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Essential Matrix: Difference between revisions
→Background and Derivation
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We now consider two cameras: | We now consider two cameras: | ||
Camera 1 is at the origin of world space (or it's object space) <math>P = (I | 0)</math>. | Camera 1 is at the origin of world space (or it's object space) <math>P = (I | 0)</math>. | ||
Camera 2 is displaced with some rotation <math>R</math> and translation <math> | Camera 2 is displaced with some rotation <math>R</math> and translation <math>-RT</math>, <math>P' = (R | -RT)</math>.<br> | ||
Any point <math>\mathbf{u} = (u,v,w)^T</math> in camera 1 is represented by an epipolar line in camera 2.<br> | Any point <math>\mathbf{u} = (u,v,w)^T</math> in camera 1 is represented by an epipolar line in camera 2.<br> | ||
Under camera 2, the position of camera 1 is <math>-RT</math> and <math>P' (u,v,w,0)^T = R\mathbf{u}</math> is somewhere on this epipolar line. | Under camera 2, the position of camera 1 is <math>-RT</math> and <math>P' (u,v,w,0)^T = R\mathbf{u}</math> is somewhere on this epipolar line. | ||