Fig. 12

Variation of point height estimates with distance for all cameras. Cameras calibrated with chessboard (A), stars (B) and stars and terrain (C) are plotted separately. For each camera, height errors assuming uncertainties in just intrinsics (red), intrinsics and digitisation (blue), and intrinsics, digitisation and orientation (green) are shown to give an idea of the contribution of each source of uncertainty to the overall error. Errors are generated using a Monte Carlo procedure by sampling 10,000 random cameras from the PDF of intrinsics and orientation for each camera, assuming the pixel of interest is located offset from the image center by a random digitsation error, finding the standard deviation in the Z coordinate of the 3D unit vector corresponding to that pixel for all random cameras, and then multiplying it by a distance to get the height uncertainty at that point. For chessboard and star calibration the contribution of uncertainty in the intrinsics to the overall height uncertainty is relatively minor, while it is higher for stars and terrain combined. Note that we assume the contribution of uncertainty in the cameras location is minor as this is generally very small (on the order of a few meters or less) compared to the heights and distances being measured (typically on the order of kilometers)