Skip to main content

Advertisement

SpringerLink
Log in

A Bayesian model of the disambiguation of gravitoinertial force by visual cues

  • Research Article
  • Published:
Experimental Brain Research Aims and scope Submit manuscript

Abstract

The otoliths are stimulated in the same fashion by gravitational and inertial forces, so otolith signals are ambiguous indicators of self-orientation. The ambiguity can be resolved with added visual information indicating orientation and acceleration with respect to the earth. Here we present a Bayesian model of the statistically optimal combination of noisy vestibular and visual signals. Likelihoods associated with sensory measurements are represented in an orientation/acceleration space. The likelihood function associated with the otolith signal illustrates the ambiguity; there is no unique solution for self-orientation or acceleration. Likelihood functions associated with other sensory signals can resolve this ambiguity. In addition, we propose two priors, each acting on a dimension in the orientation/acceleration space: the idiotropic prior and the no-acceleration prior. We conducted experiments using a motion platform and attached visual display to examine the influence of visual signals on the interpretation of the otolith signal. Subjects made pitch and acceleration judgments as the vestibular and visual signals were manipulated independently. Predictions of the model were confirmed: (1) visual signals affected the interpretation of the otolith signal, (2) less variable signals had more influence on perceived orientation and acceleration than more variable ones, and (3) combined estimates were more precise than single-cue estimates. We also show that the model can explain some well-known phenomena including the perception of upright in zero gravity, the Aubert effect, and the somatogravic illusion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Notes

  1. In the vestibular literature, it is conventional for the X, Y, and Z axes to correspond to forward, upward, and lateral, respectively. We have chosen to use axes that are conventional in the vision literature.

  2. The noise would actually be 3d in X–Y–Z space, but here we consider it collapsed onto the Z–Y plane. Note that Eq. 3 is valid for any head-centric plane, but for simplicity we discuss it in terms of the Z–Y plane only.

  3. This conversion requires the assumption that ||G|| = 9.81 m/s2. This can be thought of as a prior on ||G||. This prior also has some variability associated with it, and that will generate additional variability in the otolith likelihood.

  4. Pitch is a circular variable and acceleration is not. So plots of the likelihood functions in pitch-acceleration space should be cylindrical plots. Each point on the cylinder has a position along the circumference that represents pitch and a position perpendicular to the circumference that represents acceleration. For simplicity, we show the unwrapped cylinders in our figures.

  5. For simplicity, we do not consider separately kinesthetic and somatosensory signals because the forces that affect them are the same as the forces that drive the otoliths.

  6. Note that any error in scaling the scene will lead to an error in the velocity and acceleration estimates.

  7. The maximum angular acceleration, which occurred very briefly at the beginning of platform motion, was ∼12.5°/s2. We had to place the rotation axis in the floor of the platform to maximize the motion range. The axis was ∼100 cm beneath and ∼26 cm in front of the center of the subject’s head. Thus, the angular acceleration generated small tangential and centripetal acceleration at the head. These accelerations were quite small and had virtually no influence on the total gravitoinertial force profiles.

  8. In pilot testing, we found that people experienced both forward translation and pitch when presented the non-visual stimuli. Thus, it was reasonable to ask subjects which of two intervals yielded greater perceived acceleration and which of two intervals yields greater perceived pitch. Nonetheless, the mere instruction to interpret the otolith signal one way (e.g., as pitch, not acceleration) does not mean subjects are capable of completely succeeding, which can lead both to bias (when they attribute some of the signal to the acceleration instead) and increased variability (when the amount they attribute to acceleration varies from trial to trial).

  9. Note that the posterior is centered on non-zero inertial acceleration, which means that the model predicts a perceived inertial acceleration that is slightly greater than zero. To our knowledge, no one has examined whether the conditions that produce the Aubert effect also cause a perceived acceleration.

