Journal of Mathematical Biology

, Volume 65, Issue 6–7, pp 1245–1266 | Cite as

Mathematical requirements of visual–vestibular integration

  • Douglas A. HanesEmail author


This article addresses the intersection between perceptual estimates of head motion based on purely vestibular and purely visual sensation, by considering how nonvisual (e.g. vestibular and proprioceptive) sensory signals for head and eye motion can be combined with visual signals available from a single landmark to generate a complete perception of self-motion. In order to do this, mathematical dimensions of sensory signals and perceptual parameterizations of self-motion are evaluated, and equations for the sensory-to-perceptual transition are derived. With constant velocity translation and vision of a single point, it is shown that visual sensation allows only for the externalization, to the frame of reference given by the landmark, of an inertial self-motion estimate from nonvisual signals. However, it is also shown that, with nonzero translational acceleration, use of simple visual signals provides a biologically plausible strategy for integration of inertial acceleration sensation, to recover translational velocity. A dimension argument proves similar results for horizontal flow of any number of discrete visible points. The results provide insight into the convergence of visual and vestibular sensory signals for self-motion and indicate perceptual algorithms by which primitive visual and vestibular signals may be integrated for self-motion perception.


Vestibular Parallax Optokinetic Dimension Optic flow 

Mathematics Subject Classification (2000)

