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

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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.

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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.

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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.

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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

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  1. Paul R. MacNeilage
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  2. Martin S. Banks
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  4. Heinrich H. Bülthoff
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Correspondence to Paul R. MacNeilage.

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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

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