Pointing Errors in Non-metric Virtual Environments

  • Alexander Muryy
  • Andrew Glennerster
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11034)


There have been suggestions that human navigation may depend on representations that have no metric, Euclidean interpretation but that hypothesis remains contentious. An alternative is that observers build a consistent 3D representation of space. Using immersive virtual reality, we measured the ability of observers to point to targets in mazes that had zero, one or three ‘wormholes’ – regions where the maze changed in configuration (invisibly). In one model, we allowed the configuration of the maze to vary to best explain the pointing data; in a second model we also allowed the local reference frame to be rotated through 90, 180 or 270 degrees. The latter model outperformed the former in the wormhole conditions, inconsistent with a Euclidean cognitive map.


Human navigation Spatial representation Virtual reality Metric model Motion parallax Binocular disparity Topological model Labelled graph View-based 



This research was supported by EPSRC/Dstl grant EP/N019423/1.

Supplementary Information. Additional figures, movies and raw data are available at:


  1. 1.
    Gallistel, C.: The Organization of Learning. The MIT Press, Cambridge (1990)Google Scholar
  2. 2.
    O’Keefe, J., Nadel, L.: The Hippocampus as a Cognitive Map. Oxford University Press, Oxford (1978)Google Scholar
  3. 3.
    Tolman, E.C.: Cognitive maps in rats and men. Psychol. Rev. 55, 189–208 (1948)CrossRefGoogle Scholar
  4. 4.
    Meilinger, T., Strickrodt, M., Bülthoff, H.H.: Qualitative differences in memory for vista and environmental spaces are caused by opaque borders, not movement or successive presentation. Cognition 155, 77–95 (2016)CrossRefGoogle Scholar
  5. 5.
    Warren, W.H., Rothman, D.B., Schnapp, B.H., Ericson, J.D.: Wormholes in virtual space: from cognitive maps to cognitive graphs. Cognition 166, 152–163 (2017)CrossRefGoogle Scholar
  6. 6.
    Gillner, S., Mallot, H.A.: Navigation and acquisition of spatial knowledge in a virtual maze. J. Cogn. Neurosci. 10, 445–463 (1998)CrossRefGoogle Scholar
  7. 7.
    Foo, P., Warren, W.H., Duchon, A., Tarr, M.J.: Do humans integrate routes into a cognitive map? Map - versus landmark-based navigation of novel shortcuts. J. Exp. Psychol. Learn. Mem. Cogn. 31, 195–215 (2005)CrossRefGoogle Scholar
  8. 8.
    Chrastil, E.R., Warren, W.H.: From cognitive maps to cognitive graphs. PLoS One. 9, e112544 (2014)CrossRefGoogle Scholar
  9. 9.
    Byrne, R.W.: Memory for urban geography. Q. J. Exp. Psychol. 31, 147–154 (1979)CrossRefGoogle Scholar
  10. 10.
    Tversky, B.: Distortions in cognitive maps. Geoforum 23, 131–138 (1992)CrossRefGoogle Scholar
  11. 11.
    Chrastil, E.R., Warren, W.H.: Active and passive spatial learning in human navigation: acquisition of graph knowledge. J. Exp. Psychol. Learn. Mem. Cogn. 41, 1162–1178 (2015)CrossRefGoogle Scholar
  12. 12.
    Ishikawa, T., Montello, D.R.: Spatial knowledge acquisition from direct experience in the environment: individual differences in the development of metric knowledge and the integration of separately learned places. Cogn. Psychol. 52, 93–129 (2006)CrossRefGoogle Scholar
  13. 13.
    Meilinger, T., Riecke, B.E., Bülthoff, H.H.: Local and global reference frames for environmental spaces. Q. J. Exp. Psychol. 67, 542–569 (2014)CrossRefGoogle Scholar
  14. 14.
    Moar, I., Bower, G.H.: Inconsistency in spatial knowledge. Mem. Cognit. 11, 107–113 (1983)CrossRefGoogle Scholar
  15. 15.
    Poucet, B.: Spatial cognitive maps in animals: new hypotheses on their structure and neural mechanisms. Psychol. Rev. 100, 163–182 (1993)CrossRefGoogle Scholar
  16. 16.
    Kuipers, B., Byun, Y.-T.: A robot exploration and mapping strategy based on a semantic hierachy of spatial representations. J. Robot. Auton. Syst. 8, 47–63 (1991)CrossRefGoogle Scholar
  17. 17.
    Kuipers, B., Tecuci, D.G., Stankiewicz, B.J.: The skeleton in the cognitive map: a computational and empirical exploration. Environ. Behav. 35, 81–106 (2003)CrossRefGoogle Scholar
