Deeper understanding of the homography decomposition for vision-based control

1. What is homography in image processing?
2. What is homography used for?
3. What is a homography mapping?
4. What is homography estimation?

What is homography in image processing?

In the field of computer vision, any two images of the same planar surface in space are related by a homography (assuming a pinhole camera model). This has many practical applications, such as image rectification, image registration, or camera motion—rotation and translation—between two images.

What is homography used for?

Homography is generally used to map a plane to another plane while fundamental matrix is used to calculate depths of scene structure with objects of varying depths.

What is a homography mapping?

In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive. It is a bijection that maps lines to lines, and thus a collineation.

What is homography estimation?

The homography can be estimated using for instance the Direct Linear Transform (DLT) algorithm (see 1 for more information). As the object is planar, the transformation between points expressed in the object frame and projected points into the image plane expressed in the normalized camera frame is a homography.