References

  • Adelson EH, Movshon JA (1982) Phenomenal coherence of moving visual patterns. Nature 300:523–525

    Article  PubMed  CAS  Google Scholar 

  • Alais D, Burr D (2004) The ventriloquist effect results from near-optimal bimodal integration. Curr Biol 14:257–262

    Article  PubMed  CAS  Google Scholar 

  • Angelaki DE, McHenry MQ, Dickman JD, Newlands SD, Hess BJ (1999) Computation of inertial motion: neural strategies to resolve ambiguous otolith information. J Neurosci 19:316–327

    PubMed  CAS  Google Scholar 

  • Angelaki DE, Shiakh AG, Green AM, Dickman JD (2004) Neurons compute internal models of the physical laws of motion. Nature 430:560–564

    Article  PubMed  CAS  Google Scholar 

  • Berger DR (2003) Spectral texturing for real-time applications. In: Siggraph 2003 sketches and applications. ACM Press, New York. DOI 10.1145/095400.965509

  • Benson AJ, Hutt ECB, Brown SF (1989) Thresholds for the perception of whole body angular movement about a vertical axis. Aviat Space Environ Med 60:205–213

    PubMed  CAS  Google Scholar 

  • Cheung B, Money K, Wright H, Bateman W (1995) Spatial disorientation - implicated accidents in Canadian forces, 1982–1992. Aviat Space Environ Med 66(6):579–585

    PubMed  CAS  Google Scholar 

  • Dichgans J, Held R, Young LR, Brandt T (1972) Moving visual scenes influence the apparent direction of gravity. Science 178:1217–1219

    Article  PubMed  CAS  Google Scholar 

  • Einstein A (1907) Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen. Jahrbuch der Radioaktivität und Elektronik 4:411–462

    Google Scholar 

  • Ercoline WR (1997) Classification of the USAF SD mishaps. In: Braithwaite MG, DeRoche SL, Alvarez EA, Reese MA (eds) Proceedings of the first tri-service conference on rotary-wing spatial disorientation: spatial disorientation in the operational rotary-wing environment. USAARL report no. 97-15

  • Ernst MO, Banks MS (2002) Humans integrate visual and haptic information in a statistically optimal fashion. Nature 415:429–433

    Article  PubMed  CAS  Google Scholar 

  • Gepshtein S, Banks MS (2003) Viewing geometry determines how vision and haptics combine in size perception. Curr Biol 13:483–488

    Article  PubMed  CAS  Google Scholar 

  • Ghahramani Z, Wolpert DM, Jordan MI (1997) Computational models of sensorimotor integration. In: Morasso PG, Sanguineti V (eds) Self-organization, computational maps, and motor control. Elsevier, Amsterdam, pp 117–147

    Google Scholar 

  • Gibson JJ (1950) The perception of the visual world. Houghton-Miffin, Boston

    Google Scholar 

  • Gibson JJ (1966) The senses considered as perceptual systems. Houghton-Mifflin, Boston

    Google Scholar 

  • Gillingham KK, Previc FH (1993) Spatial orientation in flight. AL-TR-1993–0022. Brooks Air Force Base, Armstrong Laboratory, Texas

  • Glasauer S (1995) Linear acceleration perception: frequency dependence of the hilltop illusion. Acta Otolaryngol Suppl 520:37–40

    PubMed  Google Scholar 

  • Glasauer S, Mittelstaedt H (1998) Perception of spatial orientation in microgravity. Brain Res Brain Res Rev 28(1–2):185–193

    Article  PubMed  CAS  Google Scholar 

  • Goldberg J, Fernandez C (1971) Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. I. Resting discharge and response to constant angular accelerations. J Neurophysiol 34:635–660

    PubMed  CAS  Google Scholar 

  • Groen EL, Valenti Clari MSV, Hosman RJAW (2001) Evaluation of perceived motion during a simulated takeoff run. J Aircraft 38(4):600–606

    Article  Google Scholar 

  • Harris LR, Jenkin M, Zikovitz DC (2000a) Vestibular capture of the perceived distance of passive linear self motion. Arch Ital Biol 138(1):63–7

    CAS  Google Scholar 

  • Harris LR, Jenkin M, Zikovitz DC (2000b) Visual and non-visual cues in the perception of linear self motion. Exp Brain Res 135:12–21

    Article  CAS  Google Scholar 

  • Helmholtz H (1866) Treatise on physiological optics. Ed. trans. JPC Southall. Thoemmes Press, Bristol, 2000

  • Hillis JM, Ernst MO, Banks MS, Landy MS (2002) Combining sensory information: mandatory fusion within, but not between, senses. Science 298:1627–1630

