Homography

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This figure explains the concept of Homography in computer vision — specifically, how to map one image to another when viewing the same plane in the world from two different viewpoints (i.e., two different camera positions).

 

• C and C′ are two camera centers.
• A 3D point X lies on a plane π.
• The point projects to image 1 as ui​ and to image 2 as uj​.
• Because the point lies on the same plane, there's a homography H that maps one image point to the other.

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• Homography H

 

$u_j=\mathbf{H}{\mathbf{u}}_i$

$u_j,u_i$ : 2D points in two different images (image coordinates in homogeneous form).

H : 3×3 homography matrix that transforms point $u_i$ from image 1 into the corresponding point $u_j$ in image 2.

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Term	Meaning
Planar structure	Homography is valid only when the scene is planar (e.g., a flat surface like a wall or checkerboard).
8 DoF	The matrix H has 9 values but is up to a scale, so it has 8 degrees of freedom.
Plane-induced H	The homography arises from a plane π in 3D space viewed by two cameras.