Exploring Errors in Reading a Visualization via Eye Tracking Models Using Stochastic Geometry

  • Michael G. HilgersEmail author
  • Aaron Burke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11589)


Information visualizations of quantitative data are rapidly becoming more complex as the dimension and volume of data increases. Critical to modern applications, an information visualization is used to communicate numeric data using objects such as lines, rectangles, bars, circles, and so forth. Via visual inspection, the viewer assigns numbers to these objects using their geometric properties of size and shape. Any difference between this estimation and the desired numeric value we call the “visual measurement error”. The research objective of this paper is to propose models of the visual measure error utilizing stochastic geometry. The fundamental technique in building our models is the conceptualization of eye fixation points as might be determined by an eye-tracking experiment of viewers estimating size and shape of a visualization’s object configurations. The fixation points are first considered as a stochastic point process whose characteristics require comment before proceeding to the statistical shape analysis of the visualization. Once clarified the fixation points are reinterpreted as a sampling of the shape and size of the landmark configurations of geometric landmarks on the visualization. The ultimate end of these models is to find optimal shape and size parameters leading to minimum visual measurement error.


Information visualization Reading error Stochastic shape analysis 


  1. 1.
    Michalos, M., Tselenti, P., Nalmpantis, S.: Visualization techniques for large datasets. J. Eng. Sci. Technol. Rev. 5, 72–76 (2012)Google Scholar
  2. 2.
    Cleveland, W.S., McGill, R.: Graphical perception: the visual decoding of quantitative information on graphical displays of data. J. Roy. Stat. Soc. Ser. A (Gen.) 150, 192–229 (1987)CrossRefGoogle Scholar
  3. 3.
    Matzen, Laura E., Haass, Michael J., Divis, Kristin M., Stites, Mallory C.: Patterns of attention: how data visualizations are read. In: Schmorrow, Dylan D., Fidopiastis, Cali M. (eds.) AC 2017. LNCS (LNAI), vol. 10284, pp. 176–191. Springer, Cham (2017). Scholar
  4. 4.
    Baddeley, A., Rubak, E., Turner, R.: Spatial Point Patterns: Methodology and Applications with R. Chapman and Hall/CRC (2015)Google Scholar
  5. 5.
    Stoyan, D., Stoyan, H.: Fractals, Random Shapes, and Point Fields: Methods of Geometrical Statistics. Wiley, Hoboken (1994)zbMATHGoogle Scholar
  6. 6.
    Jacob, R.J., Karn, K.S.: Eye tracking in human-computer interaction and usability research: ready to deliver the promises. In: The Mind’s Eye, pp. 573–605. Elsevier (2003)Google Scholar
  7. 7.
    Manhartsberger, M., Zellhofer, N.: Eye tracking in usability research: what users really see. In: Usability Symposium, pp. 141–152 (2005)Google Scholar
  8. 8.
    Moller, J., Waagepetersen, R.P.: Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC (2003)Google Scholar
  9. 9.
    Chiu, S.N., Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and Its Applications. Wiley, Hoboken (2013)CrossRefGoogle Scholar
  10. 10.
    Johnson, N.L., Kemp, A.W., Kotz, S.: Univariate Discrete Distributions. Wiley, Hoboken (2005)CrossRefGoogle Scholar
  11. 11.
    Kingman, J.F.C.: Poisson Processes. Clarendon Press (1992)Google Scholar
  12. 12.
    Kendall, W.S.: A diffusion model for Bookstein triangle shape. Adv. Appl. Probab. 30, 317–334 (1998)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kendall, D.G.: The diffusion of shape. Adv. Appl. Probab. 9, 428–430 (1977)CrossRefGoogle Scholar
  14. 14.
    Dryden, I., Mardia, K.: Statistical Analysis of Shape. Wiley, Hoboken (1998)zbMATHGoogle Scholar
  15. 15.
    Bookstein, F.L.: Size and shape spaces for landmark data in two dimensions. Stat. Sci. 1, 181–222 (1986)CrossRefGoogle Scholar
  16. 16.
    Kendall, D.G.: Shape manifolds, procrustean metrics, and complex projective spaces. Bull. Lond. Math. Soc. 16, 81–121 (1984)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kendall, D.G.: Exact distributions for shapes of random triangles in convex sets. Adv. Appl. Probab. 17, 308–329 (1985)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Kendall, D.G.: Further developments and applications of the statistical theory of shape. Theor. Probab. Appl. 31, 407–412 (1987)CrossRefGoogle Scholar
  19. 19.
    Bookstein, F.L.: A statistical method for biological shape comparisons. J. Theor. Biol. 107, 475–520 (1984)CrossRefGoogle Scholar
  20. 20.
    Johnson, N.L., Kotz, S., Balakrishnan, N.: Continuous Univariate Distributions, Volume 2 of Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. Wiley, New York (1995)Google Scholar
  21. 21.
    Olver, F.W., Lozier, D.W., Boisvert, R.F., Clark, C.W.: NIST Handbook of Mathematical Functions Hardback and CD-ROM. Cambridge University Press, Cambridge (2010)Google Scholar
  22. 22.
    Bylinskii, Z., Borkin, M.A., Kim, N.W., Pfister, H., Oliva, A.: Eye fixation metrics for large scale evaluation and comparison of information visualizations. In: Burch, M., Chuang, L., Fisher, B., Schmidt, A., Weiskopf, D. (eds.) ETVIS 2015. MATHVISUAL, pp. 235–255. Springer, Cham (2017). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Missouri University of Science and TechnologyRollaUSA

Personalised recommendations