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

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.

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 Creators:
Ohtake, Yutaka1, Author           
Belyaev, Alexander1, Author           
Seidel, Hans-Peter1, Author           
Kim, Myung-Soo, Editor
Affiliations:
1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              

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 Abstract: 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.

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Language(s): eng - English
 Dates: 2004-06-302003
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 201818
Other: Local-ID: C125675300671F7B-87B4CF5FB4E9EE9AC1256CB7006C0EC9-smi03obs
 Degree: -

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Title: SMI 2003
Place of Event: Seoul, Korea
Start-/End Date: 2003-05-12 - 2003-05-16

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Title: Shape Modeling International 2003 (SMI 2003)
Source Genre: Proceedings
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Publ. Info: Los Alamitos, USA : IEEE
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 153 - 161 Identifier: -