Skip to main content

Modeling and Visualization of Empirical Data

  • Chapter
State of the Art in Computer Graphics

Abstract

Many engineering and scientific applications in such diverse disciplines as medicine, biomedical research, geophysics, and robotics depend on the modeling and visualization of empirical data. Although the sources of data for each of these applications differ and considerable domain knowledge may be necessary to interpret the data, there is a great deal of commonality in the required modeling and visualization techniques. In this paper, we explore techniques in registration, segmentation, 3D reconstruction, and rendering, which are common to applications that depend on empirical data. The emphasis is on volumetric data sampled on regular grids, with examples from radiology, neuroscience, embryology, geophysics, and computer vision.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anandan, P., Computing dense displacement fields with confidence measures in scenes containing occlusion, Image Understanding Workshop,New Orleans, LA, December 1984, pp. 236–246; McLean, Va: Science Applications Int. Corp.

    Google Scholar 

  2. Arun, K.S., Huang, T.S., and Blostein, S.D., Least-squares fitting of two 3-D point sets, IEEE Trans. Patt. Anal. Mach. Intell., Vol. 9, No. 5, pp. 698–700, September 1987.

    Article  Google Scholar 

  3. Ayache, N., Boissonnat, J.D., Brunet, E., Cohen, L., Chieze, J.P., Geiger, B., Monga, O., Rocchisani, J M, and Sander, P., Building highly structured volume representations in 3D medical images, Proc. 3rd Internat. Symposium on Computer Assisted Radiology, CAR’89, pp. 765–772, June 1989, New York: Springer-Verlag.

    Google Scholar 

  4. Ballard, D.H., and Brown, C.M., Computer Vision, Englewood Cliffs, NJ: Prentice-Hall, 1982.

    Google Scholar 

  5. Bergen, J.R., Anandan, P., Hanna, K.J., and Hingorani, R., Hierarchical Model-based Motion Estimation, in Second European Conference on Computer Vision (ECCV’92),Sandini, G., Ed., Santa Margherita Liguere, Italy, May 1992, pp. 237–252, Berlin: Springer-Verlag.

    Google Scholar 

  6. Boissonnat, J.D., Geometric structures for three-dimensional shape representation, ACM TOG, Vol. 3, pp. 266–286, 1984.

    Google Scholar 

  7. Boissonnat, J.D., Shape reconstruction from planar cross-sections, Comput. Vis., Graph. and Image Process., Vol. 44, pp. 1–29, 1988.

    Article  Google Scholar 

  8. Bomans, M., Höhne, K.H., Tiede, U., and Riemer, M., 3-D segmentation of MR images of the head for 3-D display, IEEE Trans. on Medical Imaging, Vol. 9, No. 2, pp. 177–183, June 1990.

    Article  Google Scholar 

  9. Born, M., and Wolf, E., Principles of Optics. Oxford: Pergamon Press, 1984.

    Google Scholar 

  10. Byrne, J.P., Undrill, P.E., and Phillips, R.P., Feature based image registration using parallel computation methods, First Conf. on Visualization in Biomedical Computing, Atlanta, GA, May 1990, Los Alamitos, CA: IEEE Computer Society Press, pp. 304–310.

    Google Scholar 

  11. Cappelletti, J.D., and Rosenfeld, A., Three-dimensional boundary following, Comput. Vis., Graph. and Image Process., Vol. 48, pp. 80–92, 1989.

    Article  Google Scholar 

  12. Carlbom, I., Terzopoulos, D., and Harris, K.M., Reconstructing and Visualizing Models of Neuronal Dendrites, in Scientific Visualization of Physical Phenomena, Patrikalakis, N.M., Ed., Tokyo: Springer-Verlag, 1991, pp. 623–638. Presented at CGI ‘81: Visualization of Physical Phenomena, Cambridge, MA, June 26–28, 1991.

    Google Scholar 

  13. Carlbom, I., Chakravarty, I., and Hsu, W.M, SIGGRAPH’91 workshop report: Integrating computer graphics, computer vision, and image processing in scientific applications, Comput. Graph., Vol. 26, No. 1, pp. 8–17, 1992.

    Article  Google Scholar 

  14. Chakravarty, I., Nichol, B., and Ono, T., The integration of computer graphics and image processing techniques for the display and manipulation of geophysical data, Proc. Comp. Graph. Tokyo ‘86, Tokyo, Japan, 1986. Reprinted in Advanced Computer Graphics, Kunii, T., Ed., Tokyo: Springer-Verlag, 1986.

