Univariate subdivision schemes for noisy data with geometric applications

Nira Dyn, Allison Heard, Kai Hormann, Nir Sharon*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Abstract We introduce and analyze univariate, linear, and stationary subdivision schemes for refining noisy data by fitting local least squares polynomials. This is the first attempt to design subdivision schemes for noisy data. We present primal schemes, with refinement rules based on locally fitting linear polynomials to the data, and study their convergence, smoothness, and basic limit functions. Then, we provide several numerical experiments that demonstrate the limit functions generated by these schemes from initial noisy data. The application of an advanced local linear regression method to the same data shows that the methods are comparable. In addition, several extensions and variants are discussed and their performance is illustrated by examples. We conclude by applying the schemes to noisy geometric data.

Original languageEnglish
Article number1495
Pages (from-to)85-104
Number of pages20
JournalComputer Aided Geometric Design
StatePublished - 4 Jul 2015


  • Convergence analysis
  • Least squares
  • Noisy data
  • Subdivision schemes


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