On Robust Regression in Photogrammetric Point Clouds

Many applications in computer vision require robust linear regression on photogrammetrically reconstructed point clouds. Due to the modeling process from perspective images the uncertainty of an object point depends heavily on its location in object space w.r.t. the cameras. Standard algorithms for robust regression are based on distance measures from the regression surface to the points, but these distances are biased by varying uncertainties. In this paper a description of the local object point precision is given and the Mahalanobis distance to a plane is derived to allow unbiased regression. Illustrative examples are presented to demonstrate the effect of the statistically motivated distance measure.