Continuous Projection for Fast L1 Reconstruction

Reinhold Preiner, Oliver Mattausch, Murat Arikan, Renato Pajarola, Michael Wimmer
Continuous Projection for Fast L1 Reconstruction
ACM Transactions on Graphics (Proc. of ACM SIGGRAPH 2014), 33(4):47:1-47:13, August 2014. [paper_small] [paper] [slides] [video]

Information

Abstract

With better and faster acquisition devices comes a demand for fast robust reconstruction algorithms, but no L1-based technique has been fast enough for online use so far. In this paper, we present a novel continuous formulation of the weighted locally optimal projection (WLOP) operator based on a Gaussian mixture describing the input point density. Our method is up to 7 times faster than an optimized GPU implementation of WLOP, and achieves interactive frame rates for moderately sized point clouds. We give a comprehensive quality analysis showing that our continuous operator achieves a generally higher reconstruction quality than its discrete counterpart. Additionally, we show how to apply our continuous formulation to spherical mixtures of normal directions, to also achieve a fast robust normal reconstruction.

Project Page: https://www.cg.tuwien.ac.at/~preiner/projects/clop/

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paper_small: compressed quality (7,8 MB)
paper: high quality (60 MB)
slides: Siggraph 2014 presentation slides

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BibTeX

@article{preiner2014clop,
  title =      "Continuous Projection for Fast L1 Reconstruction",
  author =     "Reinhold Preiner and Oliver Mattausch and Murat Arikan and
               Renato Pajarola and Michael Wimmer",
  year =       "2014",
  abstract =   "With better and faster acquisition devices comes a demand
               for fast robust reconstruction algorithms, but no L1-based
               technique has been fast enough for online use so far. In
               this paper, we present a novel continuous formulation of the
               weighted locally optimal projection (WLOP) operator based on
               a Gaussian mixture describing the input point density. Our
               method is up to 7 times faster than an optimized GPU
               implementation of WLOP, and achieves interactive frame rates
               for moderately sized point clouds. We give a comprehensive
               quality analysis showing that our continuous operator
               achieves a generally higher reconstruction quality than its
               discrete counterpart. Additionally, we show how to apply our
               continuous formulation to spherical mixtures of normal
               directions, to also achieve a fast robust normal
               reconstruction.  Project Page:
               https://www.cg.tuwien.ac.at/~preiner/projects/clop/",
  month =      aug,
  issn =       "0730-0301",
  journal =    "ACM Transactions on Graphics (Proc. of ACM SIGGRAPH 2014)",
  number =     "4",
  volume =     "33",
  pages =      "47:1--47:13",
  keywords =   "point set, Gaussian mixture, Hierarchical EM, upsampling,
               dynamic reconstruction, L1 reconstruction",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2014/preiner2014clop/",
}