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Exploring Temporal Effects in Animations Depicting Spatial Data Uncertainty by: Charles R. Ehlschlaeger, Department of Geography, Hunter College, 695 Park Ave., New York City, NY 10021 E-MAIL:
[email protected] Abstract Accounting for spatial dependence when representing spatial data uncertainty requires stochastic simulation to fully represent the effects on spatial applications. Interpreting dozens or hundreds of simulation realizations can be a difficult task when there isn't a clear numerical result for the application. Previous research used animations of sequential perspective views in a random order to allow users to visualize possible application results. One of the hypotheses presented in that research was the relative amount of time an application result was visible would provide an understanding of the likelihood of the result occurring. This research tested that hypothesis and whether different ordering schemes provide a better understanding of complex spatial analyses. An application uncertainty model applied to a least-cost path algorithm had realizations made into animations using three ordering schemes: random ordering of realizations, placing similar realizations adjacent in the animation, and placing divergent realizations adjacent in the animation. A “traveling salesman” algorithm was used to sort the ordering of “similar realization” animations and “divergent realization” animations. Surveys testing animation viewers’ ability to estimate stochastic simulation results were collected to determine whether different ordering schemes provide a better understanding of application uncertainty caused by uncertain data. Keywords animation, visualization, cartography, GIS, uncertainty, viewshed analysis, stochastic simulation, traveling salesman problem, application uncertainty. Background What is application uncertainty? What is spatial data uncertainty? Least cost path analysis with "certain results" Least cost path analysis with "uncertain results" (from Ehlschlaeger, et al., 1997). The difference between "representing uncertainty" and "measuring error" Visualizing application uncertainty Visualizing spatial data uncertainty has long history: Special Issue: Computers & Geosciences: Vol. 23, No. 4. (1997) Static maps: Bertin (1981); MacEachren (1992, 1994); Goodchild, et al. (1994a); and others. Most use color and texture in maps. Dynamic maps: DiBiase, et al. (1992); Fisher (1994); MacEachren (1994); van der Wel, et
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Exploring Temporal Effects in Animations Depicting Spatial Data Uncer...
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al. (1994); Goodchild, et al. (1994b); and others Visualizing application uncertainty quantitatively: Mean results: 64,034 units Deviation of results: 2,991 units Histogram of path costs Visualizing application uncertainty qualitatively using dynamic maps: Goodchild, et al. (1994b) and others. Comparing different temporal arrangements of realizations in dynamic maps. Each realization can be compared to each other to determine how similar they are. Describing the similarity of spatial data realizations difficult: two maps described by n locations have n dimensions of information Corridor analysis results and total cost of resultant routes define similarity between realizations, and be placed in n by n matrix (n is number of realizations). Treating the difference between realizations as distances, a traveling salesman problem solver allows for ordering by both least similar and most similar realizations. Ordered: Place similar realizations adjacent in animation Davis and Keller (1997) and others. Advantage: Smooth transitions between realizations. Random: Random ordering of realizations in animation Ehlschlaeger, et al. (1997) and earlier works. Advantage: Easy to implement. Divergent: Place dissimilar realizations adjacent in animations. Advantage: When uncertainty is low, demonstrates variability in realizations. Hypothesis: Different temporal arrangements of realizations will provide different levels of comprehension. Test Ask three groups to view animations, one each of the different temporal arrangements: random, divergent, and ordered. Each subject then estimates time realizations spent in each of the various possible application results. Subjects: 39 students of GIS and Beginning Cartography. Ages varied from 19 to 50. Group One
Group Two
Group Three
Introduction Animation
Introduction Animation
Introduction Animation
