Reconstruction and representation of 3D objects with radial basis functions

By J. Carr, R. Beatson, J. Cherrie, T. Mitchell, W. R. Fright, B. C. McCallum, T. R. Evans. 2001

2,195 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

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Citations in the corpus

DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation (2019, methodology): “Classical surface reconstruction methods complete a point cloud into a dense surface by fitting radial basis function (RBF) [11] to approximate implicit surface functions, or by casting the reconstruction from oriented point clouds as a Poisson problem [32].”
Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception Age (2016, neutral): “functions [39], signed-distance function [56], and truncated”
A robust hole-filling algorithm for triangular mesh (2007, methodology): “[1] used radial basis function to construct an implicit”
3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models (2023, background): “In this way, we can represent the continuous function O(·) as a set of 𝑀 points including their corresponding weights, (cid:8) (cid:9) However, in order to retain the details of a 3d shape, we often need a very large number of points ( e.g ., 𝑀 = 80 , 000 in [Carr et al. 2001]).”
Direct visibility of point sets (2007, methodology): “One way to compute visibility of a point cloud is to reconstruct the surface [Hoppe et al. 1992; Bernardini et al. 1999; Curless and Levoy 1996; Carr et al. 2001; Amenta et al. 2001; Amenta et al. 2002; Amenta and Kil 2004; Fleishman et al. 2005] and determine visibility on the reconstructed triangu”
PaMIR: Parametric Model-Conditioned Implicit Representation for Image-Based Human Reconstruction (2020, background): “Implicit surface representations [43], [44], on the other hand, overcome these challenges and demonstrate the best ﬂexibility and expressiveness for topology representation.”
Capturing tree crown formation through implicit surface reconstruction using airborne lidar data (2009, methodology): “Radial basis functions (RBFs) were used, as were implicit functions of an isosurface (Bishop, 2005; Carr et al., 1997, 2001, 2003; Wendland, 2005), and were used for classification to find the shortest path in a neural network (Bishop, 2005).”
Advances in Neural Rendering (2021, methodology): “Radial basis function networks are such mixture models and can be used as an approximator for both, implicit surface and volume functions [CBC ∗ 01a].”
Delaunay Triangulation Based Surface Reconstruction: Ideas and Algorithms (2004, methodology): “, level set methods [HOF01], radial basis function based methods [CBC01] and moving least squares methods [ABCO01].”
From Point Clouds to Mesh Using Regression (2017, methodology): “…methods parametrize the problem in terms of basis functions and formulate the optimization problem, which either ﬁts the point cloud data [4], or minimizes the difference between the gradient of indicator function of surface interior and input normals of the point in the point cloud [12].”
Interpolating and approximating implicit surfaces from polygon soup (2004, methodology): “, 1995], [Turk and O’Brien, 1999], [Carr et al., 2001], and [Turk and O’Brien, 2002] the function is represented using globally supported radial splines.”