On Visualization and Reconstruction from Non‐Uniform Point Sets using B‐splines

In this paper we present a novel framework for the visualization and reconstruction from non‐uniform point sets. We adopt a variational method for the reconstruction of 3D non‐uniform data to a uniform grid of chosen resolution. We will extend this reconstruction to an efficient multi‐resolution uni...

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Bibliographic Details
Published in:Computer graphics forum 2009-06, Vol.28 (3), p.1007-1014
Main Authors: Vucini, Erald, Moeller, Torsten, Groeller, M Eduard
Format: Article
Language:English
Subjects:
Computer graphics
Computer Graphics [I.3.5]: Computational Geometry and Object Modeling
Image Processing and Computer Vision [I.4.5]: Reconstruction
Image processing systems
Numerical Analysis [G.1.2]: Spline and piecewise polynomial approximation
Polynomials
Studies
Visualization
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Summary:In this paper we present a novel framework for the visualization and reconstruction from non‐uniform point sets. We adopt a variational method for the reconstruction of 3D non‐uniform data to a uniform grid of chosen resolution. We will extend this reconstruction to an efficient multi‐resolution uniform representation of the underlying data. Our multi‐resolution representation includes a traditional bottom‐up approach and a novel top‐down hierarchy for adaptive hierarchical reconstruction. Using a hybrid regularization functional we can improve the reconstruction results. Finally, we discuss further application scenarios and show rendering results to emphasize the effectiveness and quality of our proposed framework. By means of qualitative results and error comparisons we demonstrate superiority of our method compared to competing methods.
ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2009.01447.x