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Back-projected ray in homogeneous coordinates

  1. Jan 26, 2012 #1
    suppose I got a projective camera model. for this model I would like to back-project a ray through a point in the image plane. I know that the equation for this is the following:
    $$
    y(\lambda) = P^+_0 x_0 + \lambda c_0
    $$
    where [itex]P^+_0[/itex]denotes the pseudoinverse of the camera matrix.
    [itex]x_0[/itex] the point on the image plane and $c_0$ the center of the camera. (This is taking from the book "Multiple View Geometry in Computer Vision" page 162)

    Now I don't fully get this equation. I get that [itex]P^+_0 x_0[/itex] results in a point on the line we are looking for. Hence we have two points that we can use for constructing a line. However I don't get the parametrization using [itex]\lambda[/itex]. Why is the equation not in the form like:
    $$y(\lambda) = (1-\lambda) a + \lambda b$$

    Any help in understanding the original equation of the resulting ray would be appreciated! :D
     
  2. jcsd
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