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Outline

Title
Abstract
Methodology and Background
Data Sources
Data Uncertainties
Previous Work
Results
Visualizing Data with Uncertainty
Glyph Design
Qualitative Experimental Methodology
Qualitative Experimental Results
Summary and Conclusions
References
All Topics
Earth Sciences
Geophysics

Glyphs for visualizing uncertainty in vector fields

Profile image of Suresh LodhaSuresh Lodha

1996, IEEE Transactions on Visualization and Computer Graphics

https://doi.org/10.1109/2945.537309
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14 pages

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Abstract
sparkles

AI

Environmental data inherently possess uncertainty that traditional visualization techniques often overlook. This research introduces a new vector glyph designed to visualize uncertainty in winds and ocean currents by incorporating uncertainty in both direction and magnitude. By defining a new approach referred to as 'verity visualization', the study demonstrates enhanced visualization methods that better communicate data quality and uncertainty, employing both quantitative and qualitative assessments to compare the new glyphs against traditional glyphs. The findings suggest that these enhanced visualizations may significantly improve understanding of environmental vector field data.

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References (42)

  1. IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 2, NO. 3, SEPTEMBER 1996
  2. M.K. Beard, B.P. Buttenfield, and S.B. Clapham, "NCGIA Re- search Initiative 7 Visualization of Spatial Data Quality," Techni- cal Paper 91-26, Nat'l Center for Geographic Information and Analysis, Oct. 1991.
  3. C.M. Carswell, "Choosing Specifiers: An Evaluation of the Basic Tasks Model of Graphical Perception," Human Factors, vol. 34, no. 5, pp. 535-554, Oct. 1992.
  4. R. Clancy, J. Harding, K. Pollak, and P. May, "Quantification of Improvements in an Operational Global-Scale Ocean Thermal Analysis System," J. Atmospheric and Oceanic Technology, vol. 9, no. 1, pp. 55-66,1992.
  5. D. Clark and F. Wilson, "An Automated Method for Low Level Wind Shear Alert System (LLWAS) Data Quality Analysis," Tech. Report ATC-207, MIT Lincoln Laboratory, Lexington, Mass., May 1994.
  6. W.S. Cleveland, The Elements of Graphing Data. Wadsworth, 1985.
  7. W.S. Cleveland and R. McGill, "An Experiment in Graphical Per- ception," Int'l J. Man-Machine Studies, vol. 25, no. 5, pp. 491-500, Nov. 1986.
  8. E. Cluff, R. Burton, and W. Barrett, "A Survey and Characteriza- tion of Multidimensional Presentation Techniques," 7. Imaging Technology, vol. 17, no. 4,1991.
  9. W.C. deLeeuw and J.J. van Wijk, "A Probe for Local Flow Field Visualization," Proc. Visualization '93, pp. 3945, IEEE CS Press, Oct. 1993.
  10. G.Dutton, "Handling Positional Uncertainty in Spatial Data- bases," Proc. Fifth Int'l Symp. Spatial Data Handling, pp. 460-469. Univ. of So. Carolina, Aug. 1992.
  11. P. Fisher, "First Experiments in Viewshed Uncertainty: The Accu- racy of the Viewshed Area," Photogrammetric Engineering and Re- mote Sensing, vol. 5, no. 10, pp. 1,321-1,327,1991.
  12. P. Fisher, Visualization in Geographical Information Systems, chapter on Animation and Sound for the Visualization of Uncertain Spa- tial Information, pp. 181-185,1994.
  13. N.D. Gershon, "Visualization of Fuzzy Data Using Generalized Animation," Proc. Visualization '92, pp. 268-273, IEEE CS Press, Oct. 1992.
  14. M. Goodchild, B. Buttenfield, and J. Wood, Visualization in Geo- graphical Information Systems, chapter on Introduction to Visual- izing Data Validity, pp. 141-149,1994.
  15. R.M. Hodur, "Evaluation of a Regional Model with an Update Cycle," Monthly Weather Review, vol. 115, no. 11, pp. 2,707-2,718, Nov. 1987.
  16. G. Hunter and M. Goodchild, "Managing Uncertainty in Spatial Databases: Putting Theory into Practice," U R E A J., vol. 5, no. 2, pp. 55-62,1993.
  17. S. Kosslyn, "Understanding Charts and Graphs," Applied Cogni- tive Psychology, vol. 3, pp. 185-226,1989.
  18. D. Law, "Effects of Precipitation, Convection, and Waves on NOAA Network Profilers," Proc. 25th Int'l Conf. Radar Meteorol- ogy, pp. 4346, Am. Meteorological Soc., Boston, June 1991.
  19. Y. Leung et al., "Visualization of Fuzzy Scenes and Probability Fields," Proc. Fifth Int'l Symp. Spatial Data Handling, pp. 480490. Univ. of So. Carolina, Aug. 1992.
  20. L.K. Lewis, J.M. Wilczak, A.B. White, and L. Zhang, "Newly De- veloped X-Windows Tools for Analyzing the Boundary-Layer Structure," Technical Report, Environmental Technology Labo- ratory-NOAA, National Oceanic and Atmospheric Administra- tion, Boulder, Col., Apr. 1994. traction of Surface Currents from Codar Crossed-Loop Data: Ap- B.J. Lipa and D.E. Barrick, "Least-Squares Methods for the Ex- plication at ARSLOE," IEEE 1. Oceanic Engineering, Gal. 8, no. h, D. Lone. P. Mantev. C.M. Wittenbrink, T. Haininp;, and B. Mon- pp. 226-253, Oct. 1983. tague, 'REINAS the Real-Time Environmental InTormation Net- work and Analysis System," Proc. COMPCON, pp. 482487, San Francisco, IEEE, Mar. 1995.
