Subscribe

Issue No.03 - March (2012 vol.18)

pp: 421-433

Yun Jang , ETH Zurich, Zurich and Sejong University, Seoul

David S. Ebert , Purdue University, West Lafayette

Kelly Gaither , The University of Texas at Austin, Austin

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2011.54

ABSTRACT

In many scientific simulations, the temporal variation and analysis of features are important. Visualization and visual analysis of time series data is still a significant challenge because of the large volume of data. Irregular and scattered time series data sets are even more problematic to visualize interactively. Previous work proposed functional representation using basis functions as one solution for interactively visualizing scattered data by harnessing the power of modern PC graphics boards. In this paper, we use the functional representation approach for time-varying data sets and develop an efficient encoding technique utilizing temporal similarity between time steps. Our system utilizes a graduated approach of three methods with increasing time complexity based on the lack of similarity of the evolving data sets. Using this system, we are able to enhance the encoding performance for the time-varying data sets, reduce the data storage by saving only changed or additional basis functions over time, and interactively visualize the time-varying encoding results. Moreover, we present efficient rendering of the functional representations using binary space partitioning tree textures to increase the rendering performance.

INDEX TERMS

Basis functions, functional representation, time-varying data, volume rendering.

CITATION

Yun Jang, David S. Ebert, Kelly Gaither, "Time-Varying Data Visualization Using Functional Representations",

*IEEE Transactions on Visualization & Computer Graphics*, vol.18, no. 3, pp. 421-433, March 2012, doi:10.1109/TVCG.2011.54REFERENCES

