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Essential Matrix: Difference between revisions
→Determining rotation \mathbf{R} and translation \mathbf{t}
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* Here, <math>R</math> is your rotation and <math>S = [T]_{\times}</math> | * Here, <math>R</math> is your rotation and <math>S = [T]_{\times}</math> | ||
* <math>T = V (0, 0, 1)^T</math>, the third column of <math>V</math> or third row of <math>V^T</math> | * <math>T = V (0, 0, 1)^T</math>, the third column of <math>V</math> or third row of <math>V^T</math> | ||
** Note that this only gives you the direction of the translation. The magnitude is not determined. | |||
* Some sources such as Wikipedia use <math>[T]_{\times} = U Z U^T</math> and <math>T = U (0, 0, 1)^T</math>. | * Some sources such as Wikipedia use <math>[T]_{\times} = U Z U^T</math> and <math>T = U (0, 0, 1)^T</math>. | ||
** This is equivalent to <math>RT</math> in our notation. | ** This is equivalent to <math>RT</math> in our notation. | ||