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  Reconstruction of Volume Data with Quadratic Super Splines

Rössl, C., Zeilfelder, F., Nürnberger, G., & Seidel, H.-P. (2004). Reconstruction of Volume Data with Quadratic Super Splines. IEEE Transactions on Visualization and Computer Graphics, 10, 397-409.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2B18-2 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2B19-F
Genre: Journal Article

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rzns_qss_tvcg.pdf (Any fulltext), 8MB
 
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Rössl, Christian1, Author           
Zeilfelder, Frank1, Author           
Nürnberger, Günther, Author
Seidel, Hans-Peter1, Author           
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1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              

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 Abstract: We propose a new approach to reconstruct nondiscrete models from gridded volume samples. As a model, we use quadratic trivariate super splines on a uniform tetrahedral partition. We discuss the smoothness and approximation properties of our model and compare to alternative piecewise polynomial constructions. We observe as a non-standard phenomenon that the derivatives of our splines yield optimal approximation order for smooth data, while the theoretical error of the values is nearly optimal due to the averaging rules. Our approach enables efficient reconstruction and visualization of the data. As the piecewise polynomials are of the lowest possible total degree two, we can efficiently determine exact ray intersections with an iso-surface for ray-casting. Moreover, the optimal approximation properties of the derivatives allow to simply sample the necessary gradients directly from the polynomial pieces of the splines. Our results confirm the efficiency of the quasi-interpolating method and demonstrate high visual quality for rendered isosurfaces.

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Language(s): eng - English
 Dates: 2005-05-242004
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: eDoc: 231861
Other: Local-ID: C125675300671F7B-136B570DDA9525FAC1256E5300465D7C-rzns:qss:2004
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Title: IEEE Transactions on Visualization and Computer Graphics
Source Genre: Journal
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Pages: - Volume / Issue: 10 Sequence Number: - Start / End Page: 397 - 409 Identifier: -