What does the last row of a homography matrix mean?

1. What does the homography matrix do?
2. What is preserved in a homography?
3. How do you apply a homography matrix to a point?
4. How many points do you need to estimate a homography between two images?

What does the homography matrix do?

An example of such a transformation matrix is the Homography. It allows us to shift from one view to another view of the same scene by multiplying the Homography matrix with the points in one view to find their corresponding locations in another view (Equation 1).

What is preserved in a homography?

Homographies are transformations of a Euclidean space that preserve the alignment of points. Specific cases of homographies correspond to the conservation of more properties, such as parallelism (affine transformation), shape (similar transformation) or distances (Euclidean transformation).

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 points do you need to estimate a homography between two images?

To calculate a homography between two images, you need to know at least 4 point correspondences between the two images. If you have more than 4 corresponding points, it is even better. OpenCV will robustly estimate a homography that best fits all corresponding points.