is a concept in the mathematical
science of geometry
. It is defined as a relation between two figures, such that any given point in one figure corresponds to one and only one point in the other, and vice versa.
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 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
. The homography matrix is sometimes known as a homograph
, a term which has a different meaning in linguistics
3D plane to plane equation
We have two cameras a and b, looking at points in a plane.
Passing the projections of from in b to a point in a:
is the rotation matrix by which b is rotated in relation to a; t is the translation vector from a to b; and are the normal vector of the plane and the distance to the plane respectively.
and are the cameras' intrinsic parameter matrices.
The figure shows camera b looking at the plane at distance d.
are used, because matrix multiplication cannot directly perform the division required for perspective projection
When the image region in which the homography is computed is small or the image has
been acquired with a large focal length, an affine homography
is a more appropriate
model of image displacements. An affine homography is a special type of a general
homography whose last row is fixed to