Homography
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Homography is a concept in the mathematical science of geometry. It is defined as a relation between two figures, such that to any point in one figure corresponds one and only one point in the other, and vise versa.
[edit] Computer Vision Applications
In the field of Computer Vision, a homography is defined in 2 dimensional space as a mapping between a point on a ground plane from as seen from one camera, to the same point on the ground plane as seen from a second camera. This has many practical applications, most notably it provides a method for compositing 2D or 3D objects into an image or video with the correct pose.
[edit] 3d plane to plane equation
Having two cameras.
Passing from a point p1 to a point p2.
where H12 is
R is the rotation matrix. t is the translation vector. n and d are the normal vector of the plane and the distance to the plane respectively.
K1 and K2 are the cameras intrisic parameters matrices.
[edit] Mathematical definition
And:
Where:
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