A signal processing approach to fair surface design

By Gabriel Taubin. 1995

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Citations in the corpus

Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning (2018, background): “The Laplacian smoothing (Taubin 1995) on each channel of the input features is deﬁned as: where 0 γ ≤ 1 is a parameter which controls the weighting between the features of the current vertex and the features of its neighbors.”
Spectral compression of mesh geometry (2000, background): “Recent years have seen an increase of interest in signal processing approaches [20,6] to 3D mesh manipulation, and their extension to multiresolution analyses [15,9].”
Mesh editing with poisson-based gradient field manipulation (2004, methodology): “A signal processing approach was presented in [Taubin 1995].”
Fast and Effective Feature-Preserving Mesh Denoising (2007, methodology): “Hence, we can simply choose ¼ 1=18 in Taubin’s algorithm.”
An image-based modeling framework for patient-specific computational hemodynamics (2008, methodology): “, through the use of a Taubin type non-shrinking smoothing filter [29] on the final triangulated surface.”
Non-iterative, feature-preserving mesh smoothing (2003, methodology): “Similarly, shapes extracted from volume data (obtained by MRI or CT devices, for instance) often contain significant amounts of noise, be it topological [Guskov and Wood 2001; Wood et al. 2002] or geometric [Taubin 1995; Desbrun et al. 1999], that must be removed before further processing.”
Surface light fields for 3D photography (2000, background): “(7) The sum ranges over the vertices of the s-times-subdivided octahedron (with Ns vertices, each corresponding to a direction !k), and ∆PL denotes the umbrella Laplacian [29].”
3D Reconstruction by Shadow Carving: Theory and Practical Evaluation (2007, unknown): “The postprocessing is carried out by low-pass filtering the surface using the algorithm proposed by Taubin [44][45].”
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing (2008, methodology): “, evolving a surface so as to progressively decrease an energy functional) is a common methodology in geometric processing with applications to spanning surface diffusion [11], denoising of scanned meshes [12], shape optimization and surface design [13], minimal surfaces [14], etc.”
Laplace-Beltrami eigenfunctions for deformation invariant shape representation (2007, unknown): “To mention a few, Taubin’s seminal paper [Tau95] proposes graph Laplacian with Tutte weights for surface fairing.”
Multiresolution signal processing for meshes (1999, methodology): “Taubin [26] presents a two step relaxation operator R = (I + μL)(I + λL), with μ andλ tuned to minimize shrinkage of the mesh.”
Anisotropic diffusion of surfaces and functions on surfaces (2003, methodology): “Apart from the linear finite element approach of Clarenz et al [11], we have also implemented Taubin’s signal processing approach (see [49]) and Desbrun et al’s implicit fairing approach (see [12]), for comparison with our approach.”
A review of algorithms for filtering the 3D point cloud (2017, unknown): “Based on Taubin’s method [70] that applied the Laplacian operators to filter the mesh, Linsen [71] developed a filtering operator containing three features: locality, non-shrinkage and including geometrical aspects.”
The ball-pivoting algorithm for surface reconstruction (1999, background): “The only change required in the algorithm to implement this refinement is an outer loop to move the active slice, and the addition of the instructions to unfreeze edges between lines 1–2 of figure 5.”
Graph convolutional networks: a comprehensive review (2019, background): “According to [62], the convolution in GCN [37] is related to Laplacian smoothing [63] and more convolution layers result in less distinguishable representations even for nodes from different clusters.”
Interactive and anisotropic geometry processing using the screened Poisson equation (2011, methodology): “…work has shown that the filtering of mesh geometry can be expressed in terms of the solution to a Poisson equation [Pinkall and Polthier 1993; Taubin 1995; Desbrun et al. 1999] and that geometry-awareness can be incorporated by anisotropically weighting the Laplace operator [Clarenz et al.…”
A generalized grid connectivity–based parameterization for subsurface flow model calibration (2011, methodology): “This is a direct consequence of the equivalence between the Laplacian eigenvectors and the DFT basis [Taubin, 1995; Mohar, 1997].”
Extracting dislocations and non-dislocation crystal defects from atomistic simulation data (2010, methodology): “For visualization purposes, one can smooth the defect surface as well as the dislocation lines using a volume/curvature-preserving low-pass filter algorithm [17].”