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I am trying to derive the inverse depth equation used in monocular SLAM algorithms. Specifically the equation 8 of the ORB SLAM paper

I am very close, except I do not understand where the (u_j-c) term comes form. I get the same formulae with only the c (principal point) component.

I am thinking it is because u_j in this case is indexed from the start of the epipolar line instead of the image (0,0). Is this correct?

Best, Marc

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