On certain configurations of points in Rn which are unisolvent for polynomial interpolation
Journal of Approximation Theory
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
On multivariate Lagrange interpolation
Mathematics of Computation
The approximation power of moving least-squares
Mathematics of Computation
Meshless parameterization and surface reconstruction
Computer Aided Geometric Design
Proceedings of the conference on Visualization '01
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
The domain of a point set surface
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Data-dependent MLS for faithful surface approximation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
MLS-based scalar fields over triangle meshes and their application in mesh processing
Proceedings of the 2009 symposium on Interactive 3D graphics and games
Technical Section: Variational Bayesian noise estimation of point sets
Computers and Graphics
An adaptive moving least squares method for non-uniform points set fitting
ACACOS'10 Proceedings of the 9th WSEAS international conference on Applied computer and applied computational science
Adaptive moving least squares for scattering points fitting
WSEAS Transactions on Computers
The theory and application of an adaptive moving least squares for non-uniform samples
WSEAS Transactions on Computers
A survey of methods for moving least squares surfaces
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
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In recent years, the moving least-square (MLS) method has been extensively studied for approximation and reconstruction of surfaces. The MLS method involves local weighted least-squares polynomial approximations, using a fast decaying weight function. The local approximating polynomial may be used for approximating the underlying function or its derivatives. In this paper we consider locally supported weight functions, and we address the problem of the optimal choice of the support size. We introduce an error formula for the MLS approximation process which leads us to developing two tools: One is a tight error bound independent of the data. The second is a data dependent approximation to the error function of the MLS approximation. Furthermore, we provide a generalization to the above in the presence of noise. Based on the above bounds, we develop an algorithm to select an optimal support size of the weight function for the MLS procedure. Several applications such as differential quantities estimation and up-sampling of point clouds are presented. We demonstrate by experiments that our approach outperforms the heuristic choice of support size in approximation quality and stability.