High Accuracy Computation of Rank-Constrained Fundamental Matrix

Sugaya, Yasuyuki; Kanatani, Kenichi

doi:10.5244/c.21.19

Cited by 14 publications

(12 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bartoli and Sturm 1) regarded the SVD of the fundamental matrix as its parameterization and did search in an augmented space. Sugaya and Kanatani 19) directly searched a 7-D space by the Levenberg-Marquardt (LM) method. External access.…”

Section: Introductionmentioning

confidence: 99%

Compact Fundamental Matrix Computation

Kanatani

Sugaya

2010

IPSJ Transactions on Computer Vision and Applications

View full text Add to dashboard Cite

A very compact algorithm is presented for fundamental matrix computation from point correspondences over two images. The computation is based on the maximum likelihood (ML) principle, minimizing the reprojection error. The rank constraint is incorporated by the EFNS procedure. Although our algorithm produces the same solution as all existing ML-based methods, it is probably the most practical of all, being small and simple. By numerical experiments, we confirm that our algorithm behaves as expected.

show abstract

Section: Introductionmentioning

confidence: 99%

Compact Fundamental Matrix Computation

Kanatani

Sugaya

2010

IPSJ Transactions on Computer Vision and Applications

View full text Add to dashboard Cite

show abstract

“…On the other hand, the second type of methods considers the rank constraint explicitly. In [16] a Levenberg-Marquard (LM) approach is proposed to optimize the singular value decomposition (SVD) of the fundamental matrix. In [20] and [1] the rank constraint is imposed by setting its determinant to 0, leading to a 3rd-order polynomial constraint.…”

Section: Introductionmentioning

confidence: 99%

A convex optimization approach to robust fundamental matrix estimation

Cheng

López

Camps

et al. 2015

2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

View full text Add to dashboard Cite

This paper considers the problem of estimating the fundamental matrix from corrupted point correspondences. A general nonconvex framework is proposed that explicitly takes into account the rank-2 constraint on the fundamental matrix and the presence of noise and outliers. The main result of the paper shows that this non-convex problem can be solved by solving a sequence of convex semi-definite programs, obtained by exploiting a combination of polynomial optimization tools and rank minimization techniques. Further, the algorithm can be easily extended to handle the case where only some of the correspondences are labeled, and, to exploit co-ocurrence information, if available. Consistent experiments show that the proposed method works well, even in scenarios characterized by a very high percentage of outliers.

show abstract

“…Examples of parametric models with both principal and ancillary constraint vectors include the stereo and motion problems of estimating the fundamental matrix [3,23], flow fundamental matrix [12], and coefficients of the differential epipolar equation [2], conic fitting problems [10,14,15], and multiple-view structure from motion problems with estimation of trifocal and quadrifocal tensors [5][6][7]22]. A maximum likelihood (ML) estimate of θ which meets both criteria (1) and (2) simultaneously does not generally lend itself to explicit calculation.…”

Section: Introductionmentioning

confidence: 99%

Post-hoc Correction Techniques for Constrained Parameter Estimation in Computer Vision

Scoleri

2008

2008 Digital Image Computing: Techniques and Applications

View full text Add to dashboard Cite

We consider the task of estimating constrained parameters of geometric models which underpin an important class of computer vision problems. A typical model can often be described by two systems of equations, of which one relates image features to parameters, and the other captures internal relationships between the parameters. One way to produce constrained parameters is to first compute an unconstrained estimate by means of the image data and then correct this estimate so that the intra-parameter dependencies are satisfied. This paper focuses on the second stage of estimation and proposes two correction methods applicable to the result of unconstrained minimisation. The performance of the post-hoc correction techniques is evaluated through experiments on estimating the trifocal tensor relating three views of a scene. Results demonstrate that the devised constrained estimators achieve similar accuracy to the maximum likelihood estimator with the advantage of being faster.

show abstract

High Accuracy Computation of Rank-Constrained Fundamental Matrix

Cited by 14 publications

References 14 publications

Compact Fundamental Matrix Computation

Compact Fundamental Matrix Computation

A convex optimization approach to robust fundamental matrix estimation

Post-hoc Correction Techniques for Constrained Parameter Estimation in Computer Vision

Contact Info

Product

Resources

About