Algebraic point set surfaces

By Gaël Guennebaud, Markus H. Gross. 2007

654 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computer Vision and Pattern Recognition

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In Aerospace Engineering

In Computer Vision and Pattern Recognition

Citations in the corpus

PCPNet Learning Local Shape Properties from Raw Point Clouds (2017, methodology): “…osculating jets [CP03] based on ﬁtting higher-order primitives robustly, the algebraic point set surface approach based on ﬁtting algebraic spheres [GG07], and approaches based on analyzing the distribution of Voronoi cells in the neighborhood of a point [AB99, ACSTD07, MOG11], among many others.”
Fusion of depth maps with multiple scales (2011, methodology): “2006] and Point Set Surfaces [Guennebaud and Gross 2007] cannot be modified in an obvious way to handle multiscale input.”
Rotational Projection Statistics for 3D Local Surface Description and Object Recognition (2013, methodology): “A model pointcloud was converted into a triangular mesh using the Marching Cubes algorithm (Guennebaud and Gross, 2007).”
Scale Space Meshing of Raw Data Point Sets (2011, methodology): “Variations of the MLS algo-rithm for denoising point sampled surfaces and preserving edges were proposed in [FCOS05], [GTE ∗ 06], [OGG09], [LCOL07], [GG07].”
State of research in automatic as-built modelling (2015, background): “…be used to detect planar and 3D shapes (planes, spheres, generalised cylinders), or different ﬁtting methods take advantage of the fact that implicit representations use the zeros of a function to deﬁne a shape, which can be conveniently integrated in a least squares ﬁtting formulation [125,54].”
Robust single-view geometry and motion reconstruction (2009, methodology): “2002] on our acquired data, followed by a surface reconstruction technique based on algebraic point set surfaces described in [Guennebaud and Gross 2007].”
A review of algorithms for filtering the 3D point cloud (2017, neutral): “From the above approaches, it can be seen that the plane fitting operation is unstable in regions of high curvature if the sampling rate is below a threshold.”
Deep Learning for Robust Normal Estimation in Unstructured Point Clouds (2016, methodology): “Spheres [GG07] and quadrics [CP05] have also been used to better adapt to the neighborhood and to the shape of the underlying surface.”
1 An End-to-End Framework for Evaluating Surface Reconstruction (2011, methodology): “Borrowing terminology from [Guennebaud and Gross 2007], we use two different definitions in our experiments: simple point set surfaces (abbr.”
As-Projective-As-Possible Image Stitching with Moving DLT (2013, methodology): “Further, function extrapolation is a crucial aspect that was not stressed in [6].”
State of the Art in Surface Reconstruction from Point Clouds (2014, neutral): “In both methods user input is used to augment the point cloud with tags classifying different surface attributes such as regions of surface smoothness [FCOS05b] and sharp features [GG07].”