# Estimating the Fundamental Matrix Using Second-Order Cone Programming

@inproceedings{Yang2011EstimatingTF, title={Estimating the Fundamental Matrix Using Second-Order Cone Programming}, author={Min Yang}, booktitle={AICI}, year={2011} }

Computing the fundamental matrix is the first step of many computer vision applications including camera calibration, image rectification and structure from motion. A new method for the estimation of the fundamental matrix from point correspondences is presented. The minimization of the geometric error is performed based L- infinity norm minimization framework. A single global minimum exists and it may be found by SOCP (Second-Order Cone Programming), which is a standard technique in convex…

## References

SHOWING 1-10 OF 18 REFERENCES

### Estimating the Fundamental Matrix via Constrained Least-Squares: A Convex Approach

- Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 2002

The obtained estimate of the fundamental matrix turns out to be more accurate than the one provided by the linear criterion, where the rank constraint of the matrix is imposed after its computation by setting the smallest singular value to zero.

### Multiple View Geometry and the -norm

- Computer Science, Mathematics
- 2005

It is shown that a variety of structure and motion problems, for example, triangulation, camera resectioning and homography estimation can be recast as a quasi-convex optimization problem within this framework.

### Quasiconvex Optimization for Robust Geometric Reconstruction

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2007

This paper presents a novel quasiconvex optimization framework in which the geometric reconstruction problems are formulated as a small number of small-scale convex programs that are readily solvable and provides an intuitive method to handle directional uncertainties and outliers in measurements.

### In Defense of the Eight-Point Algorithm

- Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 1997

This paper shows that by preceding the eight-point algorithm with a very simple normalization (translation and scaling) of the coordinates of the matched points, results are obtained comparable with the best iterative algorithms.

### Multiple view geometry and the L/sub /spl infin//-norm

- Computer ScienceTenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1
- 2005

It is shown that a variety of structure and motion problems, for example, triangulation, camera resectioning and homography estimation can be recast as a quasiconvex optimization problem within this framework.

### In defence of the 8-point algorithm

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

By preceding the 8 point algorithm with a very simple normalization (translation and scaling) of the coordinates of the matched points, results are obtained comparable with the best iterative algorithms.

### A new constrained parameter estimator for computer vision applications

- Computer ScienceImage Vis. Comput.
- 2004

### On the Optimization Criteria Used in Two-View Motion Analysis

- MathematicsIEEE Trans. Pattern Anal. Mach. Intell.
- 1998

The author shows that, given a reasonable initial guess of the epipolar geometry, the last two criteria are equivalent when the epipoles are at infinity, and differ from each other only a little even when the Epiphany is in the image, as shown experimentally.

### L/sub /spl infin// minimization in geometric reconstruction problems

- MathematicsProceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004.
- 2004

We investigate the use of the L/sub /spl infin// cost function in geometric vision problems. This cost function measures the maximum of a set of model-fitting errors, rather than the sum-of-squares,…

### Applications of Second Order Cone Programming

- Computer Science
- 2012

A significant special case of the problems which could be solved were those whose constraints were given by semidefinite cones, and these have a wide range of applications, some of which are discussed in Section 5, and can still be solved efficiently using interior point methods.