Essential Matrix: Difference between revisions

Essential Matrix (view source)

217 bytes added , 1 May 2020

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 [[File: Epipolar_geometry.svg | link=Wikipedia | thumb | 400px | [[Wikipedia: Epipolar Geometriy]] ]]
-A pinhole camera with <math>3 \times 4</math> projection matrix <math>P = K(R | -RT)</math> takes points <math>\mathbf{x} = (x, y, z)^T</math> and projects them to <math>\mathbf{u} = (u, v, w)^T = \mathbf{R}(\mathbf{x} - \mathbf{t})</math>.
+A pinhole camera with <math>3 \times 4</math> projection matrix <math>P = K(R \mid -RT)</math> takes points <math>\mathbf{x} = (x, y, z)^T</math> and projects them to <math>\mathbf{u} = (u, v, w)^T = \mathbf{R}(\mathbf{x} - \mathbf{t})</math>. Here, the notation <math>(R \mid -RT)</math> represents a <math>3 \times 3</math> matrix <math>R</math> concatenated with a <math>3 \times 1</math> matrix <math>-RT</math> to form a <math>3 \times 4</math> matrix.
 We now consider two cameras: