NDLI: Reconstruction of volume data with quadratic super splines

Content Provider	IEEE Xplore Digital Library
Author	Rossl, C. Seidel, H.-P. Zeilfeider, F. Nurnberger, G.
Copyright Year	1995
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 nonstandard 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 isosurface for ray-casting. Moreover, the optimal approximation properties of the derivatives allow us to simply sample the necessary gradients directly from the polynomial pieces of the splines. Our results confirm the efficiency of the quasiinterpolating method and demonstrate high visual quality for rendered isosurfaces.
Sponsorship	IEEE Computer Society Technical Committee on Computer Graphics IEEE Computer Society
Page Count	13
File Size	2673240
Starting Page	397
Ending Page	409
File Format	PDF
ISSN	10772626
Volume Number	10
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2004-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Data visualization Image reconstruction Isosurfaces Biomedical imaging Density functional theory Computed tomography Magnetic resonance imaging Numerical simulation Mesh generation ray-casting. Spline and piecewise polynomial approximation trivariate splines volume visualization
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Signal Processing Computer Vision and Pattern Recognition Software

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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