EPIPOLAR GEOMETRY WITH A FUNDAMENTAL MATRIX IN CANONICAL FORM

In this paper, firstly we try to look for ways to avoid the camera parameters in order to reconstruct 3D model. We attempt to use the parallel stereo visual system and carry out the mathematical derivation of argumentation. Then we use epipolar geometry to solve this problem. And compare the computation algorithms of fundamental matrix. Then for the algorithm, we propose some improvement to compute the fundament matrix more precisely so that the algorithm is more stable and the robustness is stronger.

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A Stable and Accurate Algorithm for Computing Epipolar Geometry

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001498000452 ◽

1998 ◽

Vol 12 (06) ◽

pp. 817-840 ◽

Cited By ~ 10

Author(s):

Boubakeur S. Boufama ◽

Roger Mohr

Keyword(s):

Fundamental Matrix ◽

Feature Tracking ◽

Epipolar Geometry ◽

Form Solution ◽

Central Importance ◽

Novel Method ◽

3D Information ◽

Close Form ◽

Simple Equations ◽

Geometric Relationship

This paper addresses the problem of computing the fundamental matrix which describes a geometric relationship between a pair of stereo images: the epipolar geometry. In the uncalibrated case, epipolar geometry captures all the 3D information available from the scene. It is of central importance for problems such as 3D reconstruction, self-calibration and feature tracking. Hence, the computation of the fundamental matrix is of great interest. The existing classical methods14 use two steps: a linear step followed by a nonlinear one. However, in some cases, the linear step does not yield a close form solution for the fundamental matrix, resulting in more iterations for the nonlinear step which is not guaranteed to converge to the correct solution. In this paper, a novel method based on virtual parallax is proposed. The problem is formulated differently; instead of computing directly the 3 × 3 fundamental matrix, we compute a homography with one epipole position, and show that this is equivalent to computing the fundamental matrix. Simple equations are derived by reducing the number of parameters to estimate. As a consequence, we obtain an accurate fundamental matrix with a stable linear computation. Experiments with simulated and real images validate our method and clearly show the improvement over the classical 8-point method.

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A GA-BASED APPROACH FOR EPIPOLAR GEOMETRY ESTIMATION

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001413550148 ◽

2013 ◽

Vol 27 (08) ◽

pp. 1355014 ◽

Cited By ~ 3

Author(s):

NEHAL KHALED ◽

ELSAYED E. HEMAYED ◽

MAGDA B. FAYEK

Keyword(s):

Genetic Algorithm ◽

Fundamental Matrix ◽

Real Data ◽

Epipolar Geometry ◽

Optimum Estimation ◽

Geometry Estimation

In this paper, a genetic algorithm (GA)-based approach to estimate the fundamental matrix is presented. The aim of the proposed GA-based algorithm is to reduce the effect of noise and outliers in the corresponding points which affect the accuracy of the estimated fundamental matrix. Although in the proposed approach the GA is allowed to select the significant among all detected points, on the average half of the matched points have been determined to give optimum estimation of the fundamental matrix. Experiments with synthetic and real data show that the proposed approach is accurate especially in the presence of a high percentage of outliers. The proposed GA can always obtain good results in both high and low detailed images. Even for low detailed images which have a small number of matched points available to estimate the fundamental matrix, the proposed GA outperformed other methods.

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PARTICLE SWARM OPTIMIZATION BASED APPROACH TO ESTIMATE EPIPOLAR GEOMETRY FOR REMOTELY SENSED STEREO IMAGES

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xlii-5-85-2018 ◽

2018 ◽

Vol XLII-5 ◽

pp. 85-89

Author(s):

M. Mahato ◽

S. Gedam

Keyword(s):

