The NURBS book
Proceedings of the conference on Visualization '01
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Ray Tracing Point Sampled Geometry
Proceedings of the Eurographics Workshop on Rendering Techniques 2000
Ray Tracing Point Set Surfaces
SMI '03 Proceedings of the Shape Modeling International 2003
Non-iterative, feature-preserving mesh smoothing
ACM SIGGRAPH 2003 Papers
ACM SIGGRAPH 2003 Papers
Registration of point cloud data from a geometric optimization perspective
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Robust moving least-squares fitting with sharp features
ACM SIGGRAPH 2005 Papers
International Journal of Networking and Virtual Organisations
Post-processing of scanned 3D surface data
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Interactive ray tracing of point-based models
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
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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.