Fundamental matrix rank

The fundamental matrix is of rank 2. Its kernel defines the epipole.

1. Why is the rank of the fundamental matrix only 2?
2. Why does fundamental matrix have 7 degrees of freedom?
3. How do you calculate the fundamental matrix?
4. What is the difference between fundamental and essential matrix?

Why is the rank of the fundamental matrix only 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).

Why does fundamental matrix have 7 degrees of freedom?

The reason is that fundamental matrix has only seven degrees of freedom since it is defined up to a scale and det(F)=0 d e t ( F ) = 0 .

How do you calculate the fundamental matrix?

The fundamental matrix F may be written as F = [e′]×Hπ, where Hπ is the transfer mapping from one image to another via any plane π.

What is the difference between fundamental and essential matrix?

Thus both the Essential and Fundamental matrices completely describe the geometric relationship between corresponding points of a stereo pair of cameras. The only difference between the two is that the former deals with calibrated cameras, while the latter deals with uncalibrated cameras.