An extension on robust directed projection of points onto point clouds

Azariadis and Sapidis [Azariadis PN, Sapidis NS. Drawing curves onto a cloud of points for point-based modelling. Computer-Aided Design 2005;37(1):109–22] introduced a novel method of point directed projection (DP) onto a point cloud along an associated projection vector. This method is essentially based on an idea of least sum of squares by making use of a weight function for bounding the influence of noise. One problem with their method is the lack of robustness for outliers. Here, we present a simple, robust, and efficient algorithm: robust directed projection (RDP) to guide the DP computation. Our algorithm is based on a robust statistical method for outlier detection: least median of squares (LMS). In order to effectively approximate the LMS optimization, the forward search technique is utilized. The algorithm presented here is better suited to detect outliers than the DP approach and thus finds better projection points onto the point cloud. One of the advantages of our algorithm is that it automatically ignores outliers during the directed projection phase.