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Unformatted text preview: Reconstruction and Representation of 3D Objects with Radial Basis Functions J. C. Carr 1 , 2 R. K. Beatson 2 J. B. Cherrie 1 T. J. Mitchell 1 , 2 W. R. Fright 1 B. C. McCallum 1 T. R. Evans 1 1 Applied Research Associates NZ Ltd * 2 University of Canterbury (a) (b) Figure 1: (a) Fitting a Radial Basis Function (RBF) to a 438,000 pointcloud. (b) Automatic mesh repair using the biharmonic RBF. Abstract We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair in complete meshes. An objects 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, con sisting of millions of surface points, by a single RBFpreviously an impossible task. A greedy algorithm in the fitting process re duces the number of RBF centers required to represent a surface and results in significant compression and further computational advan tages. The energyminimisation characterisation of polyharmonic splines result in a smoothest interpolant. This scaleindependent characterisation is wellsuited to reconstructing surfaces from non uniformly sampled data. Holes are smoothly filled and surfaces smoothly extrapolated. We use a noninterpolating 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 realworld rangefinder data. CR Categories: I.3.5 [Computer Graphics]: Computational Ge ometry and Object ModelingCurve, surface, solid, and object representations; Keywords: Variational implicit surfaces, Radial Basis Function, RBF, mesh repair, pointcloud surfacing, surface reconstruction, geometry compression, solid modeling. * Applied Research Associates NZ Ltd, PO Box 3894, Christchurch, New Zealand. Email: [j.carr,j.cherrie,r.fright,b.mccallum]@aranz.com Web: www.aranz.com Dept. Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand, Email: r.beatson@math.canterbury.ac.nz 1 Introduction Interpolating incomplete meshes (holefilling) and reconstructing surfaces from pointclouds derived from 3D range scanners are ubiquitous problems in computer graphics and Computer Aided Design (CAD). Smoothly blending between surfaces and ensuring surfaces are manifold, and therefore manufacturable, are related problems in CAD. Similarly, smoothing and remeshing existing noisy surfaces are important problems in both CAD and computer graphics. These problems have mostly been considered indepen dent from one another and received much attention in the litera ture (see [ 8 ] and the references therein). In this paper we propose that the implicit representation of object surfaces with Radial Basis...
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 Spring '07
 WANG
 Machine Learning

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