Camera calibration matrix, fundamental matrix and essential matrix at different image resolutions

Question

I have the camera calibration matrix given at a certain image resolution. I am using correspondences between stereo images to calculate the fundamental matrix and then using that to derive the essential matrix. Now if I reduce the image resolution (lets say half the resolution) how will the camera calibration matrix, fundamental matrix and essential matrix chnage?

Answer 1

When you reduce the image resolution, the camera calibration matrix will also change by half. The fundamental matrix will remain unchanged, but the essential matrix will change depending on the camera calibration matrix.

The camera calibration matrix is a 3x3 matrix that describes the intrinsic parameters of a camera, such as the focal length, principal point, and skew coefficient. The fundamental matrix is a 3x3 matrix that describes the relationship between two stereo images, and the essential matrix is a 3x3 matrix that describes the relationship between two stereo images when the camera calibration matrices are known.

To calculate the essential matrix from the fundamental matrix and camera calibration matrix, you can use the following equation: E = K_T @ F @ K where: E is the essential matrix K_T is the transpose of the camera calibration matrix F is the fundamental matrix

When you reduce the image resolution by half, the camera calibration matrix will also change by half. This is because the focal length and principal point will also change by half. The fundamental matrix will remain unchanged, because it is only dependent on the relative orientation and position of the two cameras. The essential matrix will change, because it is dependent on both the camera calibration matrix and the fundamental matrix.