastsquares scheme. It is assumed that no prior information is available on the functional form of the unknown diffusion coefficient in the present study; thus, it is classified as the function estimation in inverse calculation.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Approach to Solving an Inverse Heat Conduction Problem Using the Levenberg‐Marquardt Algorithm

Tao¹,

Chen²,

Sun

et al. 2014

Mathematical Problems in Engineering

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This paper is intended to provide a numerical algorithm involving the combined use of the Levenberg-Marquardt algorithm and the Galerkin finite element method for estimating the diffusion coefficient in an inverse heat conduction problem (IHCP). In the present study, the functional form of the diffusion coefficient is unknown a priori. The unknown diffusion coefficient is approximated by the polynomial form and the present numerical algorithm is employed to find the solution. Numerical experiments are presented to show the efficiency of the proposed method.

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“…t(14) is called the moment matrix of order t of y. By construction, this matrix is symmetric and linear in y.…”

mentioning

confidence: 99%

Rank-Constrained Fundamental Matrix Estimation by Polynomial Global Optimization Versus the Eight-Point Algorithm

et al. 2014

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The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eight-point algorithm and two-view projective bundle adjustment. The eight-point algorithm first computes a simple linear least squares solution by minimizing an algebraic cost and then projects the result to the closest rank-deficient matrix. We propose a single-step method that solves both steps of the eight-point algorithm. Using recent results from polynomial global optimization, our method finds the rank-deficient matrix that exactly minimizes the algebraic cost. In this special case, the optimization method is reduced to the resolution of very short sequences of convex linear problems which are computationally efficient and numerically stable. The current gold standard is known to be extremely effective but is nonetheless outperformed by our rank-constrained method for bootstrapping bundle adjustment. This is here demonstrated on simulated and standard real datasets. With our initialization, bundle adjustment consistently finds a better local minimum (achieves a lower reprojection error) and takes less iterations to converge.

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Why not use the Levenberg–Marquardt method for fundamental matrix estimation?

Cited by 11 publications

References 14 publications

A Numerical Approach to Solving an Inverse Heat Conduction Problem Using the Levenberg-Marquardt Algorithm

A Numerical Approach to Solving an Inverse Heat Conduction Problem Using the Levenberg-Marquardt Algorithm

A Numerical Approach to Solving an Inverse Heat Conduction Problem Using the Levenberg‐Marquardt Algorithm

Rank-Constrained Fundamental Matrix Estimation by Polynomial Global Optimization Versus the Eight-Point Algorithm

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