    Article  PubMed  CAS  Google Scholar 

  • Howard IP (1982) Human visual orientation. Wiley, New York

    Google Scholar 

  • Howard IP, Childerson L (1994) The contribution of motion, the visual frame, and visual polarity to sensations of body tilt. Perception 23:753–762

    Article  PubMed  CAS  Google Scholar 

  • Kersten D, Mamassian P, Yuille A (2004) Object perception as Bayesian inference. Ann Rev Psychol 55:271–304

    Article  Google Scholar 

  • Knill DC, Saunders JA (2003) Do humans optimally integrate stereo and texture information for judgments of surface slant? Vis Res 43:2539–2558

    Article  PubMed  Google Scholar 

  • Körding KP, Wolpert DM (2004) Bayesian integration in sensorimotor learning. Nature 427(6971):244–247

    Article  PubMed  CAS  Google Scholar 

  • Landy MS, Kojima H (2001) Ideal cue combination for localizing texture-defined edges. J Opt Soc Am A Opt Image Sci Vis 18:2307–2320

    PubMed  CAS  Google Scholar 

  • Landy MS, Maloney LT, Johnston EB, Young M (1995) Measurement and modeling of depth cue combination: in defense of weak fusion. Vis Res 35:389–412

    Article  PubMed  CAS  Google Scholar 

  • Lessard CS, Matthews R, Yauch D (2000) Effects of rotation on somatogravic illusions. IEEE Eng Med Biol Mag 19:59–65

    Article  PubMed  CAS  Google Scholar 

  • Longuet-Higgins HC, Prazdny K (1980) The interpretation of a moving retinal image. Proc R Soc Lond B 208:385–397

    Article  PubMed  CAS  Google Scholar 

  • Malcolm R, Melvill-Jones G (1970) A quantitative study of vestibular adaptation in humans. Acta Otolaryngol 70:126–135

    PubMed  CAS  Google Scholar 

  • Maybeck PS (1979) Stochastic models, estimation and control. Academic, NewYork

    Google Scholar 

  • Merfeld DM, Zupan L, Peterka RJ (1999) Humans use internal models to estimate gravity and linear acceleration. Nature 398:615–618

    Article  PubMed  CAS  Google Scholar 

  • Merfeld DM, Zupan LH, Gifford CA (2001) Neural processing of gravito-inertial cues in humans. II. Influence of the semicircular canals during eccentric rotation. J Neurophysiol 85(4):1648–1660

    PubMed  CAS  Google Scholar 

  • Merfeld DM, Park S, Gianna-Poulin C, Black FO, Wood S (2005) Vestibular perception and action employ qualitatively different mechanisms. I. Frequency response of VOR and perceptual response during translation and tilt. J Neurophysiol 94:186–198

    Article  PubMed  Google Scholar 

  • Mittelstaedt H (1983) A new solution to the problem of the subjective vertical. Naturwissenschaften 70(6):272–281

    Article  PubMed  CAS  Google Scholar 

  • Mittelstaedt ML, Mittelstaedt H (2001) Idiothetic navigation in humans: estimation of path length. Exp Brain Res 139:318–332

    Article  PubMed  CAS  Google Scholar 

  • Oruç I, Maloney LT, Landy MS (2003) Weighted linear cue combination with possibly correlated error. Vis Res 43:2451–2468

    Article  PubMed  Google Scholar 

  • Otakeno S, Matthews RSJ, Folio L, Previc FH, Lessard CS (2002) The effects of visual scenes on roll and pitch thresholds in pilots versus nonpilots. Aviat Space Environ Med 73:98–101

    PubMed  Google Scholar 

  • Previc FH, Varner DC, Gillingham KK (1992) Visual scene effects on the somatogravic illusion. Aviat Space Environ Med 63:1060–1064

    PubMed  CAS  Google Scholar 

  • Reymond G, Kemeny A (2000) Motion cueing in the Renault driving simulator. Vehicle Syst Dynam 34(4):249–259

    Article  Google Scholar 

  • Reymond G, Droulez J, Kemeny A (2002) Visuovestibular perception of self-motion modeled as a dynamic optimization process. Biol Cybern 87(4):301–314