Particle Swarm Optimization ◽

Fundamental Matrix ◽

Particle Swarm ◽

Epipolar Geometry ◽

Remotely Sensed ◽

Stereo Image ◽

Stereo Images ◽

Swarm Optimization ◽

Validation Tool ◽

Ransac Algorithm

Abstract. A novel particle swarm optimization based approach for the estimation of epipolar geometry for remotely sensed images is proposed and implemented in this work. In stereo vision, epipolar geometry is described using 3&times;3 fundamental matrix and is used as a validation tool to assess the accuracy of the stereo correspondences. The validation is performed by enforcing the geometrical constraint of stereo images on the two perspective projections of a point in the scene for finding inliers. In the proposed method, the steps of particle swarm optimization such as the initialization of the position and velocity of the particles, the objective function to compute the best position found by the swarm as well as by each particle experienced so far, the updating rule of velocity for the improvement of the position of each particle, is designed and implemented to estimate the fundamental matrix. To demonstrate the effectiveness of the proposed approach, the results are obtained on a pair of remotely sensed stereo image. A comparison of the result obtained using the proposed algorithm with RANSAC algorithm is carried out. The comparison shows that, the proposed method is effective to estimate robust fundamental matrix by giving improved number of inliers than RANSAC.

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A EUCLIDEAN FORMULATION OF INTERIOR ORIENTATION COSTRAINTS IMPOSED BY THE FUNDAMENTAL MATRIX

ISPRS Annals of Photogrammetry Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-annals-iii-3-75-2016 ◽

2016 ◽

Vol III-3 ◽

pp. 75-82

Author(s):

I. Kalisperakis ◽

G. Karras ◽

E. Petsa

Keyword(s):

Computer Vision ◽

Fundamental Matrix ◽

Projective Transformation ◽

Epipolar Geometry ◽

Relative Orientation ◽

The Other ◽

Principal Point ◽

First Case ◽

Optical Axes ◽

Image Planes

Epipolar geometry of a stereopair can be expressed either in 3D, as the relative orientation (i.e. translation and rotation) of two bundles of optical rays in case of calibrated cameras or, in case of unclalibrated cameras, in 2D as the position of the epipoles on the image planes and a projective transformation that maps points in one image to corresponding epipolar lines on the other. The typical coplanarity equation describes the first case; the Fundamental matrix describes the second. It has also been proven in the Computer Vision literature that 2D epipolar geometry imposes two independent constraints on the parameters of camera interior orientation. In this contribution these constraints are expressed directly in 3D Euclidean space by imposing the equality of the dihedral angle of epipolar planes defined by the optical axes of the two cameras or by suitably chosen corresponding epipolar lines. By means of these constraints, new closed form algorithms are proposed for the estimation of a variable or common camera constant value given the fundamental matrix and the principal point position of a stereopair.

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A EUCLIDEAN FORMULATION OF INTERIOR ORIENTATION COSTRAINTS IMPOSED BY THE FUNDAMENTAL MATRIX

ISPRS Annals of Photogrammetry Remote Sensing and Spatial Information Sciences ◽

10.5194/isprsannals-iii-3-75-2016 ◽

2016 ◽

Vol III-3 ◽

pp. 75-82

Author(s):

I. Kalisperakis ◽

G. Karras ◽

E. Petsa

Keyword(s):

Computer Vision ◽

Fundamental Matrix ◽

Projective Transformation ◽

Epipolar Geometry ◽

Relative Orientation ◽

The Other ◽

Principal Point ◽

First Case ◽

Optical Axes ◽

Image Planes

Epipolar geometry of a stereopair can be expressed either in 3D, as the relative orientation (i.e. translation and rotation) of two bundles of optical rays in case of calibrated cameras or, in case of unclalibrated cameras, in 2D as the position of the epipoles on the image planes and a projective transformation that maps points in one image to corresponding epipolar lines on the other. The typical coplanarity equation describes the first case; the Fundamental matrix describes the second. It has also been proven in the Computer Vision literature that 2D epipolar geometry imposes two independent constraints on the parameters of camera interior orientation. In this contribution these constraints are expressed directly in 3D Euclidean space by imposing the equality of the dihedral angle of epipolar planes defined by the optical axes of the two cameras or by suitably chosen corresponding epipolar lines. By means of these constraints, new closed form algorithms are proposed for the estimation of a variable or common camera constant value given the fundamental matrix and the principal point position of a stereopair.

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