Lower bounds for norms of inverses of interpolation matrices for radial basis functions
Journal of Approximation Theory
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
Radial basis functions for the multivariate interpolation of large scattered data sets
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Smooth surface reconstruction from noisy range data
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Edge-driven Image Interpolation using Adaptive Anisotropic Radial Basis Functions
Journal of Mathematical Imaging and Vision
Error bounds for anisotropic RBF interpolation
Journal of Approximation Theory
Least-squares hermite radial basis functions implicits with adaptive sampling
Proceedings of Graphics Interface 2013
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In this paper we deal with the problem of reconstructing surfaces from unorganized sets of points, while capturing the significant geometry details of the modelled surface, such as edges, flat regions, and corners. This is obtained by exploiting the good approximation capabilities of the radial basis functions (RBF), the local nature of the method proposed in [1], and introducing information on shape features and data anisotropies detected from the given surface points. The result is a shape-preserving reconstruction, given by a weighted combination of locally aniso tropic interpolants. For each local interpolant the anisotropy is obtained by replacing the Euclidean norm with a suitable metric which takes into account the local distribution of the points. Thus hyperellipsoid basis functions, named anisotropic RBFs, are defined. Results from the application of the method to the reconstruction of object surfaces in @?^3 are presented, confirming the effectiveness of the approach.