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Direct linear transformation is an algorithm which solves a set of variables from a set of similarity relations:

where x k {\displaystyle \mathbf {x} _{k}} and y k {\displaystyle \mathbf {y} _{k}} are known vectors, ∝ {\displaystyle \,\propto } denotes equality up to an unknown scalar multiplication, and A {\displaystyle \mathbf {A} } is a matrix which contains the unknowns to be solved.

This type of relation appears frequently in projective geometry. Practical examples include the relation between 3D points in a scene and their projection onto the image plane of a pinhole camera, and homographies.

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