# On the Estimation of the Fundamental Matrix: A Convex Approach to Constrained Least-Squares

@inproceedings{Chesi2000OnTE, title={On the Estimation of the Fundamental Matrix: A Convex Approach to Constrained Least-Squares}, author={Graziano Chesi and Andrea Garulli and Antonio Vicino and Roberto Cipolla}, booktitle={ECCV}, year={2000} }

In this paper we consider the problem of estimating the fundamental matrix from point correspondences. It is well known that the most accurate estimates of this matrix are obtained by criteria minimizing geometric errors when the data are affected by noise. It is also well known that these criteria amount to solving non-convex optimization problems and, hence, their solution is affected by the optimization starting point. Generally, the starting point is chosen as the fundamental matrix…

## 9 Citations

### Solving quadratic distance problems: an LMI-based approach

- MathematicsIEEE Trans. Autom. Control.
- 2003

A general framework in which some classes of minimum distance problems are tackled via linear matrix inequality (LMI) techniques, providing both a simple algorithmic procedure for a posteriori optimality testing and a structural condition on the related homogeneous form that ensures optimality a priori.

### LMI-based techniques for solving quadratic distance problems

- MathematicsProceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)
- 2001

A general framework in which some classes of minimum distance problems are tackled via LMI techniques is presented, providing both a simple algorithmic procedure for a posteriori optimality testing and a structural condition on the related homogeneous form that ensures optimality a priori.

### Calculation of the Location Coordinates of an Object Observed by a Camera

- Computer ScienceICMMI
- 2013

This algorithm is more accurate and faster than the algorithms presented in the literature based on the minimization of the quadratic forms of errors and makes it possible for the robot to automatically approach the object and carry out the technological operations.

### Interpolation Method of 3D Position Errors Decreasing in the System of Two Cameras

- PhysicsICMMI
- 2015

This chapter proposes the method of 3D position errors decreasing in the system of two cameras using the interpolation of errors between ideal and real coordinates of image points.

### The Decreasing of 3D Position Errors in the System of Two Cameras by Means of the Interpolation Method

- PhysicsICIRA
- 2015

The analysis of accuracy of determining the 3D coordinates of points on the plane template in the shape of rectangle is presented and the interpolation of the real coordinates of image points was used.

### Accuracy of Determining the Coordinates of Points Observed by Camera

- PhysicsICIRA
- 2014

Analysis of accuracy of determining the coordinates of points on the plane template in the shape of rectangle using Edimax IC-7100P camera from three different points of view is presented.

### The Algorithm Camera Computing the Object Location

- Computer ScienceICIRA
- 2013

The algorithm Camera of calculation of the position and orientation coordinates of the object observed by the camera is presented and allows the robot to automatically approach the object and carry out technological operations.

### A Visual Servoing Techinique based on Epipoles Motion Estimation

- Physics
- 2002

A new image-based visual servoing, based on the epipolar geometry, is presented. The estimation of the epipoles position, obtained by points correspondences extracted from two different images,…

### Neural Computation of the Fundamental Matrix

- MathematicsICAISC
- 2004

A neural approach to the computation of the fundamental matrix is proposed and the special configuration of the back-propagation neural network was developed and both, linear and non-linear versions are also discussed.

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