    Article  PubMed  Google Scholar 

  • Roach NW, Heron J, McGraw PV (2006) Resolving multisensory conflict: a strategy for balancing the costs and benefits of audio-visual integration. Proc R Soc B Biol Sci 273(1598):2159–2168

    Google Scholar 

  • Royden CS, Crowell JA, Banks MS (1994) Estimating heading during eye movements. Vis Res 34(23):3197–3214

    Article  PubMed  CAS  Google Scholar 

  • Seidman SH, Telford L, Paige GD (1998) Tilt perception during dynamic linear acceleration. Exp Brain Res 119(3):307–314

    Article  PubMed  CAS  Google Scholar 

  • Stocker AA, Simoncelli EP (2006) Noise characteristics and prior expectations in human visual speed perception. Nat Neurosci 9(4):578–585

    Article  PubMed  CAS  Google Scholar 

  • Stone LS, Thompson P (1992) Human speed perception is contrast dependent. Vis Res 32(8):1535–1549

    Article  PubMed  CAS  Google Scholar 

  • Tokumaru O, Kaida K, Ashida H, Mizumoto C, Tatsuno J (1998) Visual influence on magnitude of somatogravic illusion evoked on spatial disorientation demonstrator. Aviat Space Eviron Med 69:111–116

    CAS  Google Scholar 

  • van Boxtel JJ, Wexler M, Droulez J (2003) Perception of plane orientation from self-generated and passively observed optic flow. J Vis 3(5):318–332

    Article  PubMed  Google Scholar 

  • Weiss Y, Simoncelli EP, Adelson EH (2002) Motion illusions as optimal percepts. Nat Neurosci 5:598–604

    Article  PubMed  CAS  Google Scholar 

  • Wexler M, Panerai F, Lamouret I, Droulez J (2001) Self-motion and the perception of stationary objects. Nature 409(6816):85–88

    Article  PubMed  CAS  Google Scholar 

  • Wichmann FA, Hill NJ (2001) The psychometric function: I. Fitting, sampling, and goodness-of-fit. Perc Psychophys 63:1293–1313

    CAS  Google Scholar 

  • Yuille AL, Bülthoff HH (1996) Bayesian decision theory and psychophysics. In: Richards W, Knill DC (eds) Perception as Bayesian inference. Cambridge University Press, Cambridge, pp 123–162

  • Zupan LH, Merfeld DM (2003) Neural processing of gravito-inertial cues in humans. IV. Influence of visual rotational cues during roll optokinetic stimuli. J Neurophysiol 89(1):390–400

    Article  PubMed  CAS  Google Scholar 

  • Zupan LH, Merfeld DM (2005) Human ocular torsion and perceived roll responses to linear acceleration. J Vestib Res 15(4):173–183

    PubMed  Google Scholar 

  • Zupan LH, Merfeld DM, Darlot C (2002) Using sensory weighting to model the influence of canal, otolith and visual cues on spatial orientation and eye movements. Biol Cybern 86(3):209–230

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

This research was supported by NIH training grant (EY14194) to the Berkeley Vision Science program and AFOSR research grant (F49620) to Martin Banks. Thanks to MarcErnst for helpful discussion and the MPI workshop for techincal assistance. Special thanks to three reviewers who provided thoughtful and thorough comments on the manuscript.

Author information

Authors and Affiliations

  1. Vision Science Program, University of California, Berkeley, CA, 94720, USA

    Paul R. MacNeilage & Martin S. Banks

  2. Department of Psychology and Wills Neuroscience Institute, University of California, Berkeley, CA, 94720, USA

    Martin S. Banks

  3. Max Planck Institute for Biological Cybernetics, Spemannstr. 38, 72076, Tübingen, Germany

    Daniel R. Berger & Heinrich H. Bülthoff

Authors
  1. Paul R. MacNeilage
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martin S. Banks
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel R. Berger
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Heinrich H. Bülthoff
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paul R. MacNeilage.

Rights and permissions

Reprints and permissions

About this article

Cite this article

MacNeilage, P.R., Banks, M.S., Berger, D.R. et al. A Bayesian model of the disambiguation of gravitoinertial force by visual cues. Exp Brain Res 179, 263–290 (2007). https://doi.org/10.1007/s00221-006-0792-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00221-006-0792-0

Keywords

Search

Navigation