This Article 
 Bibliographic References 
 Add to: 
Multiresolution Representation and Visualization of Volume Data
October-December 1997 (vol. 3 no. 4)
pp. 352-369

Abstract—A system to represent and visualize scalar volume data at multiple resolution is presented. The system is built on a multiresolution model based on tetrahedral meshes with scattered vertices that can be obtained from any initial dataset. The model is built off-line through data simplification techniques, and stored in a compact data structure that supports fast on-line access. The system supports interactive visualization of a representation at an arbitrary level of resolution through isosurface and projective methods. The user can interactively adapt the quality of visualization to requirements of a specific application task and to the performance of a specific hardware platform. Representations at different resolutions can be used together to further enhance interaction and performance through progressive and multiresolution rendering.

[1] P.K. Agarwal and P. Desikan, "An Efficient Algorithm for Terrain Simplification," Proc. Eighth ACM-SIMA Symp. Discrete Algorithms, 1997.
[2] P. Agarwal and S. Suri, “Surface Approximation and Geometric Partitions,” Proc. Fifth Symp. Discrete Algorithms, pp. 24-33, Jan. 1994.
[3] M. Bertolotto, L. De Floriani, and P. Marzano, "Pyramidal Simplicial Complexes," Proc. Fourth Int'l Symp. Solid Modeling, pp. 153-162,Salt Lake City, Utah, May17-19, 1995.
[4] A. Ciampalini, P. Cignoni, C. Montani, and R. Scopigno, "Multiresolution Decimation Based on Global Error," The Visual Computer, vol. 13, no. 5, pp. 228-246, June 1997.
[5] P. Cignoni, L. De Floriani, C. Montoni, E. Puppo, and R. Scopigno, "Multiresolution Modeling and Visualization of Volume Data Based on Simplicial Complexes," Proc. 1994 Symp. Volume Visualization, pp. 19-26, 1994.
[6] P. Cignoni, P. Marino, C. Montani, E. Puppo, and R. Scopigno, “Speeding Up Isosurface Extraction Using Interval Trees,” IEEE Trans. Visualization and Computer Graphics, vol. 3, no. 2, pp. 158-170, Apr.-June 1997.
[7] P. Cignoni, C. Montani, D. Sarti, and R. Scopigno, "On the Optimization of Projective Volume Rendering," Visualization in Scientific Computing 1995, P. Zanarini R. Scateni, and J.J. van Wijk, eds., pp. 58-71. Springer KG, Wien, 1995.
[8] P. Cignoni, C. Montani, and R. Scopigno, "Magic Sphere: An Insight Tool for 3D Data Visualization," Computer Graphics Forum, (Eurographics '94 Conf. Proc.), vol. 13, no. 3, pp. 317-328, 1994.
[9] P. Cignoni, E. Puppo, and R. Scopigno, "Representation and Visualization of Terrain Surfaces at Variable Resolution," The Visual Computer, vol. 13, no. 5, pp. 199-217, 1997.
[10] J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F.P. Brooks Jr., and W.V. Wright, "Simplification Envelopes," Computer Graphics Proc. Ann. Conf. Series (Proc. Siggraph '96), pp. 119-128, 1996.
[11] J. Danskin and P. Hanrahan,“Fast algorithms for volume ray tracing,” 1992 Workshop Volume Visualization, pp. 91-98, Oct. 1992.
[12] M. Deering, “Geometry Compression,” Proc. SIGGRAPH '95, pp. 13-20, 1995.
[13] H. Edelsbrunner, "An Acyclicity Theorem for Cell Complexes in d Dimensions," Combinatorica, vol. 10, no. 3, pp. 251-260, 1990.
[14] R. Fowler and J. Little, "Automatic Extraction of Irregular Network Digital Terrain Models," Computer Graphics, vol. 13, no. 2, pp. 199-207, Aug. 1979.
[15] R. Grosso, C. Luerig, and T. Ertl, The Multilevel Finite Element Method for Adaptive Mesh Optimization and Visualization of Volume Data Proc. IEEE Visualization '97, R. Yagel and H. Hagen, eds., pp. 387-394, 1997.
[16] B. Guo, "A Multiscale Model for Structure-Based Volume Rendering," IEEE Trans. Visualization and Computer Graphics, vol. 1, no. 4, pp. 291-301, Dec. 1995.
[17] B. Hamann, "A Data Reduction Scheme for Triangulated Surfaces," Computer Aided Geometric Design, vol. 11, no. 2, pp. 197-214 1994.
[18] B. Hamann and J. Chen, "Data Point Selection for Piecewise Trilinear Approximation," Computer Aided Geometric Design, vol. 11, 1994.
[19] H. Hoppe, “Progressive Meshes,” Proc. SIGGRAPH '96, pp. 99-108, 1996.
[20] B. Joe, "Construction of Three-Dimensional Delaunay Triangulations Using Local Transformations," Computer Aided Geometric Design, vol. 8, pp. 123-142, 1991.
[21] A. Kalvin and R. Taylor, Superfaces: Polygonal Mesh Simplification with Bounded Error IEEE Computer Graphics and Applications, vol. 16, pp. 64-77, May 1996.
