Continuous projection for fast L ₁ reconstruction

Abstract

On this mixture, a Continuous Projection operator is applied, which efficiently produces an L1 reconstruction of 72K point positions (c) at ∼ 9 FPS. In contrast, an L2 reconstruction (d) with small feature-preserving kernel exhibits heavily visible noise (top), while a larger kernel biases and oversmoothes the result (bottom). Our method runs at up to 7 times the speed of a fast GPU implementation of standard WLOP while providing comparable or even better quality, allowing for interactive robust reconstruction of unordered dynamic point sets. AbstractWith 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.

Deep points consolidation

“…Preiner et al [2014] develop an accelerated version of WLOP by using a more compact representation of the original input points. WLOP-based consolidation methods are robust since they do not rely on the normals of the input points.…”

Survey on sparsity in geometric modeling and processing

“…6(b) gives one denoised result with sharp features. [17] robust to noises, outliers WLOP [18] robust to noises, outliers CLOP [19] robust to noises, outliers TV( 1 ) based/ [20] robust to noises, outliers Subdivision [21] robust to noises, outliers Mesh Denoising 0 -norm of Edge Operator [13] sharp feature preserving 1 -analysis Compressed Sensing [14] sharp feature preserving TV( 1 ) based [15] sharp feature preserving Shape Matching…”

“…In LOP/WLOP, the majority of the time is spent on the evaluation of the attractive forces from all points in P , Preiner et al [19] efficiently reduce the set P of unordered input points to a much more compact mixture of Gaussians M = {ws, Θs} that reflects the density distribution of the points. That is, M defines a probability density function(pdf) as a weighted sum of |M| Gaussian components…”

“…One might justifiably wonder whether sparsity based regularization and sparse representation can be useful at all for geometry processing tasks. The answer has been largely positive: in the past few years, variations and extensions of 1 minimization have been applied to many geometry processing tasks, including mesh denoising [13,14,15], point surface reconstruction [16], point cloud consolidation [17,18,19,20,21], mesh segmentation [22,23,24,25], and point cloud registration [26]. In almost all of these applications, using sparsity as a prior leads to stateof-the-art results.…”

Calibration Template Method Based on Statistical Distribution

“…There is the research of surface reconstruction in SIGGRAPH 2014, such as without mesh real time surface reconstruction [1], the continuous projection reconstruction [2], and the real sense floating surface reconstruction [3], etc. Artec spider scanner is a color scanner that suitable for middle and small objects, but the scanning effect depends on its operator.…”