91E30 92C20 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Banks MS, Ehrlich SM, Backus BT, Crowell JA (1996) Estimating heading during real and simulated eye movements. Vis Res 36(3): 431–443CrossRefGoogle Scholar
  2. Barmack NH (2003) Central vestibular system: vestibular nuclei and posterior cerebellum. Brain Res Bull 60: 511–541CrossRefGoogle Scholar
  3. Beck JC, Rothnie P, Straka H, Wearne SL, Baker R (2006) Precerebellar hindbrain neurons encoding eye velocity during vestibular and optokinetic behavior in the goldfish. J Neurophysiol 96: 1370–1382CrossRefGoogle Scholar
  4. Bertin RJV, Berthoz A (2004) Visuo-vestibular interaction in the reconstruction of travelled trajectories. Exp Brain Res 154: 11–21CrossRefGoogle Scholar
  5. Bertin RJV, Israël I, Lappe M (2000) Perception of two-dimensional, simulated ego-motion trajectories from optic flow. Vis Res 40: 2951–2971CrossRefGoogle Scholar
  6. Bremmer F, Lappe M (1999) The use of optical velocities for distance discrimination and reproduction during visually simulated self motion. Exp Brain Res 127(1): 33–42CrossRefGoogle Scholar
  7. Büttner-Ennever JA, Horn AKE, Graf W, Ugolini G (2002) Modern concepts of brainstem anatomy: from extraocular motoneurons to proprioceptive pathways. Ann NY Acad Sci 956: 75–84CrossRefGoogle Scholar
  8. Cutting JE, Vishton PM, Flückiger M, Baumberger B, Gerndt JD (1997) Heading and path information from retinal flow in naturalistic environments. Percept Psychophys 59(3): 426–441CrossRefGoogle Scholar
  9. Frenz H, Lappe M (2005) Absolute travel distance from optic flow. Vis Res 45: 1679–1692CrossRefGoogle Scholar
  10. Frost BJ, Wylie DR, Wang Y-C (1990) The processing of object and self-motion in the tectofugal and accessory optic pathways of birds. Vis Res 30(11): 1677–1688CrossRefGoogle Scholar
  11. Goldberg JM, Fernández C (1984) The vestibular system. In: Brookhart JM, Mountcastle VB, Darian-Smith I (eds) Handbook of physiology—the nervous system III. American Physiological Society, Baltimore, pp 977–1022Google Scholar
  12. Gordon DA (1965) Static and dynamic fields in human space perception. J Opt Soc Am 55: 1296–1303CrossRefGoogle Scholar
  13. Guedry FE (1974) Psychophysics of vestibular sensation. In: Kornhuber HH (eds) Handbook of sensory physiology, vol 6. Springer, New York, pp 3–154Google Scholar
  14. Hanes DA, Keller J, McCollum G (2008) Motion parallax contribution to perception of self-motion and depth. Biol Cybern 98(4): 273–293zbMATHCrossRefGoogle Scholar
  15. Harris LR (1994) Visual motion caused by movements of the eye, head, and body. In: Smith AT, Snowden R (eds) Visual detection of motion. Academic Press, London, pp 397–436Google Scholar
  16. Harris LR, Jenkin M, Zikowitz DC (2000) Visual and non-visual cues in the perception of linear self motion. Exp Brain Res 135: 12–21CrossRefGoogle Scholar
  17. Holly JE (2000) Baselines for three-dimensional perception of combined linear and angular self-motion with changing rotational axis. J Vestib Res 10: 163–178Google Scholar
  18. Ivanenko YP, Grasso R, Israël I, Berthoz A (1997) The contribution of the otoliths and semicircular canals to the perception of two-dimensional passive whole-body motion in humans. J Physiol 502(1): 223–233CrossRefGoogle Scholar
  19. Jaekl PM, Jenkin MR, Harris LR (2005) Perceiving a stable world during active rotational and translational head movements. Exp Brain Res 163: 388–399CrossRefGoogle Scholar
  20. Klam F, Graf W (2003) Vestibular response kinematics in posterior parietal cortex neurons of macaque monkeys. Eur J Neurosci 18(4): 995–1010CrossRefGoogle Scholar
  21. Koenderink JJ, van Doorn AJ (1987) Facts on optic flow. Biol Cybern 56(4): 247–254zbMATHCrossRefGoogle Scholar
  22. Koenderink JJ, van Doorn AJ (1976) Local structure of movement parallax of the plane. J Opt Soc Am 66: 717–723CrossRefGoogle Scholar
  23. Lackner JR, DiZio P (1988) Visual stimulation affects the perception of voluntary leg movements during walking. Perception 17: 71–80CrossRefGoogle Scholar
  24. Lappe M, Bremmer F, van den Berg AV (1999) Perception of self-motion from visual flow. Trends Cogn Sci 3(9): 329–336CrossRefGoogle Scholar
  25. Longuet-Higgins HC, Prazdny K (1980) The interpretation of a moving retinal image. Proc R Soc Lond B 208: 385–397CrossRefGoogle Scholar
  26. Malcolm R, Melvill Jones G (1974) Erroneous perception of vertical motion by humans seated in the upright position. Acta Otolaryngolica 77: 274–283CrossRefGoogle Scholar
  27. McCrea RA, Gdowski GT, Boyle R, Belton T (1999) Firing behavior of vestibular neurons during active and passive head movements: Vestibulo-spinal and other non-eye-movement related neurons. J Neurophysiol 82: 416–428Google Scholar
  28. Mulavara AP, Bloomberg JJ (2002/2003) Identifying head-trunk and lower limb contributions to gaze stabilization during locomotion. J Vestib Res 12(5–6): 255–269Google Scholar
  29. Nakayama K, Loomis JM (1974) Optical velocity patterns, velocity-sensitive neurons, and space perception: a hypothesis. Perception 3(1): 63–80CrossRefGoogle Scholar
  30. Nawrot M, Stroyan K (2009) The motion/pursuit law for visual depth perception from motion parallax. Vis Res 49: 1969–1978CrossRefGoogle Scholar
  31. Perrone JA, Stone LS (1994) A model of self-motion estimation within primate extrastriate visual cortex. Vis Res 34: 2917–2938CrossRefGoogle Scholar
  32. Pozzo I, Berthoz A, Lefort L (1990) Head stabilization during various locomotor tasks in humans: 1. Normal subjects. Exp Brain Res 82: 97–106CrossRefGoogle Scholar
  33. Regan D (1986) Visual Processing of Four Kinds of Relative Motion. Vis Res 26(1): 127–145CrossRefGoogle Scholar
  34. Royden CS (1994) Analysis of misperceived observer motion during simulated eye rotations. Vis Res 34: 3215–3222CrossRefGoogle Scholar
  35. Royden CS, Banks MS, Crowell JA (1992) The perception of heading during eye movements. Nature 360: 583–585CrossRefGoogle Scholar
  36. Simpson JI, Leonard CS, Soodak RE (1988) The accessory optic system of rabbit. II. Spatial organization of direction selectivity. J Neurophysiol 60(6): 2055–2072Google Scholar
  37. Stone LS, Perrone JA (1997) Human heading estimation during visually simulated curvilinear motion. Vis Res 37(5): 573–590CrossRefGoogle Scholar
  38. van den Berg AV (1992) Robustness of perception of heading from optic flow. Vis Res 32: 1285–1296CrossRefGoogle Scholar
  39. Vishton PM, Cutting JE (1995) Wayfinding, displacements, and mental maps: Velocity fields are not typically used to determine one’s aimpoint. J Exp Psychol Hum Percept Perform 21: 978–995CrossRefGoogle Scholar
  40. Wang RF, Cutting JE (1999) Where we go with a little good information. Psychol Sci 10(1): 71–75CrossRefGoogle Scholar
  41. Warren WH, Hannon DJ (1990) Eye movements and optical flow. J Opt Soc Am A 7(1): 160–169CrossRefGoogle Scholar
  42. Wearne S, Raphan T, Cohen B (1998) Control of spatial orientation of the angular vestibuloocular reflex by the nodulus and uvula. J Neurophysiol 79: 2690–2715Google Scholar
  43. Wood SJ, Reschke MF, Sarmiento LA, Clément G (2007) Tilt and translation motion perception during off-vertical axis rotation. Exp Brain Res 182(3): 365–377CrossRefGoogle Scholar
  44. Wright WG, DiZio P, Lackner JR (2005) Vertical linear self-motion perception during virtual visual and actual-inertial stimulation: More than weighted summation of sensory inputs. J Vest Res 15(4): 185–195Google Scholar
  45. Yakushin SB, Raphan T, Cohen B (2006) Spatial properties of central vestibular neurons. J Neurophysiol 95(1): 464–478CrossRefGoogle Scholar
  46. Yong N, Paige GD, Seidman SH (2007) Multiple sensory cues underlying the perception of translation and path. J Neurophysiol 97(2): 1100–1113CrossRefGoogle Scholar
  47. Zacharias GL, Young LR (1981) Influence of combined visual and vestibular cues on human perception and control of horizontal rotation. Exp Brain Res 41(2): 159–171CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Legacy Research CenterPortlandUSA

Personalised recommendations