  21. P. Mantey et al., "REINAS: Real-Time Environmental Information Network and Analysis System: Phase 111-Systems Design," Tech. Report UCSC-CRL-94-08, CE and CS Boards, Univ. of California, Saka Cmz, 1994.
  22. G.L. Mellor, "User's Guide for a Three-Dimensional, Primitive Equation, Numerical Ocean Model," Tech. Report, Princeton Univ., 1993.
  23. H. Moellering, "The Proposed Standard for Digital Cartographic Data: Report of the Digital Cartographic Data Standards Task Force," The American Cartographer, vol. 15, no. 1,1988.
  24. M. Monmonier, "Strategies for the Interactive Exploration of Geographic Correlation," Proc. Fourth Int'l Symp. Spatial Data Handling, vol. 1, pp. 512-521. IGU, July 1990.
  25. M. Monmonier, "Time and Motion as Strategic Variables in the Analysis and Communication of Correlation," Proc. Fifth Int'l Symp. Spatial Data Handling, pp. 72-81. Univ. of So. Carolina, Aug. 1992.
  26. A. Pang, "Spray Rendering," IEEE Computer Graphics and Applica- tions, vol. 14, no. 5, pp. 57-63,1994.
  27. A. Pang and N. Alper, "Bump Mapped Vector Fields," Proc. SPIE b ISGT Conf, Electronic Imaging, vol. 2410: Visual Data Exploration and Analysis 11, pp. 78-86, color plate p. 205. SPIE, Feb. 1995.
  28. A. Pang, J. Furman, and W. Nuss, "Data Quality Issues in Visuali- zation," SPIE vol. 2278 Visual Data Exploration and Analysis, pp. 12-23. SPIE, Feb. 1994.
  29. J.K. Petersen, "Map Processors," GISILIS '89, pp. 134-142. Am. Congress on Surveying & Mapping, Nov. 1989.
  30. R.M. Pickett and G.G. Grinstein, "Iconographic Displays for Visu- alizing Multidimensional Data," Proc. Int'l Con$ Systems, Man, and Cybernetics, pp. 514-519, IEEE, 1988.
  31. F.H. Post, "Glyph Versus Icon Terminology," personal communi- cation, Nov. 1995. Prof. Post has spent some time considering the terminology, and decided that both are fine, while they prefer to use iconic, because they have low density displays-large glyphs/icons that are few in number. He also stressed the termi- nology of small icons for high density and large icons for low density.
  32. F.J. Post, T. van Walsum, F.H. Post, and D. Silver, "Iconic Tech- niques for Feature Visualization," Proc. Visualization '95, pp. 288- 295, Atlanta, Ga., IEEE, Nov. 1995..
  33. W. Ribarsky, E. Ayers, J. Eble, and S. Mukherjea, "Glyphmaker: Creating Customized Visualizations of Complex Data," Computer, vol. 27, no. 7, pp. 57-64,1994.
  34. S. Smith, R.D. Bereeron, and G.G. Grinstein, "Stereophonic and Y , -- Surface Sound Generation for Exploratory Data Anafysis," Proc. CHI'90 Conf., pp. 125-132, ACM, 1990.
  35. B.N. Taylor' and C.E. Kuyatt, "Guidelines for Evaluating and Ex- pressing the Uncertainty of NIST Measurement Results. Tech. Re- port, Nat'l Inst. of Standards and Technology Technical Note 1297, Gaithersburg, Md., Jan. 1993.
  36. E.R. Tufte, The Visual Display of Quantitative Information. Graphics Press, 1983.
  37. E.R. Tufte, Envisioning Information. Graphics Press, 1990.
  38. J.W. Tukey, Exploratory Data Analysis. Addison-Wesley, 1977.
  39. J.Wilczak et al., "Contamination of Wind Profiler Data by Mi- grating Birds: Characteristics of Corrupted Data and Potential Solutions. Tech. Report, Environmental Technology Laboratory- NOAA, 1994.
  40. G.Wills et al., "Statistical Exploration of Spatial Data," Proc. Fourth Int'l Symp. Spatial Data Handling, vol. 1, pp. 491-500. IGU, July 1990.
  41. C.M. Wittenbrink, "Designing Optimal Parallel Volume Render- ing Algorithms," PhD thesis, Univ. of Washington, 1993.
  42. C.M. Wittenbrink, E. Saxon, J.J. Furman, A.T. Pang, and S. Lodha, "Glyphs for Visualizing Uncertainty in Environmental Vector Fields," vol. 2410, Proc. PIE b I S b T Conf., Electronic Imaging: Visual Data Exploration and Analysis, pp, 87-100. SPIE, Feb. 1995. Craig M. Wittenbrink (S'85-M'87-S'88-S'90- M'93) is a postdoctoral researcher at t h e Uni- versity of California, Santa Cruz, where he does research in environmental visualization. He received the BS degree in electrical engi- neering and computer science from the Univer- sity of Colorado in 1987, and the MS and PhD degrees in 1990 and 1993, respectively, both in electrical engineering, from the University of Washington. He was a design engineer with Boeinq Aerospace from 1987 to 1989, where he developed computer imaie generators. He was a co-chair of the 1995 IEEE/ACM Parallel Rendering Symposium and is widely pub- lished in parallel-image, visualization, and graphics processing. He is a member of ACM, Siggraph, and the IEEE Computer Society. http://www.cse.ucsc.edu/-Craig.

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