Homography Matrix Correlations

1. What is a homography matrix?
2. How do you apply a homography matrix to a point?
3. What is the difference between fundamental matrix and homography?
4. Why does homography have 4 points?

What is a 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.

What is the difference between fundamental matrix and homography?

Whereas a homography relates coplanar image space points, the essential matrix relates any set of points in an image to points in another image taken by the same camera. Because the essential matrix is more generic than a homography it requires more points to calculate. findEssentialMat requires >= 5 points.

Why does homography have 4 points?

Hence 8 correspondence points are required. But in the case of homography, each correspondence solves two constraints. Hence only 4 correspondence points are sufficient. Save this answer.