Computer vision: Regarding a line through origin in camera coordinate

Question

I've a question regarding a line in camera coordinate.

Suppose the pixel/screen coordinate of a point is (u,v). And the camera coordinate (coordinate system relative to camera) of (u,v) is (p,q,r) where (u,v) is given and a line L goes through the point (0,0,0) [origin camera location] and (p,q,r) where r is given. Is it possible to find (p,q)?

I know that the parametric equation of a line is:

(x-a, y-b, z-c)= t(x_0, y_0, z_0)

But I know only (a,b,c) which is (0,0,0) and z_0 which is r. Can anyone kindly tell me if it is possible to find the value of (p,q)? Can I use (u,v) in some way?

Answer 1

It's not possible until you have more information about what something like (u, v) represents. Think of it this way. Suppose you claimed you could figure it out just based on (u, v) and r. Now, what if I just relabeled your pixels? A pixel doesn't have to represent any specific distance, so if I said (125, 100) was (250, 200) instead, that would make sense too. Suppose I just swap in a higher resolution chip for a lower resolution chip.

To actually recover (p, q), you'd have to know what physical distance a pixel corresponds to. You'd also have to know whether the pinhole in your camera model is (0,0) in your pixel reference frame, etc.