Camera and laser scanner calibration final approach questions
The solution I gave in the other answer assumed that the plane in question was fixed relative to the camera location.  Thus a mapping from the 2D pixel locations to a 2D location on the plane could be made.  Using the same calibration points, a reverse mapping can also be made.  These mappings contain the distortion of the lens, the location of the camera relative to the plane, and the perspective effects.  The mappings can be made more accurate by using higher order equations and more calibration points.

Once you have the 2D coordinates on the plane, call them (x,y), you can convert into real world 3D coordinates using a vector parameterization of the plane:

$$ \vec r =  x \vec a + y \vec b + \vec c  $$

Where $\vec a$ is the 3D real world unit vector in the x direction on the plane, $\vec b$ is the 3D real world unit vector in the y direction on the plane, and $\vec c$ is the 3D real world unit vector of the origin on the plane.

If the situation is more complicated than that, e.g. the laser plane moves, or the camera moves, then a different solution is called for.

I have Python code for a generalized mapping solution.  You can contact me at the email address on my profile page.

Hope this helps.

Ced