    Google Scholar 

  15. Christiansen, H.N., and Sederberg, T.W., Conversion of complex contour line definitions into polygonal element mosaics, Comput. Graph.,Vol. 12, pp. 187–192, 1982 (SIGGRAPH 82).

    Google Scholar 

  16. Cline, H.E., Lorensen, W.E., Ludke, S., Crawford, C.R., and Teeter, B.C., Two algorithms for the three-dimensional reconstruction of tomograms. Medical Physics, Vol. 15, No. 3, pp. 320–327, May/June 1988.

    Google Scholar 

  17. Cohen, L.D., and Cohen, I., Finite element methods for active contour models and balloons from 2D to 3D, Technical Report 9124, CEREMADE, Université Paris IX, Paris, France, December 1991.

    Google Scholar 

  18. Cullip, T.J., Frederiksen, R.E., Gauch, J.M., and Pizer, S.M., Algorithms for 2D and 3D image description based on the IAS, First Conf. on Visualization in Biomedical Computing, Atlanta, GA, May 1990, Los Alamitos, CA: IEEE Computer Society Press, pp. 102–107.

    Google Scholar 

  19. Drebin, R.A., Carpenter, L., and Hanrahan, P., Volume rendering, Comput. Graph.,Vol. 22, pp. 65–74, 1988 (SIGGRAPH 88).

    Article  Google Scholar 

  20. Duda, R.O., and Hart, P.E., Pattern Classification and Scene Analysis, New York: J. Wiley and Sons, 1973.

    MATH  Google Scholar 

  21. Dudgeon, D.E., and Mersereau, R.M., Multidimensional Digital Signal Processing, Englewood Cliffs, NJ: Prentice Hall, 1984.

    MATH  Google Scholar 

  22. Duncan, J.S., Staib, L.H., Birkholzer, T., Owen, R., Anandan, P., and Bozma, I., Medical image analysis using model-based optimization, First Conf. on Visualization in Biomedical Computing, Atlanta, GA, May 1990, Los Alamitos, CA: IEEE Computer Society Press, pp. 370–377.

    Google Scholar 

  23. Farin, G., Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide, San Diego, CA: Academic Press, 1988.

    MATH  Google Scholar 

  24. Farrell, E.J., Yang, W.C., and Zappulla, R.A., Animated 3D CT imaging, IEEE Comput. Graph. and Appl., Vol. 5, No. 12, pp. 26–32, December 1985.

    Article  Google Scholar 

  25. Feller, W., An Introduction to Probability Theory and Its Applications, New York: John Wiley and Sons, 1957.

    MATH  Google Scholar 

  26. Foley, J.D., van Dam, A., Feiner, S.K., and Hughes, J.F., Computer Graphics: Principles and Practice, Reading, MA: Addison-Wesley, 1990.

    Google Scholar 

  27. Frederiksen, R.E., Coggins, J M, Cullip, T.J., and Pizer, S.M., Interactive object definition in medical images using multiscale, geometric image descriptions, First Conf. on Visualization in Biomedical Computing, Atlanta, GA, May 1990, Los Alamitos, CA: IEEE Computer Society Press, pp. 108–114.

    Google Scholar 

  28. Frieder, G., Gordon, D., and Reynolds, R.A., Back-to-front display of voxel-based objects, IEEE Comput. Graph. and Appl., Vol. 5, No. 1, pp. 52–60, January 1985.

    Article  Google Scholar 

  29. Fuchs, H., Kedem, Z.M., and Uselton, S.P., Optimal surface reconstruction from planar contours, CACM, Vol. 20, No. 10, pp. 693–702, 1977.

    MathSciNet  MATH  Google Scholar 

  30. Giertsen, C., Halvorsen, A., and Flood, P.R., Graph-directed modeling from serial sections, The Visual Computer, Vol. 6, pp. 284–290, 1990.

    Article  Google Scholar 

  31. Gonzalez, R.C., and Wintz, P., Digital Image Processing, Reading, MA: Addison-Wesley, 1977.

    MATH  Google Scholar 

  32. Gordon, D., and Reynolds, R.A., Image space shading of 3-dimensional objects, Comput. Vis., Graph. and Image Process., Vol. 29, pp. 361–376, 1985.

    Article  Google Scholar 

  33. Gordon, D., and Udupa, J.K., Fast surface tracking in three-dimensional binary images, Comput. Vis., Graph. and Image Process., Vol. 45, pp. 196–214, 1989.

