A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Journal of Approximation Theory
Fast Evaluation of Radial Basis Functions: Moment-Based Methods
SIAM Journal on Scientific Computing
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Spectral processing of point-sampled geometry
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods
SIAM Journal on Scientific Computing
Fast Evaluation of Radial Basis Functions: Methods for Generalized Multiquadrics in $\RR^\protectn$
SIAM Journal on Scientific Computing
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Implicit Surfaces that Interpolate
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
A comparison and evaluation of interpolation methods for visualising discrete 2D survey data
APVis '04 Proceedings of the 2004 Australasian symposium on Information Visualisation - Volume 35
Implicit Meshes for Surface Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Reconstructing multi-scale variational partition of unity implicit surfaces with attributes
Graphical Models - Special issue on SMI 2004
Rapid prototyping 3D objects from scanned measurement data
Image and Vision Computing
Mesh deformation based on radial basis function interpolation
Computers and Structures
Efficient Surface Reconstruction using Generalized Coulomb Potentials
IEEE Transactions on Visualization and Computer Graphics
Clip Art Rendering of Smooth Isosurfaces
IEEE Transactions on Visualization and Computer Graphics
ICCOMP'05 Proceedings of the 9th WSEAS International Conference on Computers
Fast PDE approach to surface reconstruction from large cloud of points
Computer Vision and Image Understanding
Implicit Surface Reconstruction with an Analogy of Polar Field Model
PSIVT '09 Proceedings of the 3rd Pacific Rim Symposium on Advances in Image and Video Technology
Spectral moving removal of non-isolated surface outlier clusters
Computer-Aided Design
Photometric and geometric restoration of document images using inpainting and shape-from-shading
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Surface reconstruction from point clouds by transforming the medial scaffold
Computer Vision and Image Understanding
A hierarchical sampling approach for polygonizing variational implicit surfaces
Computers and Graphics
Efficient surface reconstruction from noisy data using regularized membrane potentials
IEEE Transactions on Image Processing
Shape preserving surface reconstruction using locally anisotropic radial basis function interpolants
Computers & Mathematics with Applications
Out-of-core MLS reconstruction
CGIM '07 Proceedings of the Ninth IASTED International Conference on Computer Graphics and Imaging
A system for reconstruction of solid models from large point clouds
Machine Graphics & Vision International Journal
Toward an automatic hole characterization for surface correction
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part I
SMI 2011: Full Paper: Harmonic point cloud orientation
Computers and Graphics
Proceedings of the 2011 SIGGRAPH Asia Conference
CAD and mesh repair with Radial Basis Functions
Journal of Computational Physics
Surface reconstruction from large point clouds using virtual shared memory manager
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Journal of Computational Physics
Smooth Shape-Aware Functions with Controlled Extrema
Computer Graphics Forum
Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs
Journal of Computational Physics
Efficient surface reconstruction from noisy data using regularized membrane potentials
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
Surface reconstruction from noisy point clouds using coulomb potentials
VG'07 Proceedings of the Sixth Eurographics / Ieee VGTC conference on Volume Graphics
SMI 2013: Efficient computation of constrained parameterizations on parallel platforms
Computers and Graphics
Personal and Ubiquitous Computing
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This paper shows that scattered range data can be smoothed at low cost by fitting a Radial Basis Function (RBF) to the data and convolving with a smoothing kernel (low pass filtering). The RBF exactly describes the range data and interpolates across holes and gaps. The data is smoothed during evaluation of the RBF by simply changing the basic function. The amount of smoothing can be varied as required without having to fit a new RBF to the data. The key feature of our approach is that it avoids resampling the RBF on a fine grid or performing a numerical convolution. Furthermore, the computation required is independent of the extent of the smoothing kernel, i.e., the amount of smoothing. We show that particular smoothing kernels result in the applicability of fast numerical methods. We also discuss an alternative approach in which a discrete approximation to the smoothing kernel achieves similar results by adding new centres to the original RBF during evaluation. This approach allows arbitrary filter kernels, including anisotropic and spatially varying filters, to be applied while also using established fast evaluation methods. We illustrate both techniques with LIDAR laser scan data and noisy synthetic data.