Stability of pose estimation using n points

Question

I am using chessboard to estimate translation vector between it and the camera. Firstly, the intrinsic camera parameters are calculated, then translation vector are estimated using n points detected from the chessboard.

I found a very strange phenomenon: the translation vector is accurate and stable when using more points in the chessboard, and such phenomenon is more obvious when the distance is farer. For instance, the square in the chessboard is 1cm*1cm, when the distance is 3m, translation vector is accurately estimated when using 25 points, while it is inaccurate and unstable using the minimal 4 points. However, when the distance is 0.6m, estimation results of translation vector using 4 points and 25 points are similar, which are all accurate.

How to explain this phenomenon (in theory)? what's the relationship between stable estimation result and distance, and number of points?

Thanks.

Answer 1

When you are using a smaller number of points, the calculation of the translation vector is more sensitive to the noise in coordinates of those points. Point coordinates are noisy due to a finite resolution of the camera (among other things). A that noise only increases with distance. So using a larger number of points should provide for a better estimation.