Direct linear transformation: Difference between revisions

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

: <math> \mathbf{x}_{k} \simpropto \mathbf{A} \, \mathbf{y}_{k} </math> &nbsp; for <math> \, k = 1, \ldots, N </math>

where <math> \mathbf{x}_{k} </math> and <math> \mathbf{y}_{k} </math> are known vectors, <math> \, \simpropto </math> denotes equality up to an unknown scalar multiplication, and <math> \mathbf{A} </math> is a matrix (or linear transformation) which contains the unknowns to be solved.

This type of relation appears frequently in [[projective geometry]]. Practical examples are the relation between 3D points in a scene and their projection onto the image plane of a [[Pinhole camera model|pinhole camera]] and [[Homography|homographies]].