    Article  Google Scholar 

  34. Guéziec, A., and Ayache, N., Smoothing and matching of 3-D space curves, Technical Report 1544, INRIA, France, October 1991.

    Google Scholar 

  35. Hanrahan, P., Three-pass affine transforms for volume rendering, Comput. Graph., Vol. 24, No. 5, pp. 71–78, 1990.

    Article  Google Scholar 

  36. Herman, G.T., and Abbott, A.H., Reproducibility of landmark locations on CT-based three-dimensional images, Proc. NCGA’89,Fairfax, VA, April 1989, pp. 144–148, National Computer Graphics Association.

    Google Scholar 

  37. Höhne, K.H., Bomans, M., Pommert, A., Riemer, M., and Tiede, U., 3D segmentation and display of tomographic imagery, Proc. Int. Conf. on Pattern Recognition, Rome, Italy, pp. 1271–1276, Los Alamitos, CA: IEEE Computer Society Press, 1988.

    Google Scholar 

  38. Höhne, K.H., Bomans, M., Pommert, A., Riemer, M., Schiers, C., Tiede, U., and Wiebecke, G., 3D Visualization of Tomographic Volume Data Using the Generalized Voxel-model, in Proc. Volume Visualization Workshop, Upson, C., Ed., Dept. Computer Science, University of North Carolina, Chapel Hill, NC, pp. 51–57, 1989.

    Google Scholar 

  39. Höhne, K.H., Bomans, M., Pommert, A., Riemer, M., Schiers, C., Tiede, U., and Wiebecke, G., 3D visualization of tomographic volume data using the generalized voxel model, The Visual Computer, Vol. 6, pp. 28–36, 1990.

    Article  Google Scholar 

  40. Horn, B.K.P., and Schunck, B.G., Determining optical flow, Artificial Intelligence, Vol. 17, pp. 185–203, 1981.

    Article  Google Scholar 

  41. Horn, B.K.P., Relative orientation, Int. Jour. Comp. Vision, Vol. 4, pp. 59–78, January 1990.

    Article  Google Scholar 

  42. Hsu, W.M, Personal communication, 1992.

    Google Scholar 

  43. Kass, M., Witkin, A., and Terzopoulos, D., Snakes: Active contour models, Int. Jour. Comp. Vision, Vol. 1, No. 4, pp. 321–331, 1987.

    Article  Google Scholar 

  44. Kaufman, A., Volume Visualization, Los Alamitos, CA: IEEE Computer Society Press, 1991.

    Google Scholar 

  45. Keppel, E., Approximating complex surfaces by triangulation of contour lines, IBM Research and Development, Vol. 19, pp. 2–11, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  46. Lavalleé, S., Szeliski, R., and Brunie, L., Matching 3-D smooth surfaces with their 2-D projections using 3-D distance maps, SPIE Vol. 1570 Geometric Methods in Computer Vision, San Diego, CA, The International Society for Optical Engineering, pp. 322–336, July 1991.

    Google Scholar 

  47. Le Gall, D., MPEG: A video compression standard for multimedia applications, CACM, Vol. 34, No. 4, pp. 46–58, 1991.

    Google Scholar 

  48. Leitner, F., Marque, I., LaVallee, S., and Cinquin, P., Dynamic segmentation: Finding the edge with differential equations and `spline snakes’, Technical Report TIMB - TIM 3 - IMAG, Faculté de Médecine, 38700 La Tronche, France, 1990.

    Google Scholar 

  49. Levin, D.N., Pelizzari, C.A., Chen, G.T.Y., Chen, C.T., and Cooper, M.D., Retrospective geometric correlation of MR, CT, and PET images, Radiology, Vol. 169, No. 3, pp. 817–823, December 1988.

    Google Scholar 

  50. Levoy, M., Display of surfaces from volume data, IEEE Comput. Graph. and Appl., Vol. 8, No. 3, pp. 29–37, May 1988.

    Article  Google Scholar 

  51. Levoy, M., Volume rendering by adaptive refinement, The Visual Computer, Vol. 6, pp. 2–7, 1990.

    Article  Google Scholar 

  52. Levoy, M., A hybrid ray tracer for rendering polygon and volume data, IEEE Comput. Graph. and Appl., Vol. 10, No. 2, pp. 33–40, March 1990.

