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Jean LAURENS Bayesian Modelling of Visuo-Vestibular Interactions with Jacques DROULEZ

Jean LAURENS Bayesian Modelling of Visuo-Vestibular Interactions with Jacques DROULEZ Laboratoire de Physiologie de la Perception et de l'Action, CNRS, Collège de France, Paris. Laurens, Droulez, Biol. Cyber. 2006. Probabilistic computation. Bayesian model. Semicircular Canals

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Jean LAURENS Bayesian Modelling of Visuo-Vestibular Interactions with Jacques DROULEZ

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  1. Jean LAURENS Bayesian Modelling of Visuo-Vestibular Interactions with Jacques DROULEZ Laboratoire de Physiologie de la Perception et de l'Action, CNRS, Collège de France, Paris Laurens, Droulez, Biol. Cyber. 2006

  2. Probabilistic computation Bayesian model Semicircular Canals (noisy) Otoliths (ambiguous) F G A P(sensory inputs | motion) Internal model of sensors Priors P(motion) a PlausibleImprobable Motion estimates P(motion | sensory inputs) = P(sensory inputs | motion).P(motion)

  3. A priori • VOR dynamic • Somatogravic effect

  4. Angular acceleration Canal signal Linear acceleration Otolith signal Linear velocity Head position Geometrical aspects Double integration Angular velocity Head orientation H-1 ∫ ∫ Double integration ∫ ∫

  5. Angular acceleration Canal signal Linear acceleration Otolith signal Linear velocity Head position Noise issues ? Noise Double integration Angular velocity Head orientation H-1 ∫ ∫ Double integration ∫ ∫ ?

  6. Angular acceleration Canal signal Linear acceleration Otolith signal Linear velocity Head position A priori A priori Noise Double integration Angular velocity Head orientation H-1 ∫ ∫ Double integration ∫ ∫ A priori

  7. Visual signal Angular acceleration Canal signal Linear acceleration Otolith signal Linear velocity Head position Visual informations Noise A priori Noise Double integration Angular velocity Head orientation H-1 ∫ ∫ Double integration ∫ ∫ A priori

  8. Plan • Introduction to Bayesian inference • Visuo-vestibular interactions (Monkey) • 3D Stimulations (Monkey, Human)

  9. Bayesian inference • Probability exam: normal and pronged dice (Gezinkter Würfel) D1 : normal D2 : pronged 6 in 50% throws

  10. Bayesian inference P(6 | D1) = 1/6 P(6 | D2) = 3/6 Likelihood : P(D1 | 6) = 1/4 P(D2 | 6) = 3/4 ?

  11. Bayesian inference • A priori: P(D1) = 9/10 P(D2) = 1/10

  12. Bayesian inference • Bayes formula Likelihood A priori • P(6 | D2).P(D2) • P(D2 | 6) = • P(6)

  13. Bayesian inference A priori : P(D1) = 9/10 P(D2) = 1/10 Likelihood : P(6 | D1) = 1/6 P(6 | D2) = 3/6 A posteriori : P(D1 | 6) = k * 1/6 * 9/10 = 3/4 P(D2 | 6) = k * 3/6 * 1/10 = 1/4 ?

  14. Bayesian inference • More observations Likelihood A priori • P(2 | D2).P(6 | D2).P(D2) • P(D2 | 6,2) = • P(6,2)

  15. Bayesian inference and vestibular information V = 0 Likelihood : P(Vest. Signal| Motion) A priori : P(Motion) F P(Motion | Vest. Signal) = P(Vest. Signal| Motion).P(Motion)

  16. Angular acceleration Canal signal Visual signal Rotations around a vertical axis A priori 40 °/s Noise η 10 °/s Angular velocity H-1 ∫ τ = 4 s Noise η 7 °/s

  17. Results: rotation in dark 1 Rotation Vel. 0.5 0 Estimated vel. (τ = 20 s) Velocity Storage -0.5 Vest. Signal (τ = 4 s) -1 0 50 100 Rotation Stop time (s)

  18. Optokinetic stimulation Raphan, Matsuo, Cohen, 1979 OKN OKAN Light Dark 1 Stimulation velocity(Ω) 0.5 Estimated velocity (Ω) 0 0 20 40 60 80

  19. Optokinetic stimulation Normal OKN velocity (°/s) No canals Light Dark 1 Stimulation velocity (°/s) No velocity storage Raphan, Cohen, Matsuo 1977 0.5 0 0 20 40 60 80

  20. Optokinetic stimulation 1 Normal 0.5 0 0 20 40 60 80 Light Dark 1 No canals 0.5 0 0 20 40 60 80

  21. Canals plugging Rotation in dark 1 0 τ = 0.1 s -1 0 10 20 Rotation Stop Optokinetic stimulation 1 0.5 0 0 10 20 Dark Light Angelaki & al. 1996