- [1] F.F. Bernardon, S.P. Callahan, J.L.D. Comba, and C.T. Silva, “Interactive Volume Rendering of Unstructured Grids with Time-Varying Scalar Fields,”
Proc. Eurographics Symp. Parallel Graphics and Visualization, pp. 51-58, 2006.- [2] F.F. Bernardon, S.P. Callahan, J.L.D. Comba, and C.T. Silva, “An Adaptive Framework for Visualizing Unstructured Grids with Time-Varying Scalar Fields,”
J. Parallel Computing, vol. 33, no. 6, pp. 391-405, 2007.- [3] M. Bertram, M.A. Duchaineau, B. Hamann, and K.I. Joy, “Bicubic Subdivision-Surface Wavelets for Large-Scale Isosurface Representation and Visualization,”
Proc. IEEE 11th Visualization Conf., pp. 389-396, Oct. 2000.- [4] J.C. Carr, R.K. Beatson, J.B. Cherrie, T.J. Mitchell, W.R. Fright, B.C. McCallum, and T.R. Evans, “Reconstruction and Representation of 3D Objects with Radial Basis Functions,”
Proc. ACM SIGGRAPH, pp. 67-76, Aug. 2001.- [5] J. Chen, D. Silver, and M. Parashar, “Real Time Feature Extraction and Tracking in a Computational Steering Environment,”
Proc. High Performance Computing Symp. HPC '03, Soc. for Modeling and Simulation Int'l, pp. 155-160, 2003.- [6] I. Daubechies, I. Guskov, P. Schröder, and W. Sweldens, “Wavelets on Irregular Point Sets,”
Philosophical Trans. Royal Soc. A: Math., Physical and Eng. Sciences, vol. 357, no. 1760, pp. 2397-2413, 1999.- [7] W. de Leeuw and R. van Liere, “BM3D: Motion Estimation in Time Dependent Volume Data,”
Proc. IEEE Visualization (VIS), pp. 427-434, 2002.- [8] W. de Leeuw and R. van Liere, “MCMR: A Fluid View on Time Dependent Volume Data,”
VISSYM '03: Proc. Symp. Data Visualisation, pp. 149-156, 2003.- [9] R. Franke and H. Hagen, “Least Squares Surface Approximation Using Multiquadrics and Parametric Domain Distortion,”
Computer Aided Geometric Design, vol. 16, no. 3, pp. 177-196, Mar. 1999.- [10] R. Grosso and T. Ertl, “Mesh Optimization and Multilevel Finite Element Approximations,” H.-C. Hege and K. Polthier, eds.,
Proc. Visualization and Math., pp. 19-30, 1998.- [11] M. Hadwiger, C. Sigg, H. Scharsach, K. Bühler, and M.H. Gross, “Real-Time Ray-Casting and Advanced Shading of Discrete Isosurfaces,”
Computer Graphics Forum, vol. 24, no. 3, pp. 303-312, 2005.- [12] I. Ihm and S. Park, “Wavelet-Based 3D Compression Scheme for Interactive Visualization of Very Large Volume Data,”
Computer Graphics Forum, vol. 18, no. 1, pp. 3-15, 1999.- [13] Y. Jang, R.P. Botchen, A. Lauser, D.S. Ebert, K.P. Gaither, and T. Ertl, “Enhancing the Interactive Visualization of Procedurally Encoded Multifield Data with Ellipsoidal Basis Functions,”
Computer Graphics Forum, vol. 25, no. 3, pp. 587-596, 2006.- [14] Y. Jang, M. Weiler, M. Hopf, J. Huang, D.S. Ebert, K.P. Gaither, and T. Ertl, “Interactively Visualizing Procedurally Encoded Scalar Fields,”
Proc. EG/IEEE TCVG Symp. Visualization (VisSym '04), pp. 35-44, 2004.- [15] L. Jiang, H. Liu, M. Parashar, and D. Silver,
Rule-Based Visualization in a Computational Steering Collaboratory, Computational Science—ICCS 2004. Springer Berlin/Heidelberg, 2005.- [16] E.J. Kansa, “Volumetric Radial Basis Functions Methods Applied to Gas Dynamics,”
Proc. Int'l Workshop MeshFree Methods, 2003.- [17] E.J. Kansa, H. Power, G.E. Fasshauer, and L. Ling, “A Volumetric Integral Radial Basis Function Method for Time-Dependent Partial Differential Equations. I. Formulation,”
Eng. Analysis with Boundary Elements, vol. 28, no. 10, pp. 1191-1206, 2004.- [18] C.-L. Ko, H.-S. Liao, T.-P. Wang, K.-W. Fu, C.-Y. Lin, and J.-H. Chuang, “Multi-Resolution Volume Rendering of Large Time-Varying Data Using Video-Based Compression,”
Proc. IEEE Pacific Visualization Symp., pp. 135-142, 2008.- [19] C. Ledergerber, G. Guennebaud, M. Meyer, M. Bacher, and H. Pfister, “Volume MLS Ray Casting,”
IEEE Trans. Visualization and Computer Graphics, vol. 14, no. 6, pp. 1539-1546, 2008.- [20] S. Lefebvre, S. Hornus, and F. Neyret, “Octree Textures on the GPU,”
GPU Gems 2—Programming Techniques for High-Performance Graphics and General-Purpose Computation, M. Pharr, ed., chapter 37, pp. 595-613, Addison Wesley, Mar. 2005.- [21] E.B. Lum, K.L. Ma, and J. Clyne, “Texture Hardware Assisted Rendering of Time-Varying Volume Data,”
Proc. Conf. Visualization '01, pp. 263-270, 2001.- [22] K.-L. Ma and H. Shen, “Compression and Accelerated Rendering of Time-Varying Volume Data,”
Proc. Workshop Computer Graphics and Virtual Reality, 2000.- [23] K. Madsen, H.B. Nielsen, and O. Tingleff, “Methods for Non-Linear Least Squares Problems,” July 1999.
- [24] B.S. Morse, T.S. Yoo, P. Rheingans, D.T. Chen, and K.R. Subramanian, “Interpolating Implicit Surfaces from Scattered Surface Data Using Compactly Supported Radial Basis Functions,”
Proc. Int'l Conf. Shape Modeling and Applications (SMI '01), pp. 89-98, May 2001.- [25] C. Muelder and K.-L. Ma, “Interactive Feature Extraction and Tracking by Utilizing Region Coherency,”
