# Getting the essential from the fundamental matrix

Is it possible to get E from F? I suppose that can't work, because then I could calculate the the extrinsic (and maybe also intrinsic?) parameters of the cameras without a calibration object of known size etc. like so:

1. Pick (8) corresponding points in images i1 and i2
2. Calculate F with the eight-point-algorithm
3. Calculate E from F
4. Determine relative position and orientation of cameras from E (and maybe it is also possible to get the intrinsic parameters, K?)

You can only get the essential matrix from the fundamental matrix if you know the camera intrinsics:

E = K' * F * K

where K is the intrinsic matrix and K' is its transpose.

• I believe this is wrong. K' is not the transpose but the essential matrix of one of the cameras and K of the other camera, respectively. But your main statement is correct for sure? Jul 30 '15 at 15:01
• @user1809923, It's not wrong. I have just defined what K and K' mean. I am assuming that the same camera was used to take both images. And the apostrophe denotes transpose in MATLAB. Otherwise, without any math markup support the equation would get messy.
– Dima
Jul 30 '15 at 15:06
• Yes, my statement is correct. If you want to find the camera pose from the fundamental matrix, you would have to assume some values for the intrinsics. For example, you can get the focal length and pixel size from EXIF. You can then further refine your estimate using bundle adjustment, but you always have to start with something. The best thing is to calibrate your camera ahead of time.
– Dima
Jul 30 '15 at 15:09
• okay, thanks. If we have one camera, you of course are correct. Also I messed up myself, K is not the essential matrix but the matrix comprising the intrinsic parameters... ;) Aug 6 '15 at 13:16