Chapter 13 Robust Regression 13.1 Basic Methods in Robust Regression 13.1.1 Concept of Robust Regression In many fields such as robotics (Poppinga et al. 2008), computer vision (Mitra and Nguyen 2003), digital photogrammetry (Yang and Förtsner 2010), surface recon- struction (Nurunnabi et al. 2012), computational geometry (Lukács et al. 1998) as well as in the increasing applications of laser scanning (Stathas et al. 2003), it is a fundamental task for extracting features from 3D point cloud. Since the physical limitations of the sensors, the occlusions, multiple reflectance and noise can pro- duce off-surface points, robust fitting techniques are required. Robust fitting means an estimation technique which is able to estimate accurate model parameters not only despite small-scale noise in the data set but occasionally large scale mea- surement errors (outliers). Outliers definition is not easy. Perhaps considering the problem from the practical point of the view, we can say that data points, which appearance in the data set causes dramatically change in the result of the parameter estimation can be labeled as outliers. Basically there are two different methods to handle outliers: (a) weighting out outliers (b) discarding outliers Weighting outliers means that we do not kick out certain data points labeled as outlier but during the parameter estimation process we take them with a low weight into consideration in the objective function. Such a technique is the good old Danish method. The other technique will try to identify data points, which make “troubles” during the parameter estimation process. Troubles mean that their existence in the data set © Springer International Publishing AG 2018 J. L. Awange et al., Mathematical Geosciences, https://doi.org/10.1007/978-3-319-67371-4_13 405