Proc. IEEE Pacific Visualization Symp. (PacificVis '09), pp. 17-24, 2009.- [26] S. Muraki, “Approximation and Rendering of Volume Data Using Wavelet Transforms,”
Proc. IEEE Conf. Visualization (Visualization '92), pp. 21-28, 1992.- [27] K.G. Nguyen and D. Saupe, “Rapid High Quality Compression of Volume Data for Visualization,”
Computer Graphics Forum, vol. 20, no. 3, pp. 49-56, 2001.- [28] G.M. Nielson, “Scattered Data Modeling,”
IEEE Computer Graphics and Applications, vol. 13, no. 1, pp. 60-70, Jan. 1993.- [29] G.M. Nielson, T.A. Foley, B. Hamann, and D. Lane, “Visualizing and Modeling Scattered Multivariate Data,”
IEEE Computer Graphics and Applications, vol. 11, no. 3, pp. 47-55, May 1991.- [30] S. Park, L. Linsen, O. Kreylos, J.D. Owens, and B. Hamann, “A Framework for Real-Time Volume Visualization of Streaming Scattered Data,”
Proc. 10th Int'l Fall Workshop Vision, Modeling, and Visualization, pp. 225-232, Nov. 2005.- [31] F. Pighin, J.M. Cohen, and M. Shah, “Modeling and Editing Flows Using Advected Radial Basis Functions,”
Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 223-232, 2004.- [32] A.L. Rocca, A.H. Rosales, and H. Power, “Radial Basis Function Hermite Collocation Approach for the Solution of Time Dependent Convection Diffusion Problems,”
Eng. Analysis with Boundary Elements, vol. 29, no. 4, pp. 359-370, 2005.- [33] V.V. Savchenko, A.A. Pasko, O.G. Okunev, and T.L. Kunii, “Function Representation of Solids Reconstructed from Scattered Surface Points and Contours,”
Computer Graphics Forum, vol. 14, no. 4, pp. 181-188, 1995.- [34] H.-W. Shen, L.-J. Chiang, and K.-L. Ma, “A Fast Volume Rendering Algorithm for Time-Varying Fields Using a Time-Space Partitioning (TSP) Tree,”
Proc. IEEE Conf. Visualization '99, pp. 371-377, 1999.- [35] H.-W. Shen and C.R. Johnson, “Differential Volume Rendering: A Fast Volume Visualization Technique for Flow Animation,”
Proc. IEEE Conf. Visualization '94, pp. 180-187, 1994.- [36] Z. Shi, Y. Tamura, and T. Ozaki, “Nonlinear Time Series Modelling with the Radial Basis Functions-Based State-dependent Autoregressive Model,”
Int'l J. Systems Science, vol. 30, no. 7, pp. 717-727, 1999.- [37] D. Silver and X. Wang, “Tracking and Visualizing Turbulent 3D Features,”
IEEE Trans. Visualization and Computer Graphics, vol. 3, no. 2, pp. 129-141, Apr.-June 1997.- [38] D. Silver and X. Wang, “Tracking Scalar Features in Unstructured Data Sets,”
Proc. Visualization '98, pp. 79-86, 1998.- [39] B.-S. Sohn, C. Bajaj, and V. Siddavanahalli, “Feature Based Volumetric Video Compression for Interactive Playback,”
Proc. IEEE Symp. Volume Visualization and Graphics (VVS '02), pp. 89-96, 2002.- [40] E.J. Stollnitz, T.D. DeRose, and D.H. Salesin, “Wavelets for Computer Graphics: A Primer, Part 1,”
IEEE Computer Graphics and Applications, vol. 15, no. 3, pp. 76-84, May 1995.- [41] W. Sweldens, “The Lifting Scheme: A Construction of Second Generation Wavelets,”
SIAM J. Math. Analysis, vol. 29, no. 2, pp. 511-546, 1998.- [42] G. Turk and J.F. O'Brien, “Modelling with Implicit Surfaces that Interpolate,”
ACM Trans. Graphics, vol. 21, no. 4, pp. 855-873, 2002.- [43] F.-Y. Tzeng and K.-L. Ma, “Intelligent Feature Extraction and Tracking for Visualizing Large-Scale 4D Flow Simulations,”
Proc. ACM/IEEE Conf. Supercomputing (SC '05), 2005.- [44] E. Vuçini, T. Möller, and M.E. Gröller, “On Visualization and Reconstruction from Non-Uniform Point Sets Using B-Splines,”
Computer Graphics Forum, vol. 28, no. 3, pp. 1007-1014, 2009.- [45] M. Weiler, R.P. Botchen, S. Stegmeier, T. Ertl, J. Huang, Y. Jang, D.S. Ebert, and K.P. Gaither, “Hardware-Assisted Feature Analysis of Procedurally Encoded Multifield Volumetric Data,”
Computer Graphics and Applications, vol. 25, no. 5, pp. 72-81, 2005.- [46] R. Westermann, “Compression Domain Rendering of Time-Resolved Volume Data,”
Proc. IEEE Conf. Visualization '95, pp. 168-175, 1995.- [47] D. Whalen and M.L. Norman, “Competition Data Set and Description,” In 2008 IEEE Visualization Design Contest, http://vis.computer.org/VisWeek2008/viscontests.html . 2008.
- [48] O. Wilson, A.V. Gelder, and J. Wilhelms, “Direct Volume Rendering via 3D Textures,” Technical Report UCSC-CRL-94-19, Univ. of California, 1994.
- [49] J. Woodring, C. Wang, and H.-W. Shen, “High Dimensional Direct Rendering of Time-Varying Volumetric Data,”
Proc. IEEE Visualization (VIS '03), pp. 417-424, 2003.- [50] J. Younesy, T. Moller, and H. Carr, “Visualization of Time-Varying Volumetric Data Using Differential Time-Histogram Table,”
Int'l Workshop Volume Graphics, pp. 21-29, 2005.- [51] K. Zhou, Z. Ren, S. Lin, H. Bao, B. Guo, and H.-Y. Shum, “Real-Time Smoke Rendering Using Compensated Ray Marching,”
ACM Trans. Graphics, vol. 27, no. 3, p. 36, 2008. |