Estimating differential quantities using polynomial fitting of osculating jets

By Frédéric Cazals, M. Pouget. 2003

560 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

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Citations in the corpus

ABC: A Big CAD Model Dataset for Geometric Deep Learning (2018, methodology): “We select 12 representative algorithms from the literature, and 5 of them are traditional ones, Robust Statistical Estimation on Discrete Surfaces (RoSt) [35] operating on point clouds (PC), and meshes (M), Osculating Jets (Jets) [21], also on point clouds and meshes, and Uniform weighting of adjace”
Discovering Structural Regularity in 3D Geometry (2008, methodology): “We use a robust descriptor based on polynomial fitting of osculating jets as proposed by Cazals and Pouget [2003]. For each sample point we estimate the mean and Gaussian curvatures H and K respectively.”
Ridge-valley lines on meshes via implicit surface fitting (2004, background): “2003; Cohen-Steiner and Morvan 2003] and polynomial fitting [Cazals and Pouget 2003; Goldfeather and Interrante 2004].”
Nonasymptotic rates for manifold, tangent space and curvature estimation (2017, methodology): “In such a case, geometric and topological intrinsic quantities include (but are not limited to) homology groups [22], persistent homology [10], volume [4], differential quantities [6] or the submanifold itself [14, 1, 20].”
SAL: Sign Agnostic Learning of Shapes From Raw Data (2019, methodology): “To approximate the normal n∗ we tested two options: (i) taking n∗ directly from the original scan Xi with its original orientation; and (ii) using local normal estimation using Jets [10] followed by consistent orientation procedure based on minimal spanning tree using the CGAL library [1].”
Voronoi-Based Curvature and Feature Estimation from Point Clouds (2011, methodology): “The tessellation of the Voronoi cells was done using the 3D Delaunay Triangulation package of CGAL [cga].”
A Survey of Surface Reconstruction from Point Clouds (2017, methodology): “Other methods for normal estimation consist of using a weighted covariance matrix [PMG04] and higher-order approximations via osculating jets [CP05].”
Linear rotation-invariant coordinates for meshes (2005, methodology): “There are several advanced methods for computation of normals, such as [Meek and Walton 2000; Meyer et al. 2002; Cazals and Pouget 2003; Cohen-Steiner and Morvan 2003].”
PointCleanNet: Learning to Denoise and Remove Outliers from Dense Point Clouds (2019, methodology): “…as outliers using statistical meth-ods, e.g., [Agg15]; projecting points to estimated local surfaces (e.g., MLS surface, jet-ﬁtting, etc.) [FCOS05, CP05, CP07]; consolidating similar patches to cancel out iid noise perturbations (e.g., non-local means, dictionary-based sparse coding), e.g.,…”