Table of Contents

## What is epipolar plane?

The epipolar plane is the plane defined by a 3D point M and the optical centres C and C’. The epipolar line is the straight line of intersection of the epipolar plane with the image plane. It is the image in one camera of a ray through the optical centre and image point in the other camera.

**How do you find the epipolar line?**

Similar to the Essential matrix, we can compute the epipolar lines l = FT p and l = Fp from just the Fundamental matrix and the corresponding points.

**What is fundamental matrix Opencv?**

In simple words, Fundamental Matrix F, maps a point in one image to a line (epiline) in the other image. This is calculated from matching points from both the images. A minimum of 8 such points are required to find the fundamental matrix (while using 8-point algorithm).

### What does it mean when your epipolar lines are all horizontal across the two images?

Furthermore, the epipolar lines are parallel to the line OL–OR between the centers of projection, and can in practice be aligned with the horizontal axes of the two images. This means that for each point in one image, its corresponding point in the other image can be found by looking only along a horizontal line.

**What is epipolar error?**

Epipolar errors: For two cameras arranged in stereo a point in one camera view must fall along a line in a second camera view. This line is that point’s epipolar line. The distance between a point’s epipolar line and its corresponding point in that second camera view is the epipolar error.

**What is epipolar resampling?**

Epipolar resampling is the procedure of eliminating vertical disparity between stereo images. Due to its importance, many methods have been developed in the computer vision and photogrammetry field.

#### Do epipolar lines need to converge?

If the image planes are aligned and their optical axes are parallel, the two epipolar lines (left and right) converge. In such a case, correspondent pixels rely on the same epipolar line in both images, which simplifies the matching process.

**What do you do with fundamental matrix?**

With your fundamental matrix, you can determine the camera matrices P and P’ in a canonical form as stated (HZ,pp254-256). From these camera matrices you can theoretically triangulate a projective reconstruction that differs to the real scene in terms of an unknown projective transformation.

**Why is the epipolar constraint useful?**

The epipolar constraint is one of the fundamental relations in multi-view geometry because it allows the estimation of the 3D coordinates of point p from its images x1 and x2, given R and T. That is, it allows scene geometry reconstruction.

## What are epipolar images?

Epipolar images are stereo pairs in which the left and right images are oriented in such a way that ground feature points have the same y-coordinates on both images.

**Can epipolar lines be parallel?**

Epipolar lines form a bundle of parallel lines in both images. Any pair of images can be transformed so that epipolar lines are parallel and horizontal in each image as in Fig. 3.