OpenCV: Calculate angle between camera and pixel

Question

I\'d like to know how I can go about calculating the angle of some pixel in a photo relative to the webcam that I\'m using. I\'m new to this sort of thing and I\'m using a

Answer 1

Recipe:

1 - Calibrate the camera, obtaining the camera matrix K and distortion parameters D. In OpenCV this is done as described in this tutorial.

2 - Remove the nonlinear distortion from the pixel positions of interest. In OpenCV is done using the undistortPoints routine, without passing arguments R and P.

3 - Back-project the pixels of interest into rays (unit vectors with the tail at the camera center) in camera 3D coordinates, by multiplying their pixel positions in homogeneous coordinates times the inverse of the camera matrix.

4 - The angle you want is the angle between the above vectors and (0, 0, 1), the vector associated to the camera's focal axis.

Answer 2

You don't need to know the distance to the object, only the resolution and angle of view of the camera.

Computing the angle requires only simple linear interpolation. For example, let's assume a camera with a resolution of 1920x1080 that covers a 45 degree angle of view across the diagonal.

In this case, sqrt(1920² + 1080²) gives 2292.19 pixels along the diagonal. That means each pixel represents 45/2292.19 = .0153994 degrees.

So, compute the distance from the center (in pixels), multiply by .0153994, and you have its angle from the center (for that camera -- for yours, you'll obviously have to use its resolution and angle of view).

Of course, this is somewhat approximate -- its accuracy will depend on how much distortion the lens has. With a zoom lens (especially wider angle) you can generally count on that being fairly high. With a fixed focal length lens (especially if it doesn't cover an angle wider than 90 degrees or so) it'll usually be pretty low.

If you want to improve accuracy, you can start by taking a picture of a flat rectangle with straight lines just inside the angle of view of the camera, then compute the distortion based on the deviation from perfectly straight in the resulting picture. If you're working with an extremely wide angle lens, this may be nearly essential. With a lens covering a narrower angle of view (especially, as already mentioned, if it's fixed focal length) it's rarely likely to be worthwhile (such lenses often have only a fraction of a percent of distortion).