Continuous Projection for Fast L1 Reconstruction

Reinhold Preiner, Oliver Mattausch, Murat Arikan, Renato Pajarola, Michael Wimmer

Research output: Contribution to journalArticlepeer-review


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:
Original languageEnglish
Pages (from-to)47:1-47:13
JournalACM Transactions on Graphics
Issue number4
Publication statusPublished - 1 Aug 2014
Externally publishedYes
EventSIGGRAPH 2014 - Vancouver, Canada
Duration: 10 Aug 201414 Aug 2014


  • point set, Gaussian mixture, Hierarchical EM, upsampling, dynamic reconstruction, L1 reconstruction

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