The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix

@article{Torr2004TheDA,
  title={The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix},
  author={Philip H. S. Torr and David William Murray},
  journal={International Journal of Computer Vision},
  year={2004},
  volume={24},
  pages={271-300}
}
  • P. Torr, D. W. Murray
  • Published 21 September 1997
  • Computer Science
  • International Journal of Computer Vision
This paper has two goals. The first is to develop a variety of robust methods for the computation of the Fundamental Matrix, the calibration-free representation of camera motion. The methods are drawn from the principal categories of robust estimators, viz. case deletion diagnostics, M-estimators and random sampling, and the paper develops the theory required to apply them to non-linear orthogonal regression problems. Although a considerable amount of interest has focussed on the application of… 

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References

SHOWING 1-10 OF 65 REFERENCES

Robust methods for estimating pose and a sensitivity analysis

TLDR
It is shown that for small field of view systems, offsets in the image center do not significantly affect the location of the camera in a world coordinate system, and errors in the focal length significantly affect only the component of translation along the optical axis in the pose computation.

Robust detection of degenerate configurations for the fundamental matrix

TLDR
It is demonstrated that proper modelling of degeneracy in the presence of outlier enables the detection of outliers which would otherwise be missed.

On determining the fundamental matrix : analysis of different methods and experimental results

TLDR
This paper defines precisely this matrix and shows clearly how it is related to the epipolar geometry and to the essential matrix introduced earlier by Longuet-Higgins, and shows that this matrix, defined up to a scale factor, must be of rank two.

Robust regression methods for computer vision: A review

TLDR
The least-median-of-squares (LMedS) method, which yields the correct result even when half of the data is severely corrupted, is described and compared with the class of robust M-estimators.

Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation

TLDR
The presented approach to error estimation applies to a wide variety of problems that involve least-squares optimization or pseudoinverse and shows, among other things, that the errors are very sensitive to the translation direction and the range of field view.

Outlier detection and motion segmentation

We present a new method for solving the problem of motion segmentation, identifying the objects within an image moving independently of the background. We utilize the fact that two views of a static

A multi-frame approach to visual motion perception

TLDR
This paper presents an algorithm based on multiple frames that employs only the rigidity assumption, is simple and mathematically elegant and, experimentally, proves to be a major improvement over the two-frame algorithms.

A computer algorithm for reconstructing a scene from two projections

A simple algorithm for computing the three-dimensional structure of a scene from a correlated pair of perspective projections is described here, when the spatial relationship between the two

Optimal motion and structure estimation

  • J. WengN. AhujaThomas S. Huang
  • Computer Science
    Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition
  • 1989
TLDR
The authors present approaches to estimatingerrors in the optimal solutions, investigate the theoretical lower bounds on the errors in the solutions and compare them with actual errors, and analyze two types of algorithms of optimization: batch and sequential.
...