# 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} }

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…

## 747 Citations

### New approach to calculating the fundamental matrix

- Mathematics
- 2020

The estimation of the fundamental matrix (F) is to determine the epipolar geometry and to establish a geometrical relation between two images of the same scene or elaborate video frames. In the…

### Robust Self-Calibration and Fundamental Matrix Estimation in 3D Computer Vision

- Computer Science
- 2013

Three robust algorithms have been proposed that utilize existing constraints for self-calibration from the fundamental matrix and are less affected by noise than existing algorithms based on these constraints.

### Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint

- Computer ScienceInternational Journal of Computer Vision
- 2004

An algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise, i.e., each data point having a different covariance matrix, achieves the accuracy of nonlinear optimization techniques at much less computational cost.

### An approach for estimating the fundamental matrix

- Computer Science2011 6th Colombian Computing Congress (CCC)
- 2011

A method for estimating the fundamental matrix is introduced using subsets of corresponding points and an optimisation criterion is used to select the best estimated fundamental matrix.

### Random sampling methods for two-view geometry estimation

- Computer Science
- 2007

This thesis treats efficient estimation algorithms for the epipolar geometry, the model underlying two views of the same scene or object, by investigating techniques for faster fundamental matrix estimation using RANSAC.

### Efficient image features selection and weighting for fundamental matrix estimation

- Computer ScienceIET Comput. Vis.
- 2016

The authors introduce how to find matched features from scene images efficiently and moderately improves the weighting function based on M-estimator to increase the accuracy of the fundamental matrix estimation.

### Fusing appearance and geometric constraints for estimating the epipolar geometry

- Computer Science2013 IEEE Workshop on Applications of Computer Vision (WACV)
- 2013

This paper presents a robust method for estimating the fundamental matrix based on all image features, and not only matching points, by selecting the best correspondent keypoints between views through a proper weighting function that fuses local appearance of keypoints and distance to the epipolar lines.

### A method for the evaluation of projective geometric consistency in weakly calibrated stereo with application to point matching

- Computer ScienceComput. Vis. Image Underst.
- 2014

### Is Dense Optic Flow Useful to Compute the Fundamental Matrix?

- Computer ScienceICIAR
- 2008

This paper considers the state-of-the-art optic flow method of Brox et al. (ECCV 2004) and compares the results computed from its dense flow fields to the ones estimated from a RANSAC method that is based on a sparse set of SIFT-matches.

### Error Assessment of Fundamental Matrix Parameters

- MathematicsLecture Notes in Electrical Engineering
- 2018

A performance analysis of widely adopted matrix estimators over the point pairs found by correspondence determiners is undertaken, and RAndom RANSAC and M-estimator SAmple Consensus (MSAC) estimators were found to produce the best results over the features detected by the Harris–Stephens corner detector.

## References

SHOWING 1-10 OF 65 REFERENCES

### Robust methods for estimating pose and a sensitivity analysis

- Computer Science
- 1994

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

- Computer ScienceProceedings of IEEE International Conference on Computer Vision
- 1995

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

- Computer Science
- 1993

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

- Computer ScienceInternational Journal of Computer Vision
- 2004

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.

### A Robust Technique for Matching two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry

- Computer ScienceArtif. Intell.
- 1995

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

- Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 1989

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

- MathematicsOther Conferences
- 1993

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

- Computer ScienceInternational Journal of Computer Vision
- 2004

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

- MathematicsNature
- 1981

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

- Computer ScienceProceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition
- 1989

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.