Statistical Robust Estimation of Spatial Symmetric Transformations Based on Mahalanobis Distance

This article explores the problem of symmetric transformation in the presence of outliers for photogrammetric and remote-sensing applications. We propose a pointwise robust objective for symmetric coordinate transformation by assuming the corresponding structure of the downweighting matrix and choosing the squared Mahalanobis distance (MD) as the statistic to evaluate the downweighting factors. Compared with the previous work, our method regards all the coordinates of one point as a whole. It is practical, in principle, since the displacement and correspondence relation are pointwise; it is statistically rigorous, since the stochasticity of both frames is considered; it is flexible, since the incorporated constraints enable all kinds of transformation. By utilizing the parameter partition technique, a more intelligent iteration manner is proposed for the implementation aspect, which specially suits globally distributed geoscience data. The developed method is vetted in the synthetic and real examples, including geodetic datum conversion and point cloud registration. The algorithms have potential in many areas, including cross-source registration, image analysis, pattern recognition, surface modeling, and remote-sensing image registration.