[22] T. Kao, D. Mount, and A. Saalfeld, "Dynamic Maintenance of Delaunay Triangulations," Proc. Auto-Carto 10, pp. 219-233, 1991.
[23] D. Laur and P. Hanrahan, Hierarchical Splatting: A Progressive Refinement Algorithm for Volume Rendering Proc. ACM SIGGRAPH, pp. 285-288, 1991.
[24] J. Lee, "Comparison of Existing Methods for Building Triangular Irregular Network Models of Terrain From Grid Digital Elevation Models," Int'l J. Geographic Information Systems, vol. 5, no. 3, pp. 267-285, 1991.
[25] W.E. Lorensen and H.E. Cline, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” Computer Graphics (SIGGRAPH '87 Proc.), vol. 21, pp. 163-169, 1987.
[26] S.G. Mallat,“A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 674-693, 1989.
[27] C. Montani, R. Scateni, and R. Scopigno, "Discretized Marching Cubes," IEEE Visualization '94 Proc., pp. 281-287,Washington, D.C., 1994.
[28] S. Muraki, “Multiscale Volume Representation by a DoG Wavelet,” IEEE Trans. Visualization and Computer Graphics, vol. 1, no. 2, pp. 109-116, 1995.
[29] R. Neubauer, M. Ohlberger, M. Rumpf, and R. Schwirer, "Efficient Visualization of Large-Scale Data on Hierarchical Meshes," Proc. Visualization in Scientific Computing '97, W. Lefer and M. Grave, eds. Springer Wien, 1997.
[30] A. Pang, "Spray Rendering," IEEE Computer Graphics and Applications, vol. 14, no. 5, pp. 57-63, 1994.
[31] F.P. Preparata and M.I. Shamos, Computational Geometry. Springer-Verlag, 1985.
[32] E. Puppo, "Variable Resolution Terrain Surfaces," Proc. Eighth Canadian Conf. Computational Geometry, pp. 202-210,Ottawa, Canada, Aug.12-15, 1996.
[33] E. Puppo and R. Scopigno, "Simplification, LOD, and Multiresolution—Principles and Applications," Technical Report C97-12, CNUCE, C.N.R., Pisa, Italy, June 1997. (Also in: EUROGRAPHICS '97 Tutorial Notes, Eurographics Association, Aire-la-Ville (CH)).
[34] K.J. Renze and J.H. Oliver, Generalized Unstructured Decimation IEEE Computer Graphics and Applications, vol. 16, no. 6, pp. 24-32, Nov. 1996.
[35] J. Ruppert and R. Seidel, "On the Difficulty of Tetrahedralizing 3-Dimensional Non-Convex Polyhedra," Proc. Fifth ACM Symp. Computational Geometry, pp. 380-392, 1989.
[36] H. Samet, The Design and Analysis of Spatial Data Structures. Addison-Wesley, 1990.
[37] W.J. Schroeder, J.A. Zarge, and W.E. Lorensen, “Decimation of Triangle Meshes,” Proc. SIGGRAPH '92, pp. 65-70, 1992.
[38] P. Shirley and A. Tuchman, “A Polygonal Approximation to Direct Scalar Volume Rendering,” Computer Graphics (Proc. 1990 ACM Workshop Volume Visualization), vol. 24, no. 2, pp. 63-69, 1990.
[39] R. Westermann, "A Multiresolution Framework for Volume Rendering," Proc. ACM Workshop on Volume Visualization, ACM Press, 1994, pp. 51-57.
[40] J. Wilhelms, "Pursuing Interactive Visualization of Irregular Grids," The Visual Computer, vol. 9, pp. 450-458, 1993.
[41] J. Wilhelms and A. Van Gelder, "Octrees for Faster Isosurface Generation," ACM Trans. Graphics, vol. 11, no. 3, July 1992, pp. 201-227.
[42] J. Wilhelms and A. Van Gelder, “Multi-Dimensional Trees for Controlled Volume Rendering and Compression,” Proc. 1994 Symp. Volume Visualization, pp. 27-34, Oct. 1994.
[43] P. Williams, “Interactive Splatting of Nonrectilinear Volumes,” Proc. IEEE Visualization '92, pp. 37-44, 1992.
[44] P. Williams, “Visibility Ordering Meshed Polyhedra,” ACM Trans. Graphics, vol. 11, no. 2, pp. 103-126, 1992.
[45] R. Yagel, D. Reed, A. Law, P.-W. Shih, and N. Shareef, "Hardware Assisted Volume Rendering of Unstructured Grids by Incremental Slicing," Proc. 1996 Symp. Volume Visualization, pp. 55-62 and p. 101, Oct. 1996.
[46] T.C Zhao and M. Overmars, "Forms Library—A Graphical User Interface Toolkit for X," Technical Report 95-, Dept. of Computer Science, Utrecht University, Utrecht, The Netherlands, 1995.
[47] Y. Zhou, B. Chen, and A. Kaufman, Multiresolution Tetrahedral Framework for Visualizing Regular Volume Data Proc. IEEE Visualization '97, R. Yagel and H. Hagen, eds., pp. 135-142, 1997.

Index Terms:
Volume data visualization, multiresolution representation, tetrahedral meshes.
Paolo Cignoni, Claudio Montani, Enrico Puppo, Roberto Scopigno, "Multiresolution Representation and Visualization of Volume Data," IEEE Transactions on Visualization and Computer Graphics, vol. 3, no. 4, pp. 352-369, Oct.-Dec. 1997, doi:10.1109/2945.646238
Usage of this product signifies your acceptance of the Terms of Use.