    Article  Google Scholar 

  53. Levoy, M., Fuchs, H., Pizer, S.M., Rosenman, J., Chaney, E.L., Sherouse, G.W., Interrante, V., and Kiel, J., Volume rendering in radiation treatment planning, First Conf. on Visualization in Biomedical Computing, Atlanta, GA, May 1990, Los Alamitos, CA: IEEE Computer Society Press, pp. 4–10.

    Google Scholar 

  54. Levoy, M., Efficient ray-tracing of volume data, ACM TOG, Vol. 9, pp. 245–261, 1990.

    MATH  Google Scholar 

  55. Leymarie, F., “Tracking and Describing Deformable Objects Using Active Contour Models”, Master’s thesis, Computer Vision and Robotics Laboratory, McGill Research Centre for Intelligent Machines, McGill University, Montreal, Canada, February 1990.

    Google Scholar 

  56. Lifshitz, L.M., and Pizer, S.M., A multiresolution hierarchical approach to image segmentation based on intensity extrema, IEEE Trans. Patt. Anal. Mach. Intell., Vol. 12, pp. 529–540, June 1990.

    Article  Google Scholar 

  57. Lim, J.S., Two-Dimensional Signal and Image Processing. Englewood Cliffs, NJ: Prentice Hall, 1990.

    Google Scholar 

  58. Lin, W.C., Chen, S.Y., and Chen, C.T., A new surface interpolation technique for reconstructing 3D objects from serial cross sections, Comput. Vis., Graph. and Image Process., Vol. 48, pp. 124–143, 1989.

    Article  Google Scholar 

  59. Lipson, P., Yuille, A.L., O’Keeffe, D.O., Cavanaugh, J., Taaffe, J., and Rosenthal, D., Automated bone density calculation using feature extraction by deformable templates, First Conf. on Visualization in Biomedical Computing, Atlanta, GA, May 1990, Los Alamitos, CA: IEEE Computer Society Press, pp. 477–484.

    Google Scholar 

  60. Liu, H.K., Two and three dimensional boundary detection, Comput. Graph. and Image Process., Vol. 6, pp. 123–134, 1977.

    Article  Google Scholar 

  61. Lorensen, W.E., and Cline, H.E., Marching cubes: A high resolution 3D surface construction algorithm, Comput. Graph.,Vol. 21, pp. 163–169, 1987 (SIGGRAPH 87).

    Article  Google Scholar 

  62. Matthies, L.H., Kanade, T., and Szeliski, R, Kalman filter-based algorithms for estimating depth from image sequences, Int. Jour. Comp. Vision, Vol. 3, pp. 209–236, 1989.

    Article  Google Scholar 

  63. Meagher, D., Geometric modeling using octree encoding, Comput. Graph. and Image Process., Vol. 19, pp. 129–147, 1982.

    Article  Google Scholar 

  64. Meagher, D., Interactive solids processing for medical analysis and planning, Proc. National Computer Graphics Association, NCGA’84, May 1984.

    Google Scholar 

  65. Meinzer, H.P., Meetz, K., Scheppelmann, D., Engelmann, U., and Baur, H.J., The Heidelberg ray tracing model, IEEE Comput. Graph. and Appl., Vol. 11, No. 6, pp. 34–43, November 1991.

    Article  Google Scholar 

  66. Meyers, D., Skinner, S., and Sloan, K., Surfaces from contours: The correspondence and branching problems, Graphics Interface ‘81, Calgary, Alberta, Canada, Canadian Information Processing Society, June 1991.

    Google Scholar 

  67. Mitchell, D.P., and Netravali, A.N., Reconstruction filters in computer graphics, Comput. Graph.,Vol. 22, pp. 221–228, 1988 (SIGGRAPH 88).

    Google Scholar 

  68. Monga, O., Ayache, N., and Sander, P., From voxel to curvature, IEEE Comp.Soc. Conf. on Comp. Vision and Pattern Recognition (CVPR’91),Maui, HI, June 1991, pp. 644–649; Los Alamitos, CA. IEEE Computer Society Press.

    Google Scholar 

  69. Morgenthaler, D.G., and Rosenfeld, A., Multidimensional edge detection by hyper-surface fitting, IEEE Trans. Patt. Anal. Mach. Intell., Vol. 3, No. 4, pp. 482–486, July 1981.

    Article  Google Scholar 

  70. Ney, D.R., Fishman, E.K., Magid, D., and Drebin, R.A., Volume rendering of computed tomography data: Principles and techniques, IEEE Comput. Graph. and Appl., Vol. 10, No. 2, pp. 24–32, March 1990.

