Homography derivation

1. How is homography calculated?
2. What is a homography?
3. Why do we need 4 points for homography?
4. What is 2D homography?

How is homography calculated?

Thus, homography can be calculated using relative rotation and translation between two cameras.

What is a homography?

Homography, also referred to as planar homography, is a transformation that is occurring between two planes. In other words, it is a mapping between two planar projections of an image. It is represented by a 3x3 transformation matrix in a homogenous coordinates space.

Why do we need 4 points for homography?

In fact, we need at least 4 points, because the homography matrix has 8 free variables (each point contains and x and a y, for a total of 8 equations). To make the homography more stable, we can utilize more points and derive the least squares equation to solve the overdetermined system.

What is 2D homography?

Definition: A 2D homography is an invertible mapping h from P2 to itself. such that three points x1,x2,x3. lie on the same line if and only if. h(x1),h(x2),h(x3) do.