computer-visioncameracoordinatesline# Regarding a line through origin in camera coordinate

I have 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?

Solution

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.

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