Calculate Essential and Fundamental matrices using a calibrated camera using 4 co-planar point matches

Question

Suppose I have two images of a scene with four co-planar 3D points and their corresponding 2D points in the images. I also have the camera calibration matrix, K.

I can then estimate the relative poses of the cameras using i.e. [1]. Then, given R, t (from the pose) and K I can calculate the Essential matrix and then the Fundamental matrix.

Is the resulting Fundamental matrix deficient in any way because it is calculated from only four co-planar points?

Answer 1

Four coplanar points are not sufficient to determine a fundamental (i.e. uncalibrated) or essential (calibrated) matrix. You may only constrain a homography using them, which is all you need anyway if the scene of interest is indeed on a plane.