    Article  Google Scholar 

  71. Okutomi, M., and Kanade, T., A signal matching algorithm: An adaptive window based on a brownian motion model, Third International Conference on Computer Vision (ICCV’90),Osaka, Japan, December 1990, pp. 190–199; Los Alamitos, CA: IEEE Computer Society Press.

    Google Scholar 

  72. Oppenheim, A.V., and Schafer, R.W., Digital Signal Processing, Englewood Cliffs, NJ: Prentice Hall, 1975.

    MATH  Google Scholar 

  73. Pelizzari, C.A., Chen, G.T.Y., Spelbring, D.R., Weichselbaum, R.R., and Chen, C.T., Accurate three-dimensional registration of CT, PET, and/or MR images of the brain, Jour. Comp. Assisted Tomography, Vol. 13, No. 1, pp. 20–26, January/February 1989.

    Article  Google Scholar 

  74. Phong, B.T., Illumination for computer generated pictures, CACM, Vol. 18, pp. 311–317, June 1975.

    Google Scholar 

  75. Pizer, S.M., Gauch, J.M., Cullip, T.J., and Frederiksen, R.E., Descriptions of image intensity structure via scale and symmetry, First Conf. on Visualization in Biomedical Computing, Atlanta, GA, May 1990, Los Alamitos, CA: IEEE Computer Society Press, pp. 94–101.

    Google Scholar 

  76. Porter, T., and Duff, T., Compositing digital images, Comput. Graph.,Vol. 18, pp. 253–259, 1984 (SIGGRAPH 84).

    Article  Google Scholar 

  77. Preparata, F.P., and Shamos, M.I., Computational Geometry, New York: Springer-Verlag, 1985.

    Google Scholar 

  78. Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T., Numerical Recipes: The Art of Scientific Computing, Cambridge, UK: Cambridge University Press, 1986.

    Google Scholar 

  79. Raya, S.P., and Udupa, J.K., Shape-based interpolation of multidimensional objects, IEEE Trans. on Medical Imaging, Vol. 9, No. 1, pp. 32–42, March 1990.

    Article  Google Scholar 

  80. Rhodes, M.L., An algorithmic approach to controlling search in three-dimensional image data, Comput. Graph.,Vol. 13, pp. 134–142, 1979 (SIGGRAPH 79).

    Article  Google Scholar 

  81. Rosenfeld, A., and Kak, A.C., Digital Picture Processing, New York: Academic Press, 1976.

    Google Scholar 

  82. Sabella, P., A rendering algorithm for visualizing 3D scalar fields, Comput. Graph.,Vol. 22, pp. 51–58, 1988 (SIGGRAPH 88).

    Google Scholar 

  83. Sabella, P., and Carlbom, I., An object-oriented approach to solid modeling for empirical data, IEEE Comput. Graph. and Appl., Vol. 9, No. 5, pp. 24–35, September 1989.

    Article  Google Scholar 

  84. Samet, H., Connected component labeling using quadtrees, JACM, Vol. 28, No. 3, pp. 487–501, July 1981.

    Article  MathSciNet  MATH  Google Scholar 

  85. Sander, P.T., and Zucker, S.W., Inferring surface trace and differential structure from 3-D images, IEEE Trans. Patt. Anal. Mach. Intell., Vol. 12, No. 9, pp. 833–854, September 1990.

    Article  Google Scholar 

  86. Schröder, P., and Salem, J.B., Fast Rotation of Volume Data on Data Parallel Architectures, in Proc. Visualization ‘81,Nielson, G.M., and Rosenblum, L., Eds., San Diego, CA, October 1991, pp. 50–57, Los Alamitos, CA: IEEE Computer Society Press.

    Google Scholar 

  87. Smith, A.R., Planar 2-pass texture mapping and warping, Comput. Graph.,Vol. 21, pp. 263–272, 1987 (SIGGRAPH 87).

    Google Scholar 

  88. Szeliski, R., Bayesian Modeling of Uncertainty in Low-Level Vision, Dordrecht, The Netherlands: Kluwer Academic Publishers, 1989.

    MATH  Google Scholar 

  89. Szeliski, R., Shape from rotation, Technical Report 90/13, Digital Equipment Corporation, Cambridge Research Lab, December 1990.

    Google Scholar 

  90. Terzopoulos, D., On matching deformable models to images: Direct and iterative solutions, Topical Meeting on Machine Vision, Washington, D.C., Optical Society of America, pp. 160–167, March 1987.

