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A Multi-scale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45141

Ohtake,  Yutaka
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44112

Belyaev,  Alexander
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45449

Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

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Zitation

Ohtake, Y., Belyaev, A., & Seidel, H.-P. (2003). A Multi-scale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions. In Shape Modeling International 2003 (SMI 2003) (pp. 153-161). Los Alamitos, USA: IEEE.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-2C18-9
Zusammenfassung
In this paper, we propose a hierarchical approach to 3D scattered data interpolation with compactly supported basis functions. Our numerical experiments suggest that the approach integrates the best aspects of scattered data fitting with locally and globally supported basis functions. Employing locally supported functions leads to an efficient computational procedure, while a coarse-to-fine hierarchy makes our method insensitive to the density of scattered data and allows us to restore large parts of missed data. Given a point cloud distributed along a surface, we first use spatial down sampling to construct a coarse-to-fine hierarchy of point sets. Then we interpolate the sets starting from the coarsest level. We interpolate a point set of the hierarchy, as an offsetting of the interpolating function computed at the previous level. Fig.\,\ref{risu_multi} shows an original point set (the leftmost image) and its coarse-to-fine hierarchy of interpolated sets. According to our numerical experiments, the method is essentially faster than the state-of-art scattered data approximation with globally supported RBFs \cite{rbf} and much simpler to implement.