surface reconstruction using radial basis functions michael kunerth, philipp omenitsch and georg...
TRANSCRIPT
Surface Reconstruction using Radial Basis Functions
Michael Kunerth, Philipp Omenitsch andGeorg Sperl
1 Institute of Computer Graphicsand Algorithms
Vienna University of Technology
2 <insert 2nd affiliation (institute) here>
<insert 2nd affiliation(university) here>
3 <insert 3rd affiliation (institute) here>
<insert 3rd affiliation (university) here>
Outline
Problem Description
RBF Surface Reconstruction
Methods:Surface Reconstruction Based on Hierarchical Floating Radial Basis Functions
Least-Squares Hermite Radial Basis Functions Implicits with Adaptive Sampling
Voronoi-based Reconstruction
Adaptive Partition of Unity
Conclusion
2M. Kunerth, P. Omenitsch, G. Sperl
Problem Description
3D scanners produce point clouds
For CG surface representation needed
Level set of implicit function
Mesh extraction (e.g. marching cubes)
Surface reconstruction with radial basis functions
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Radial Basis Functions
Value depends only on distance from center
Function satisfies
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RBF Surface Reconstruction
Surface as zero level set of implicit function
Weighted sum of scaled/translated radial basis functions
Interpolation vs. approximation
Surface extraction
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RBF Surface Reconstruction cont‘d.
Gradients/normals to avoid trivial solutions
Center reduction (redundancy)
Center positions (noise)
Partition of unity
Globally supported / compactly supported RBF
Hierarchical representations
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Hierarchical Floating RBFs
Avoid trivial solution by fitting gradients to normal vectors
Assume a small number of centers
Center positions viewed as own optimization problem
Radial function: inverse quadratic function
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Hierarchical Floating RBFs cont‘d.
Floating centers: iterative process of refining initial guess of centers
Partition of unityOctree with multiple levels approximating residual errors
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Least-Squares Hermite RBF
Fit gradients to normals
Subset of points used as centers
Radial function: triharmonic function
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Least-Squares Hermite RBF cont‘d.
Adaptive greedy sampling of centersChoose random first center
Choose next center maximizing function residual and gradient difference to nearest already chosen center using the previous set‘s fitted function
Partition of unityOverlapping boxes
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Least-Squares Hermite RBF cont‘d.
Pros:Well distributed centers
Preserve local features
Accurate with few centers
Cons:Slow / high computational cost
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Voronoi-based Reconstruction
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Adaptive Partion of Unity
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Conclusion
RBF surface reconstruction methods
Main differences:Which centers should be used?
How to optimize existing centers?
different distance functions
Smoothing: less noise vs. more detail
Tradeoff: speed vs. quality
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Sources
Y Ohtake, A Belyaev, HP Seidel 3D scattered data approximation with adaptive compactly supported radial basis functions Shape Modeling Applications, 2004. Proceedings
Samozino M., Alexa M., Alliez P., Yvinec M.: Reconstruction with Voronoi Centered Radial Basis Functions. Eurographics Symposium on Geometry Processing (2006)
Ohtake Y., Belyaev A., Seidel H.-P.: Sparse Surface Reconstruction with Adaptive Partition of Unity and Radial Basis Functions. Graphical Models (2006)
Poranne R., Gotsman C., Keren D.: 3D Surface Reconstruction Using a Generalized Distance Function. Computer Graphics Forum (2010)
Süßmuth J., Meyer Q., Greiner G.: Surface Reconstruction Based on Hierarchical Floating Radial Basis Functions. Computer Graphiks Forum (2010)
Harlen Costa Batagelo and João Paulo Gois. 2013. Least-squares hermite radial basis functions implicits with adaptive sampling. In Proceedings of the 2013 Graphics Interface Conference (GI '13)
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