How to compute camera pose from Homography matrix?

1. How is homography matrix calculated?
2. How do you apply a homography matrix to a point?
3. How many degrees of freedom does 2D homography have?

How is homography matrix calculated?

What is the homography matrix? The homography matrix is a 3x3 matrix but with 8 DoF (degrees of freedom) as it is estimated up to a scale. It is generally normalized (see also 1) with h_33 = 1 or h_11^2 + h_12^2 + h_13^2 + h_21^2 + h_22^2 + h_23^2 + h_31^2 + h_32^2 + h_33^2 = 1 .

How do you apply a homography matrix to a point?

This spatial relationship is represented by a transformation known as a homography, H, where H is a 3 x 3 matrix. To apply homography H to a point p, simply compute p' = Hp, where p and p' are (3-dimensional) homogeneous coordinates. p' is then the transformed point.

How many degrees of freedom does 2D homography have?

Since the Homography matrix has 8 degrees of freedom, we need at least four pairs of corresponding points to solve for the values of the Homography matrix. We can then combine the relationships between all four points like below. Equation 7: Relationship between n pairs of matching points. Image by Author.