Robust moving least-squares fitting with sharp features

Shachar Fleishman, Daniel Cohen-Or, Cláudio T. Silva

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We introduce a robust moving least-squares technique for reconstructing a piecewise smooth surface from a potentially noisy point cloud. We use techniques from robust statistics to guide the creation of the neighborhoods used by the moving least squares (MLS) computation. This leads to a conceptually simple approach that provides a unified framework for not only dealing with noise, but also for enabling the modeling of surfaces with sharp features. Our technique is based on a new robust statistics method for outlier detection: the forward-search paradigm. Using this powerful technique, we locally classify regions of a point-set to multiple outlier-free smooth regions. This classification allows us to project points on a locally smooth region rather than a surface that is smooth everywhere, thus defining a piecewise smooth surface and increasing the numerical stability of the projection operator. Furthermore, by treating the points across the discontinuities as outliers, we are able to define sharp features. One of the nice features of our approach is that it automatically disregards outliers during the surface-fitting phase.

Original languageEnglish (US)
Title of host publicationACM Transactions on Graphics
Number of pages9
StatePublished - Jul 2005
EventACM SIGGRAPH 2005 - Los Angeles, CA, United States
Duration: Jul 31 2005Aug 4 2005


Country/TerritoryUnited States
CityLos Angeles, CA


  • Forward-search
  • Moving least squares
  • Robust statistics
  • Surface reconstruction

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software


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