IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Efficient numerical methods in non-uniform sampling theory
Numerische Mathematik
Multiresolution techniques for interactive texture-based volume visualization
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Image interpolation and resampling
Handbook of medical imaging
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Proceedings of the conference on Visualization '01
3D Scattered Data Approximation with Adaptive Compactly Supported Radial Basis Functions
SMI '04 Proceedings of the Shape Modeling International 2004
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
A Frequency-Sensitive Point Hierarchy for Images and Volumes
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
IEEE Transactions on Visualization and Computer Graphics
Efficient reconstruction from non-uniform point sets
The Visual Computer: International Journal of Computer Graphics
Interactive volume rendering of large sparse data sets using adaptive mesh refinement hierarchies
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Image Processing
Interactively visualizing procedurally encoded scalar fields
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
On the search of optimal reconstruction resolution
Pattern Recognition Letters
Enhancing the reconstruction from non-uniform point sets using persistence information
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
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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.