Essential matrix from fundamental matrix

1. What is the relation between essential and fundamental matrix?
2. What do you do with fundamental matrix?
3. What does the essential matrix depend on?

What is the relation between essential and fundamental 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.

What do you do with fundamental matrix?

The Essential Matrix can be used to get the rotation (rotation matrix R) and translation (vector t) of your second image in comparison to your first image only up to a projective reconstruction.

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.