Parameterization-free projection for geometry reconstruction

By Yaron Lipman, Daniel Cohen-Or, David Levin, H. Tal-Ezer. ACM Transactions on Graphics, 2007

468 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/51cba12767f5a89533117e3651f4d32cd2782d4a

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Curve skeleton extraction from incomplete point cloud (2009, methodology): “For each raw input cloud, we remove outliers, denoise, and subsample the raw data to 10, 000 points using the LOP operator [Lipman et al. 2007].”
A Survey of Surface Reconstruction from Point Clouds (2017, unknown): “Unlike the methods presented so far, this class of techniques do not strictly reconstruct a continuous surface, but rather ﬁt an arbitrary set of points Q onto the multivariate median of the input point cloud P while ensuring that Q is evenly distributed [LCOLTE07] – see Figure 6.”
Accurate 3D pose estimation from a single depth image (2011, background): “The criteria is to minimize the sum of weighted distances between the projected point-set and P , meanwhile preventing points in the projected point-set being too close to each other.”
P2P-NET: Bidirectional Point Displacement Net for Shape Transform (methodology): “Representative methods include point cloud consolidation via LOP [Lipman et al. 2007] and WLOP [Huang et al. 2009; Preiner et al. 2014].”
Edge-aware point set resampling (2013, methodology): “To this end, we alter the LOP operator [Lipman et al. 2007b; Huang et al. 2009] and make it normal or edge aware, allowing for resampling away from edges.”
PU-GAN: A Point Cloud Upsampling Adversarial Network (2019, methodology): “Early methods [3, 21, 14, 15, 33] for the problem are optimization-based, where various shape priors are used to constrain the point cloud generation.”
State of the Art in Surface Reconstruction from Point Clouds (2014, unknown): “Unlike noise, outliers are points that should not be used to infer the surface, either explicitly through detection [LCOLTE07], or implicitly through robust methods [MDGD ∗ 10].”
EC-Net: an Edge-aware Point set Consolidation Network (2018, methodology): “Early works in this area assumed smooth surface [1,14,15].”
A review of algorithms for filtering the 3D point cloud (2017, unknown): “Inspired by the concept of L 1 median [47–50] from statistics, Lipman et al. [51] introduced a parameterization-free projection operator, that was, Locally Optimal Projection (LOP) operator [52].”
Differentiable surface splatting for point-based geometry processing (2019, methodology): “[2013] employ an anisotropic weighted locally optimal projection (WLOP) operator [Huang et al. 2009; Lipman et al. 2007] and a progressive edge aware resampling (EAR) procedure to consolidate noisy input.”
PU-Net: Point Cloud Upsampling Network (2018, methodology): “Lipman et al. [20] present a locally optimal projection (LOP) operator for points resampling and surface reconstruction based on an L 1 median.”
Consolidation of unorganized point clouds for surface reconstruction (2009, background): “The LOP operator [Lipman et al. 2007] takes as input a noisy point cloud, possibly with outliers, and outputs a new point set which more faithfully adheres to the underlying shape.”
Patch-Based Progressive 3D Point Set Upsampling (2018, methodology): “[23] employ an anisotropic locally optimal projection (LOP) operator [22,36] to consolidate and push points away from the edges, followed by a progressive edge-aware upsampling procedure.”
Deep points consolidation (2015, methodology): “Our approach is derived from previous ones [Lipman et al. 2007; Huang et al. 2009], but with important differences.”