Essential Matrix from line correspondences

1. What is the linear algorithm to find the essential matrix?
2. What does the essential matrix depend on?
3. How many points does it take to estimate an essential matrix?
4. Why is essential matrix rank 2?

What is the linear algorithm to find the essential matrix?

The eight-point algorithm is an algorithm used in computer vision to estimate the essential matrix or the fundamental matrix related to a stereo camera pair from a set of corresponding image points. It was introduced by Christopher Longuet-Higgins in 1981 for the case of the essential matrix.

What does the essential matrix depend on?

It depends on the application which position is the more relevant. Here, the last equation is a matrix constraint, which can be seen as 9 constraints, one for each matrix element. These constraints are often used for determining the essential matrix from five corresponding point pairs.

How many points does it take to estimate an essential matrix?

Unlike a homography, where each point correspondence contributes two constraints (rows in the linear system of equations), for estimating the essential/fundamental matrix, each point only contributes one constraint (row). [because the Longuet-Higgins / Epipolar constraint is a scalar eqn.] Thus need at least 8 points.

Why is essential matrix rank 2?

The reason why F is a matrix with rank 2 is that it is mapping a 2D plane (image1) to all the lines (in image 2) that pass through the epipole (of image 2).