First Test Animation (divergent)
First Test Animation (ordered)
First Test Animation (random)
Second Test Animation (ordered)
Second Test Animation (random)
Second Test Animation (divergent)
Third Test Animation (random)
Third Test Animation (divergent)
Third Test Animation (ordered)
Line Image (groups two and three) Due to non normal distributions and the hypothesis involving paired differences, the Sign Test method was used to compare results. Null Hypothesis, H0: There is no difference between the perception of two temporal arrangements of realizations (or a temporal arrangement and spatial estimation of distance). Alternative hypothesis, Ha: There is a difference. Results
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random
divergent
ordered
lines
average error
0.27
0.23
0.19
0.12
std dev of error
0.17
0.25
0.19
0.10
lines vs random ave dif of error: 0.076 std dev of error: 0.16 subjects better w/ lines: 13 subjects better w/ random: 6 accept null hypothesis no sig dif w/ type I error risk = 0.05
lines vs divergent ave dif of error: 0.192 std dev of error: 0.34 subjects better w/ lines: 15 subjects better w/ divergent: 4 reject null hypothesis sig dif w/ type I error risk = 0.05
ordered vs random ave dif of error: 0.082 std dev of error: 0.25 subjects better w/ ordered: 26 subjects better w/ random: 13 reject null hypothesis sig dif w/ type I error risk = 0.05
ordered vs divergent ave dif of error: 0.036 std dev of error: 0.34 subjects better w/ ordered: 20 subjects better w/ divergent: 19 accept null hypothesis no sig dif w/ type I error risk = 0.05
lines vs ordered ave dif of error: 0.124 std dev of error: 0.27 subjects better w/ lines: 12 subjects better w/ random: 7 accept null hypothesis no sig dif w/ type I error risk = 0.05
divergent vs random ave dif of error: 0.046 std dev of error: 0.30 subjects better w/ divergent: 26 subjects better w/ random: 13 reject null hypothesis sig dif w/ type I error risk = 0.05 Random ordering of realizations significantly worse than both divergent and ordered realizations. The perception of line distances, on average, were better than any temporal representation. However, the limited number of subjects only allowed a significant difference for distance perception over divergent temporal ordering. Choice of line perception test could be better. For example, testing lines divided into three sections and determining the proportion of each section contributes to the entire line would be more accurate reflection of how to determine the loss of understanding caused by changing representation schemes from spatial to temporal. a (more likely) better line test Bibliography Bertin, J. (1981). Graphics and graphic information processing: Walter de Gruyter, Berlin, 273 p. Davis, T. J., and C. P. Keller (1997). Modelling and visualizing multiple spatial uncertainties, Computers in Geosciences, 23(4):397-408.
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DiBiase D., MacEachren A. M., Krygier J. B. and Reeves C. (1992). Animation and the role of map design in scientific visualization, Cartography and Geographic Information Systems, 19(4):201-214. Ehlschlaeger, C. R., A. M. Shortridge, and M. F. Goodchild (1997). "Visualizing Spatial Data Uncertainty Using Animation," Computers in Geosciences, 23(4) at http://www.elsevier.nl/locate/cgvis/ Fisher, P. F. (1994). Animation and sound for the visualization of uncertain spatial information, in Hearnshaw, H. M., and Unwin, D. J., eds., Visualization in Geographical Information Systems: John Wiley & Sons, New York, p. 181-185. Goodchild, M. F., Buttenfield, B., and Wood, J. (1994a). Introduction to visualizing data validity, in Hearnshaw, H. M., and Unwin, D. J., eds., Visualization in Geographical Information Systems: John Wiley & Sons, New York, p. 141-149. Goodchild, M. F., Chih-Chang, L., and Leung, Y. (1994b). Visualizing fuzzy maps, in Hearnshaw, H. M., and Unwin, D. J., eds., Visualization in Geographical Information Systems: John Wiley & Sons, New York, p. 158-167. MacEachren, A. M. (1992). Visualizing uncertain information, Cartographic Perspectives, 13:10-19. MacEachren, A. M. (1994). Time as a cartographic variable, in Hearnshaw, H. M., and Unwin, D. J., eds., Visualization in Geographical Information Systems: John Wiley & Sons, New York, 115-130. van der Wel, F. J. M., Hootsman, R. M., and Ormeling, F. J. (1994). Visualization of data quality, in MacEachren, A. M., and Taylor, D. F., eds., Visualization in Modern Cartography: Elsevier, Amsterdam, p. 67-92.
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