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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 M.-S. Kim (Ed.), Shape Modeling International 2003 (pp. 153-161). Los Alamitos, USA: IEEE.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2C18-9 Version Permalink: https://hdl.handle.net/21.11116/0000-000F-0C2A-6
Genre: Conference Paper

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

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Free keywords: -
 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
DOI: 10.1109/SMI.2003.1199611
BibTex Citekey: Ohtake-et-al_SMI03
 Degree: -

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Title: 2003 International Conference in Shape Modeling
Place of Event: Seoul, Korea
Start-/End Date: 2003-05-12 - 2003-05-16

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Title: Shape Modeling International 2003
  Abbreviation : SMI 2003
Source Genre: Proceedings
 Creator(s):
Kim, Myung-Soo1, Editor
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: Los Alamitos, USA : IEEE
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 153 - 161 Identifier: ISBN: 978-0-7695-1909-8