    Google Scholar 

  91. Tiede, U., Höhne, K.H., Romans, M., Pommert, A., Riemer, M., and Wiebecke, G., Investigation of medical 3D-rendering algorithms, IEEE Comput. Graph. and Appl., Vol. 10, No. 2, pp. 41–53, March 1990.

    Article  Google Scholar 

  92. Toennies, K.D., Udupa, J.K., and Herman, G.T., Segmentation of implanted bone grafts using anatomical landmarks, Proc. NCGA’89, pp. 207–214, Fairfax, VA, National Computer Graphics Association, April 1989.

    Google Scholar 

  93. Toennies, K.D., Udupa, J.K., Herman, G.T., Wornom III, I.L., and Buchman, S.R., Registration of 3D objects and surfaces, IEEE Comput. Graph. and Appl., Vol. 10, No. 3, pp. 52–62, May 1990.

    Article  Google Scholar 

  94. Tonnesen, D., Extracting surface structure from 3D data, unpublished manuscript, April 1992.

    Google Scholar 

  95. Udupa, J.K., and Ajjanagadde, V.G., Boundary and object labeling in three-dimensional images, Comput. Vis., Graph. and Image Process., Vol. 51, pp. 355–369, 1990.

    Article  Google Scholar 

  96. Upson, C., and Keeler, M., V-buffer: Visible volume rendering, Comput. Graph.,Vol. 22, pp. 59–64, 1988 (SIGGRAPH 88).

    Article  Google Scholar 

  97. Vannier, M.W., Marsh, J.L., and Warren, J.O., Three dimensional computer graphics for craniofacial surgical planning and evaluation, Comput. Graph.,Vol. 17, pp. 263–273, 1983 (SIGGRAPH 83).

    Article  Google Scholar 

  98. Vezina, G., Fletcher, P.A., and Robertson, P.K., Volume rendering on the Maspar MP-1, Technical Report TR-HJ-92–07, CSIRO Division of Information Technology, Australia, April 1992.

    Google Scholar 

  99. Vincken, K.L., de Graaf, C.N., Koster, A.S.E., Viergever, M.A., Appelman, F.J.R., and Timmens, G.R., Multiresolution segmentation of 3D images by the hyperstack, First Conf. on Visualization in Biomedical Computing, Atlanta, GA, May 1990, Los Alamitos, CA: IEEE Computer Society Press, pp. 115–122.

    Google Scholar 

  100. VitalImages, Inc., VoxelView/PLUS 1.4, The Interactive Volume Rendering System, Fairfield, IA, 1990.

    Google Scholar 

  101. Westover, L., Interactive Volume Rendering, in Proc. Volume Visualization Workshop, Upson, C., Ed., Dept. Computer Science, University of North Carolina, Chapel Hill, NC, pp. 9–16, 1989.

    Google Scholar 

  102. Westover, L., Footprint evaluation for volume rendering, Comput. Graph.,Vol. 24, pp. 367–376, 1990 (SIGGRAPH 90).

    Article  Google Scholar 

  103. Westover, L.A., “Splatting: A Parallel, Feed-Forward Volume Rendering Algorithm”, Ph.D. diss., Dept. of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, NC, 1991.

    Google Scholar 

  104. Wolberg, G., Digital Image Warping, Los Alamitos, CA: IEEE Computer Society Press, 1990.

    Google Scholar 

  105. Wolphe Jr., R.H., and Liu, C.N., Interactive visualization of 3D seismic data: A volumetric method, IEEE Comput. Graph. and Appl., Vol. 8, No. 4, pp. 24–30, July 1988.

    Article  Google Scholar 

  106. Yagel, R., Kaufman, A., and Zhang, Q., Realistic Volume Imaging, in Proc. Visualization ‘81,Nielson, G.M., and Rosenblum, L., Eds., San Diego, CA, October 1991, pp. 226–231, Los Alamitos, CA: IEEE Computer Society Press.

    Google Scholar 

  107. Zucker, S.W., and Hummel, R.A., A three-dimensional edge operator, IEEE Trans. Patt. Anal. Mach. Intell., Vol. 3, No. 3, pp. 324–331, May 1981.

    Article  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Carlbom, I. (1994). Modeling and Visualization of Empirical Data. In: Rogers, D.F., Earnshaw, R.A. (eds) State of the Art in Computer Graphics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4306-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4306-9_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8732-2

  • Online ISBN: 978-1-4612-4306-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics