Essential Matrix: Difference between revisions

Essential Matrix (view source)

224 bytes added , 30 April 2020

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 * This matrix is skew-symmetric. I.e. <math>[\mathbf{t}]^T_{\times} = -[\mathbf{t}]_{\times}</math>
-Given feature points <math>\mathbf{x}</math> and <math>\mathbf{x'}</math> from two images,
+Now if <math>\mathbf{u}'</math> is a feature point from camera 2 matching point <math>\mathbf{u}</math>, then it must lie on this epipolar line.
-we can relate them with a rotation <math>\mathbf{R}</math> and a translation <math>\mathbf{t}</math>
+Thus <math>\mathbf{u}' \in \{(u',v',w') \mid pu' + qv' + rw' = 0\} \implies \mathbf{u}'^T R[T]_{\times} \mathbf{u} = 0</math>.
-such that <math>(\mathbf{R}\mathbf{x} + \mathbf{t}) = x'</math>.
+Now <math>Q = R[T]_{\times}</math> is the essential matrix.
+Given 8 or more correspondence points between camera 1 and camera 2, you can solve for <math>Q</math> using the [[Wikipedia: Eight-point algorithm]]
 ==Properties==