opencv - Finding the intrinsic parameters of a camera without a chessboard

Question

I need to find the intrinsic parameters of a CCTV camera using a set of historic footage images (That is all I got, no control on the environment, thus no chessboard calibration).

The good news is that I have the access to some ground-truth real-world coordinates, visible in most of the images.

Just wondering if there is any solid approach to come up with the camera intrinsic parameters.

P.S. I already found the homography matrix using cv2.findHomography in Python.

P.S. I have already tested QTcalib on two machines, but it is unable to visualize the images in the first place. Not sure what is wrong with it.

Thanks in advance.

question from:https://stackoverflow.com/questions/66056520/finding-the-intrinsic-parameters-of-a-camera-without-a-chessboard

Answer 1

intrinsic parameters contain both fx fy cx cy and skew with additional distortion parameters k1-k5 r1-r2.

Assuming you have no distortion and cx and cy are perfectly in the center. Image origin at top left as a normal understanding of the image. As you say you know some ground truth level 3D points.3D measurements are with respect to camera optical axis. Then this 3D point P can be projected into camera image plane called p. The P p O(the camera optical center) with center lines forms isosceles triangle.

fx / （p_x-cx) = P_z / P_x

fx = （p_x-cx) * P_z / P_x

The same goes for the fy. and usually fx and fy are the same.

This is under the perfect assumption that you don't have distortion on camera. If you start to have distortion, then you need to find enough sample points all over the image to form distortion understanding as shown below. One or 2 points won't give you the whole picture understanding.

There are some cheats in some papers that using sea vanishing lines(see ref, it is a series of works) or perfect 3D building vanishing points to detect the distortion. We start from extrinsic to intrinsic and it can get some good guess after some trial eventually. But it is very much in research and can not apply to general cases.

Ref: Han Wang, Wei Mou, Xiaozheng Mou, Shenghai Yuan, Soner Ulun, Shuai Yang and Bok-Suk Shin, An Automatic Self-Calibration Approach for Wide Baseline Stereo Cameras Using Sea Surface Images, unmanned system