Wavelet frame based surface reconstruction from unorganized points

Bin Dong, Zuowei Shen

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Applications of wavelet frames to image restoration problems (e.g. image deblurring and inpainting) have been successful due to their redundancy and capability of sparsely approximating piecewise smooth functions like images (see e.g. [13,14,8]). However, wavelet frames have not yet been used for surface reconstruction problems. Recently in [6], connections between one of the wavelet frame based image restoration model [8,28,48] and variational models (e.g. the ROF model [45]) were rigorously established. Such connections not only grant new insights to wavelet frame based image restorations, it also case a geometric explanation to wavelet frame based approaches. This leads us to a wavelet frame based model, as well as a fast algorithm, to reconstruct implicit surfaces from unorganized point sets in R3. We will demonstrate the effectiveness of the proposed model using several commonly used examples.

Original languageEnglish (US)
Pages (from-to)8247-8255
Number of pages9
JournalJournal of Computational Physics
Issue number22
StatePublished - Sep 10 2011


  • Split Bregman
  • Surface reconstruction
  • Tight wavelet frames
  • Total variation
  • Variational method
  • Wavelet frames

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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