Computing and Rendering Point Set Surfaces

By Marc Alexa, Johannes Behr, Daniel Cohen-Or, Shachar Fleishman, David Levin, Cláudio T. Silva. IEEE Transactions on Visualization and Computer Graphics, 2003

1,208 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/b7e0ebc678153eb2c341702247d2fafb872f0465

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Citations in the corpus

Towards 3D Point cloud based object maps for household environments (2008, methodology): “To compute the vector of coefficients, we minimize the error function as in [1,40].”
Deep Learning for Robust Normal Estimation in Unstructured Point Clouds (2016, methodology): “Numerous algorithms have been developed to process point clouds, such as geometric primitive extraction [SWK07], surface reconstruction [BDLGM14, CLP10], 3D navigation [FGMP14], and point-based rendering [RL00,ZPVBG01,ABCO ∗ 03], just to name a few.”
PU-GAN: A Point Cloud Upsampling Adversarial Network (2019, methodology): “[3] inserts points at Voronoi diagram vertices in the local tangent space.”
Patch-Based Progressive 3D Point Set Upsampling (2018, methodology): “[2] insert new points at the vertices of the Voronoi diagram, which is computed on the moving least squares (MLS) surface, assuming the underlying surface is smooth.”
Algebraic point set surfaces (2007, methodology): “The by far most important and successful class of such meshless representations are point set surfaces (PSS) [Alexa et al. 2003] combining high flexibility with ease of implementation.”
Interpolating and approximating implicit surfaces from polygon soup (2004, methodology): “Moving least-squares interpolation is also a part of the non-linear projection method used in [Alexa et al., 2001], [Alexa et al., 2003], and [Fleishman et al., 2003].”
A survey of point-based techniques in computer graphics (2004, methodology): “3) [20] The moving least-squares (MLS) surfaces of [21] [22] provide an approximating or interpolating surface for a given set of point samples by local higher order polynomials and have first been applied to point-based methods by Alexa et al. [23] [24].”
PointCleanNet: Learning to Denoise and Remove Outliers from Dense Point Clouds (2019, methodology): “Denoising and outlier removal also arise prominently, and have therefore been considered in the context of surface ﬁtting to noisy point clouds, including the widely-used Moving Least Squares (MLS) approach and its robust variants [ABCO ∗ 03,MVdF03,FCOS05,ÖGG09,GP11].”
PU-Net: Point Cloud Upsampling Network (2018, background): “An early work by Alexa et al. [3] upsamples a point set by interpolating points at vertices of a Voronoi diagram in the local tangent space, where the main purpose is to enhance the point set for rendering.”