Parameterization-free projection for geometry reconstruction

Yaron Lipman, Daniel Cohen-Or, David Levin, Hillel Tal-Ezer

Research output: Contribution to journalArticlepeer-review

218 Scopus citations


We introduce a Locally Optimal Projection operator (LOP) for surface approximation from point-set data. The operator is parameterization free, in the sense that it does not rely on estimating a local normal, fitting a local plane, or using any other local parametric representation. Therefore, it can deal with noisy data which clutters the orientation of the points. The method performs well in cases of ambiguous orientation, e.g., if two folds of a surface lie near each other, and other cases of complex geometry in which methods based upon local plane fitting may fail. Although defined by a global minimization problem, the method is effectively local, and it provides a second order approximation to smooth surfaces. Hence allowing good surface approximation without using any explicit or implicit approximation space. Furthermore, we show that LOP is highly robust to noise and outliers and demonstrate its effectiveness by applying it to raw scanned data of complex shapes.

Original languageEnglish
Article number1276405
JournalACM Transactions on Graphics
Issue number3
StatePublished - 29 Jul 2007


  • Geometry projection operator
  • Point-cloud
  • Surface reconstruction


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