  18. 18.
    Schultheis, H., Bertel, S., Barkowsky, T.: Modeling mental spatial reasoning about cardinal directions. Cogn. Sci. 38, 1521–1561 (2014)CrossRefGoogle Scholar
  19. 19.
    Franz, M.O., Schölkopf, B., Mallot, H.A., Bülthoff, H.H.: Learning view graphs for robot navigation. Auton. Robots. 5, 111–125 (1998)CrossRefGoogle Scholar
  20. 20.
    Cheeseman, J.F., Millar, C.D., Greggers, U., Lehmann, K., Pawley, M.D.M., Gallistel, C.R., Warman, G.R., Menzel, R.: Way-finding in displaced clock-shifted bees proves bees use a cognitive map. Proc. Natl. Acad. Sci. 111, 8949–8954 (2014)CrossRefGoogle Scholar
  21. 21.
    Cheeseman, J.F., et al.: The cognitive map hypothesis remains the best interpretation of the data in honeybee navigation. Proc. Natl. Acad. Sci. 111, E4398 (2014). Reply to Cheung et al.CrossRefGoogle Scholar
  22. 22.
    Cheung, A., et al.: Still no convincing evidence for cognitive map use by honeybees. Proc. Natl. Acad. Sci. 111, E4396–E4397 (2014). Fig. 1CrossRefGoogle Scholar
  23. 23.
    Stachenfeld, K.L., Botvinick, M.M., Gershman, S.J.: The hippocampus as a predictive map. Nat. Neurosci. 20, 1643–1653 (2017)CrossRefGoogle Scholar
  24. 24.
    Freksa, C., Newcombe, N.S., Gärdenfors, P., Wölfl, S. (eds.): Spatial Cognition VI. LNCS (LNAI), vol. 5248. Springer, Heidelberg (2008). Scholar
  25. 25.
    Mallot, H.A., Basten, K.: Embodied spatial cognition: biological and artificial systems. Image Vis. Comput. 27, 1658–1670 (2009)CrossRefGoogle Scholar
  26. 26.
    Montello, D.R.: Scale and multiple psychologies of space. In: Frank, A.U., Campari, I. (eds.) COSIT 1993. LNCS, vol. 716, pp. 312–321. Springer, Heidelberg (1993). Scholar
  27. 27.
    Kluss, T., Marsh, W.E., Zetzsche, C., Schill, K.: Representation of impossible worlds in the cognitive map. Cogn. Process. 16, 271–276 (2015)CrossRefGoogle Scholar
  28. 28.
    Vasylevska, K., Kaufmann, H.: Towards efficient spatial compression in self-overlapping virtual environments. In: Proceedings of 2017 IEEE Symposium on 3D User Interfaces, 3DUI 2017, pp. 12–21 (2017)Google Scholar
  29. 29.
    Zetzsche, C., Wolter, J., Galbraith, C., Schill, K.: Representation of space: image-like or sensorimotor? Spat. Vis. 22, 409–424 (2009)CrossRefGoogle Scholar
  30. 30.
    Svarverud, E., Gilson, S., Glennerster, A.: A demonstration of “broken” visual space. PLoS One. 7, e33782 (2012)CrossRefGoogle Scholar
  31. 31.
    Glennerster, A.: The time course of 2-D shape discrimination in random dot stereograms. Vis. Res. 36, 1955–1968 (1996)CrossRefGoogle Scholar
  32. 32.
    Johnston, E.B.: Systematic distortions of shape from stereopsis. Vis. Res. 31, 1351–1360 (1991)CrossRefGoogle Scholar
  33. 33.
    Koenderink, J.J., van Doorn, A.J., Kappers, A.M.L., Doumen, M.J.A., Todd, J.T.: Exocentric pointing in depth. Vis. Res. 48, 716–723 (2008)CrossRefGoogle Scholar
  34. 34.
    Ogle, K.: Researches in Binocular Vision (1950)Google Scholar
  35. 35.
    McNamara, T.P., Diwadkar, V.A.: Symmetry and asymmetry of human spatial memory. Cogn. Psychol. 34, 160–190 (1997)CrossRefGoogle Scholar
  36. 36.
    McNamara, T.P.: Mental representations of spatial relations. Cogn. Psychol. 18, 87–121 (1986)CrossRefGoogle Scholar
  37. 37.
    Foo, P., Duchon, A., Warren, W.H., Tarr, M.J.: Humans do not switch between path knowledge and landmarks when learning a new environment. Psychol. Res. 71, 240–251 (2007)CrossRefGoogle Scholar
  38. 38.
    Tittle, J.S., Todd, J.T., Perotti, V.J., Norman, J.F.: Systematic distortion of perceived three-dimensional structure from motion and binocular stereopsis. J. Exp. Psychol. Hum. Percept. Perform. 21, 663–678 (1995)CrossRefGoogle Scholar
  39. 39.
    Koenderink, J.J., van Doorn, A.J.: Affine structure from motion. J. Opt. Soc. Am. A 8, 377 (1991)CrossRefGoogle Scholar
  40. 40.
    Glennerster, A., Rogers, B.J., Bradshaw, M.F.: Stereoscopic depth constancy depends on the subject’s task. Vis. Res. 36, 3441–3456 (1996)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Psychology and Clinical Language SciencesUniversity of ReadingReadingUK

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