filename     : Ozt09.pdf
entry        : toappear
conference   : Eurographics 2009
pages        : 493-501
year         : 2009
month        : March
title        : Feature Preserving Point Set Surfaces based on Non-Linear Kernel Regression
subtitle     : 
author       : A. Cengiz Öztireli, Gael Guennebaud, Markus Gross
booktitle    : Proceedings of Eurographics
ISSN/ISBN    : 
editor       : P. Dutré and M. Stamminger
publisher    : Eurographics
publ.place   : Munich, Germany
volume       : 28
issue        : 2
language     : English
keywords     : Surface Reconstruction, Moving Least Squares, Point Set Surface, Feature Preservation, Robust Statistics
abstract     : Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smooth-out small or sharp features. In this paper, we address these major issues, and present a novel point based surface definition combining the simplicity of implicit MLS surfaces~\cite{Shen04Interpolating,Kolluri05Provably} with the strength of robust statistics. To reach this new definition, we review MLS surfaces in terms of local kernel regression, opening the doors to a vast and well established literature from which we utilize robust kernel regression. Our novel representation can handle sparse sampling, generates a continuous surface better preserving fine details, and can naturally handle any kind of sharp features with controllable sharpness. Finally, it combines ease of implementation with performance competing with other non-robust approaches.