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Reconstruction and Representation of 3D Objects with Radial Basis Functions (2001)
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| Venue: | Computer Graphics (SIGGRAPH ’01 Conf. Proc.), pages 67–76. ACM SIGGRAPH |
| Citations: | 504 - 1 self |
BibTeX
@INPROCEEDINGS{Carr01reconstructionand,
author = {J. C. Carr and R. K. Beatson and J. B. Cherrie and T. J. Mitchell and W. R. Fright and B. C. McCallum and T. R. Evans},
title = {Reconstruction and Representation of 3D Objects with Radial Basis Functions},
booktitle = {Computer Graphics (SIGGRAPH ’01 Conf. Proc.), pages 67–76. ACM SIGGRAPH},
year = {2001},
pages = {67--76},
publisher = {Springer}
}
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Abstract
We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from point-cloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs allow us to model large data sets, consisting of millions of surface points, by a single RBF---previously an impossible task. A greedy algorithm in the fitting process reduces the number of RBF centers required to represent a surface and results in significant compression and further computational advantages. The energy-minimisation characterisation of polyharmonic splines result in a "smoothest" interpolant. This scale-independent characterisation is well-suited to reconstructing surfaces from nonuniformly sampled data. Holes are smoothly filled and surfaces smoothly extrapolated. We use a non-interpolating approximation when the data is noisy. The functional representation is in effect a solid model, which means that gradients and surface normals can be determined analytically. This helps generate uniform meshes and we show that the RBF representation has advantages for mesh simplification and remeshing applications. Results are presented for real-world rangefinder data.
Keyphrases
radial basis function significant compression scale-independent characterisation rbf representation incomplete mesh greedy algorithm polyharmonic radial basis function large data set polyharmonic spline result solid model surface data real-world rangefinder data smoothest interpolant point-cloud data fast method remeshing application surface point surface normal fitting process rbf center impossible task energy-minimisation characterisation single rbf functional representation uniform mesh computational advantage zero set non-interpolating approximation mesh simplification manifold surface
