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2012 | OriginalPaper | Chapter

17. Volumetric Methods for Surface Reconstruction and Manipulation

Authors : Jakob Andreas Bærentzen, Jens Gravesen, François Anton, Henrik Aanæs

Published in: Guide to Computational Geometry Processing

Publisher: Springer London

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Abstract

The RBF method (introduced in the previous chapter) involves solving a dense linear system. For huge numbers of points, this becomes too computationally demanding. Like the RBF method, volumetric methods for reconstruction produce an implicit representation of the reconstructed surface, but instead of solving a linear system, these methods proceed by solving a partial differential equation discretized on a 3D grid. Volumetric reconstruction algorithms become rather simple: essentially it boils down to repeatedly smoothing data on a 3D grid while keeping the values at some grid points constant. Having discussed the basic approach, we also explain how normals for point data can be estimated, since point normal estimates are generally required for volumetric reconstruction.
This chapter also covers the Level Set Method which, again, is based on the implicit representation of 3D surface using discrete 3D grids. However the LSM allows us to deform a surface. Distance fields are typically used as the input to the LSM and they have numerous other uses, so this chapter also covers the construction of 3D distance fields from triangle meshes.

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previous chapter Surface Reconstruction using Radial Basis Functions
next chapter Isosurface Polygonization
Footnotes
1
We say ‘similar’ because the blurring is done a bit differently, but the principle is the same.
 
2
Using MeshLab’s implementation: http://​meshlab.​sourceforge.​net/​.
 
3
For simplicity and without loss of generality, we will assume in the following that unit time step is used and that the grid spacing is unit.
 
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Erleben, K., Dohlmann, H.: Signed distance fields using single-pass GPU scan conversion of tetrahedra. In: Nguyen, H. (ed.) GPU Gems 3, pp. 741–763. Addison–Wesley, Upper Saddle River (2008)
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Metadata
Title
Volumetric Methods for Surface Reconstruction and Manipulation
Authors
Jakob Andreas Bærentzen
Jens Gravesen
François Anton
Henrik Aanæs
Copyright Year
2012
Publisher
Springer London
Book
Guide to Computational Geometry Processing

Print ISBN: 978-1-4471-4074-0

Electronic ISBN: 978-1-4471-4075-7

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-1-4471-4075-7_17

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