Reconstruction and representation of 3D objects with radial basis functions

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Reconstruction and representation of 3D objects with radial basis functions

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International Conference on Computer Graphics and Interactive Techniques archive
Proceedings of the 28th annual conference on Computer graphics and interactive techniques table of contents

Pages: 67 - 76

Year of Publication: 2001

ISBN:1-58113-374-X

Authors

J. C. Carr	Applied Research Associates NZ Ltd, University of Canterbury
R. K. Beatson	University of Canterbury
J. B. Cherrie	Applied Research Associates NZ Ltd
T. J. Mitchell	Applied Research Associates NZ Ltd, University of Canterbury
W. R. Fright	Applied Research Associates NZ Ltd
B. C. McCallum	Applied Research Associates NZ Ltd
T. R. Evans	Applied Research Associates NZ Ltd

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SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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ACM New York, NY, USA

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Downloads (6 Weeks): 53, Downloads (12 Months): 498, Citation Count: 146

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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 non-uniformly 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.

REFERENCES

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INDEX TERMS

Primary Classification:
I. Computing Methodologies
I.3 COMPUTER GRAPHICS
I.3.5 Computational Geometry and Object Modeling

General Terms:
Design, Experimentation, Performance

Keywords:
RBF, Radial Basis Function, geometry compression, mesh repair, point-cloud surfacing, solid modeling, surface reconstruction, variational implicit surfaces

REVIEW

"Martin L. Brady : Reviewer"

An application of polyharmonic radial basis functions (RBFs) to the modeling of 3D surfaces is described. The zero set of the RBF implicitly defines a surface that passes through a set of data points, and the RBF smoothly interpolates between thes more...

Collaborative Colleagues:

J. C. Carr: colleagues

R. K. Beatson: colleagues

J. B. Cherrie: colleagues

T. J. Mitchell: colleagues

W. R. Fright: colleagues

B. C. McCallum: colleagues

T. R. Evans: colleagues