Plane induced homography

1. What is planar homography?
2. What is homography in image processing?
3. Why does homography have 8 degrees of freedom?
4. What is homography estimation?

What is planar homography?

We can derive a linear relationship between the coordinates of points on an arbitrary plane in the scene and the coordinate of that point in the image. This is the planar homography and it has a number of everyday uses which might surprise you.

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.

Why does homography have 8 degrees of freedom?

Also, homography is defined upto a scale (c in above equation) i.e. it can be changed by a non zero constant without any affect on projective transformation. Thus, homography has 8 degree of freedom even though it contains 9 elements (3x3 matrix) i.e. the number of unknowns that need to be solved for is 8.

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.