Units in the camera frame of the matlab's calibration toolbox

Question

What is the units of the coordinates in camera frame by using matlab's camera calibration toolbox? Say I transform some points in pixels to camera's frame, what are the units? Is there some possible way of knowing?

I found this similar question , but no definite answer.

Answer 1

Can you please clarify how exactly you are transforming those points?

The pin-hole camera model looks like this:

w*[x,y,1] = [X,Y,Z,1]*[R;t]*K

[X,Y,Z] are the world coordinates in world units (eg millimeters), and [x,y] are the image coordinates in pixels. K is the matrix of camera intrinsics, and R and t are the camera extrinsics. w is an arbitrary scale factor.

If you take a world point [X,Y,Z,1] and multiply it by [R;t] , then you get a point in a "camera's coordinate system", where the origin is at the focal point, and the units are the same as in your world coordinates (eg millimeters).

If you take a point in the image [x,y,1] and multiply it by the inverse of K , then you get a point in "normalized image coordinates", where the origin is at the optical center, and the axis have no units. This happens because you are dividing x and y in pixels by the focal length fx and fy , which is also in pixels. So pixels cancel out.