  22. Velocity storage Rotation in Dark Optokinetic stimulation 1 1 0.5 0 0.5 -0.5 0 -1 0 50 100 0 20 40 60 80 Rotation Stop Light Dark Stimultation velocity ^ Estimated velocity (Ω) Vest. signal ^ 'Velocity storage' (Ωt0) Raphan, Cohen

  23. Equivalence with Raphan-Cohen model +

  24. Conclusion • Probabilistic modelling: • noise on vestibular signal σ= 10°/s • noise on visual signal σ = 7°/s • A priori on velocity σ = 40°/s 1 0.5 0 0 20 40 60 80 Light Dark

  25. 3D model Acceleration Tilt F ≈G F G A Gravito-inertial ambiguity

  26. Angular acceleration Canal signal Linear acceleration Otolith signal Linear velocity Head position 3D model A priori 40 - 30 °/s Noise η 10 °/s Double integration Angular velocity Head orientation ∫ ∫ Double integration ∫ ∫ A priori 3 - 5 m/s² Implementation: particle filter

  27. Somatogravic effect Acceleration 4 2 (m/s²) Y 0 A -2 0 2 4 6 8 10 Tilt 30 F 20 G roll (°) 10 0 -A -2 0 2 4 6 8 10

  28. Somatogravic: canals plugged Acceleration 4 2 (m/s²) Y 0 A -2 0 2 4 6 8 10 Tilt 30 F 20 G roll (°) 10 0 -A -2 0 2 4 6 8 10

  29. Tilt/translation discrimination Normal Acceleration (m/s²) 4 2 0 -2 -4 0 5 10 15 tilt (°) 20 0 -20 0 5 10 15 Acceleration (m/s²) 4 2 0 -2 -4 0 5 10 15 tilt (°) 20 0 -20 0 5 10 15 Angelaki, 1999 temps (s)

  30. Tilt/translation discrimination Canals plugged Acceleration (m/s²) 4 2 0 -2 -4 0 5 10 15 tilt (°) 20 0 -20 0 5 10 15 Acceleration (m/s²) 4 2 0 -2 -4 0 5 10 15 tilt (°) 20 0 -20 0 5 10 15 Angelaki, 1999 time (s)

  31. Post-rotatory tilt Angular velocity 50 (°/s) 0 y  -50 0 20 40 60 80 100 120 time (s) Angelaki, 1994

  32. Post-rotatory tilt 20 0 -20 -40 -60 60 80 100 120 20 0 -20 60 80 100 120 20 0 -20 60 80 100 120 time (s) Angelaki, 1994

  33. Centrifugation F G A Roll 60 40 (°) r 20  0 -20 0 50 100 150 time (s)

  34. OVAR 60 °/s 180 °/s Benson, Bodin, 1965 Guedry, 1974 after Guedry, 1974

  35. OVAR Angular velocity (°/s) 60 40 20 0 0 50 100 150 200 60 °/s Angular velocity (°/s) 200 100 0 0 50 100 150 200 time (s)  (°) Head tilt α 100 180 °/s 0 0 50 100 150 200

  36. OVAR G 60 °/s F 180 °/s F -A G Guedry, 1974

  37. OVAR Ang. vel. a priori: σΩ = 30°/s Acceleration a priori : σA = 5 m/s² 60 °/s 78°/s 180 °/s Rotation 2 σΩ 2.6 σΩ6σΩ Acceleration (13 m/s²) 2.6 σA 2.6 σA2.6 σA Correia 1966, Lackner 1978, Mittelstaedt 1989, Bos 2002 (90°/s) Guedry 1965, Benson 1966, Correia 1966, Wall 1990

  38. OVAR Angular velocity (°/s) 60 40 20 0 Denise, Darlot, Droulez, Berthoz 1989 0 50 100 150 200 Angular velocity (°/s) 60 40 20 0 0 50 100 150 200 time (s) Angelaki 2000, Kushiro 2002

  39. OVAR Yaw velocity (°/s) 60 40 20 0 0 20 40 60 80 time (s) Angelaki 2000, Kushiro 2002

  40. Motion sickness k.P(Sensory Signal) 4 10 accélération linéaire 2 10 rotation 0 10 inclinaison post-rotatoire -2 10 0 20 40 60 time (s)

  41. Conclusion • 3 hypothesis • Sensory signals uncertainty • A priori • Bayesian inference • Lesion modelling (observer theory) • Bayesian approach • Extensions • Predictions Laurens, Droulez, Biol. Cyber. 2006

  42. Thanks !

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