Concept

Homography (computer vision)

Summary
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 , , or camera motion—rotation and translation—between two images. Once camera resectioning has been done from an estimated homography matrix, this information may be used for navigation, or to insert models of 3D objects into an image or video, so that they are rendered with the correct perspective and appear to have been part of the original scene (see Augmented reality). 3D plane to plane equation We have two cameras a and b, looking at points P_i in a plane. Passing from the projection {}^bp_i=\left({}^bu_i;{}^bv_i;1\right) of P_i in b to the projection {}^ap_i=\left({}^au_i;{}^av_i;1\right) of P_i in a: : {}^ap_i = \frac{{}^bz_i}{{}^az_i}K_a \cdot H_{ab} \cdot K_b^{-1} \cdot {}^bp_i where {}
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