Hierarchical Representation of Time-Varying Volume Data with "4th-root-of-2" Subdivision and Quadrilinear B-Spline Wavelets

Multiresolution methods for representing data at multiple levels of detail are widely used for large-scale two- and three-dimensional data sets. We present a four-dimensional multiresolution approach for time-varying volume data. This approach supports a hierarchy with spatial and temporal scalability. The hierarchical data organization is based on /sup 4//spl radic/2 subdivision. The /sup n//spl radic/2-subdivision scheme only doubles the overall number of grid points in each subdivision step. This fact leads to fine granularity and high adaptivity, which is especially desirable in the spatial dimensions. For high-quality data approximation on each level of detail, we use quadrilinear B-spline wavelets. We present a linear B-spline wavelet lifting scheme based on /sup n//spl radic/2 subdivision to obtain narrow masks for the update rules. Narrow masks provide a basis for out-of-core data exploration techniques and view-dependent visualization of sequences of time steps.

[1]  Markus H. Gross,et al.  Compression Domain Volume Rendering for Distributed Environments , 1997, Comput. Graph. Forum.

[2]  Renato Pajarola,et al.  Topology preserving and controlled topology simplifying multiresolution isosurface extraction , 2000 .

[3]  B. C. Curtis,et al.  Very High Resolution Simulation of Compressible Turbulence on the IBM-SP System , 1999, ACM/IEEE SC 1999 Conference (SC'99).

[4]  Wim Sweldens,et al.  Lifting scheme: a new philosophy in biorthogonal wavelet constructions , 1995, Optics + Photonics.

[5]  Paolo Cignoni,et al.  Multiresolution modeling and visualization of volume data , 1997 .

[6]  Valerio Pascucci,et al.  Time critical adaptive re - finement and smoothing , 2000 .

[7]  Han-Wei Shen.  Isosurface extraction in time-varying fields using a temporal hierarchical index tree , 1998 .

[8]  Geert Uytterhoeven.  Wavelets: software and applications , 1999 .

[9]  Joseph M. Maubach,et al.  Local bisection refinement for $n$-simplicial grids generated by reflection , 2017 .

[10]  Günther Greiner,et al.  Hierarchical meshes for volume data , 1998, Proceedings. Computer Graphics International (Cat. No.98EX149).

[11]  Bernd Hamann,et al.  Wavelet representation of contour sets , 2001, Proceedings Visualization, 2001. VIS '01..

[12]  David Salesin,et al.  Wavelets for computer graphics - theory and applications , 1996, The Morgan Kaufmann series in computer graphics and geometric modeling.

[13]  Melanie Tory,et al.  4D space-time techniques: a medical imaging case study , 2001, Proceedings Visualization, 2001. VIS '01..

[14]  I. Daubechies,et al.  Non-separable bidimensional wavelets bases. , 1993 .

[15]  Rüdiger Westermann,et al.  Real-time exploration of regular volume data by adaptive reconstruction of isosurfaces , 1999, The Visual Computer.

[16]  J. Warren,et al.  Subdivision methods for geometric design , 1995 .

[17]  Bernd Hamann,et al.  An octree-based multiresolution approach supporting interactive rendering of very large volume data sets , 2001 .

[18]  Jelena Kovacevic,et al.  Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn , 1992, IEEE Trans. Inf. Theory.

[19]  T. J. Atherton,et al.  4D Volume Rendering with the Shear Warp Factorisation , 2000, 2000 IEEE Symposium on Volume Visualization (VV 2000).

[20]  J. T. Gray,et al.  Hierarchical Large-scale Volume Representation with \(\root 3 \of 2 \) Subdivision and Trivariate B-spline Wavelets , 2004 .

[21]  Charles D. Hansen,et al.  Isosurface extraction in time-varying fields using a Temporal Branch-on-Need Tree (T-BON) , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[22]  Bernd Hamann,et al.  Bicubic subdivision-surface wavelets for large-scale isosurface representation and visualization , 2000, Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145).

[23]  Arie E. Kaufman,et al.  Multiresolution tetrahedral framework for visualizing regular volume data , 1997 .

[24]  Valerio Pascucci,et al.  Hierarchical Large-scale Volume Representation with V'2 Subdivision and Trivariate B-spline Wavelets , 2004 .

[25]  Han-Wei Shen,et al.  Isosurface extraction in time-varying fields using a temporal hierarchical index tree , 1998, Proceedings Visualization '98 (Cat. No.98CB36276).

[26]  V. Pascucci,et al.  Time Critical Isosurface Refinement and Smoothing , 2000, 2000 IEEE Symposium on Volume Visualization (VV 2000).

[27]  Paolo Cignoni,et al.  Multiresolution Representation and Visualization of Volume Data , 1997, IEEE Trans. Vis. Comput. Graph..

[28]  W. Boehm,et al.  Bezier and B-Spline Techniques , 2002 .

[29]  Kwan-Liu Ma,et al.  High Performance Visualization of Time-Varying Volume Data over a Wide-Area Network , 2000, ACM/IEEE SC 2000 Conference (SC'00).

[30]  Jack Snoeyink,et al.  A prototype system for visualizing time-dependent volume data , 2001, SCG '01.

[31]  Jelena Kovacevic,et al.  Wavelet families of increasing order in arbitrary dimensions , 2000, IEEE Trans. Image Process..

[32]  Roni Yagel,et al.  Octree-based decimation of marching cubes surfaces , 1996, Proceedings of Seventh Annual IEEE Visualization '96.

[33]  D. Zorin,et al.  4-8 Subdivision , 2001 .

[34]  Zuowei Shen,et al.  Wavelets and pre-wavelets in low dimensions , 1992 .

[35]  Valerio Pascucci,et al.  Slow Growing Subdivision (SGS) in Any Dimension: Towards Removing the Curse of Dimensionality , 2002, Comput. Graph. Forum.

[36]  Thomas Ertl,et al.  The multilevel finite element method for adaptive mesh optimization and visualization of volume data , 1997 .

[37]  M. Bertram.  Multiresolution modeling for scientific visualization , 2000 .

[38]  Kwan-Liu Ma,et al.  A fast volume rendering algorithm for time-varying fields using a time-space partitioning (TSP) tree , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).