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

Abstract

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
Pages544-552
Number of pages9
Volume24
Edition3
DOIs
StatePublished - Jul 2005
EventACM SIGGRAPH 2005 - Los Angeles, CA, United States
Duration: Jul 31 2005Aug 4 2005

Other

OtherACM SIGGRAPH 2005
CountryUnited States
CityLos Angeles, CA
Period7/31/058/4/05

Fingerprint

Statistics
Convergence of numerical methods
Mathematical operators

Keywords

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

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software

Cite this

Fleishman, S., Cohen-Or, D., & Silva, C. T. (2005). Robust moving least-squares fitting with sharp features. In ACM Transactions on Graphics (3 ed., Vol. 24, pp. 544-552) https://doi.org/10.1145/1073204.1073227

Robust moving least-squares fitting with sharp features. / Fleishman, Shachar; Cohen-Or, Daniel; Silva, Cláudio T.

ACM Transactions on Graphics. Vol. 24 3. ed. 2005. p. 544-552.

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

Fleishman, S, Cohen-Or, D & Silva, CT 2005, Robust moving least-squares fitting with sharp features. in ACM Transactions on Graphics. 3 edn, vol. 24, pp. 544-552, ACM SIGGRAPH 2005, Los Angeles, CA, United States, 7/31/05. https://doi.org/10.1145/1073204.1073227
Fleishman S, Cohen-Or D, Silva CT. Robust moving least-squares fitting with sharp features. In ACM Transactions on Graphics. 3 ed. Vol. 24. 2005. p. 544-552 https://doi.org/10.1145/1073204.1073227
Fleishman, Shachar ; Cohen-Or, Daniel ; Silva, Cláudio T. / Robust moving least-squares fitting with sharp features. ACM Transactions on Graphics. Vol. 24 3. ed. 2005. pp. 544-552
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