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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
Bayesian model
Probabilisticcomputation
SemicircularCanals(noisy)
Otoliths(ambiguous)
PriorsP(motion)
P(sensory inputs | motion)Internal model of sensors
Motion estimatesP(motion | sensory inputs) = P(sensory inputs | motion).P(motion)
a
Plausible Improbable
GA
F
Geometrical aspects
Angularacceleration
∫ ∫
Otolithsignal
Canalsignal
Linearacceleration
Linearvelocity
Headposition
∫ ∫
Angularvelocity
Headorientation
Double integration
Double integration
H-1
Noise issues
Angularacceleration
∫ ∫
Otolithsignal
Canalsignal
Linearacceleration
Linearvelocity
∫ ∫
Noise
Angularvelocity
Headorientation
Headposition
Double integration
Double integration
?
?
H-1
A priori
Angularacceleration
∫ ∫
Otolithsignal
Canalsignal
Linearacceleration
Linearvelocity
∫ ∫
A priori
Angularvelocity
Headorientation
A priori
Headposition
Double integration
Double integration
H-1
Noise
Visual informations
Angularacceleration
∫ ∫
Otolithsignal
Canalsignal
Linearacceleration
Linearvelocity
∫ ∫
A priori
Angularvelocity
Headorientation
A priori
Headposition
Double integration
Double integration
H-1
Noise
Visualsignal
Noise
Plan
● Introduction to Bayesian inference
● Visuo-vestibular interactions (Monkey)
● 3D Stimulations (Monkey, Human)
Bayesian inference
● Probability exam: normal and pronged dice (Gezinkter Würfel)
D1 : normal D2 : pronged6 in 50% throws
Bayesian inference
Likelihood :
P(6 | D1) = 1/6
P(6 | D2) = 3/6
A priori :
P(D1) = 9/10
P(D2) = 1/10
A posteriori :
P(D1 | 6) = k * 1/6 * 9/10 = 3/4
P(D2 | 6) = k * 3/6 * 1/10 = 1/4?
Bayesian inference
● More observations
P(2 | D2).P(6 | D2).P(D2)
P(6,2)P(D2 | 6,2) =
Likelihood A priori
Bayesian inference and vestibular information
Likelihood :
P(Vest. Signal| Motion)
A priori :
P(Motion)
F
V = 0
P(Motion | Vest. Signal) = P(Vest. Signal| Motion).P(Motion)
Rotations around a vertical axis
Angularacceleration
∫Canalsignal
A priori40 °/s
Angularvelocity
Noise η10 °/s
Visualsignal
Noise η7 °/s
τ = 4 sH-1
Results: rotation in dark
0 50 100-1
-0.50
0.5
1
Rotation Stop
Rotation Vel.
Estimated vel. (τ = 20 s)
Vest. Signal (τ = 4 s)Velocity Storage
time (s)
Optokinetic stimulation
Light Dark
OKANOKN
0 20 40 60 80
0
0.5
1Stimulation velocity(Ω)
Estimatedvelocity (Ω)
Raphan,Matsuo,Cohen,1979
Optokinetic stimulation
Light Dark
0 20 40 60 80
0
0.5
1
No velocitystorage
Normal
No canals
Raphan, Cohen,Matsuo 1977
Stimulation velocity (°/s)
OK
N v
eloc
ity (
°/s)
Canals plugging
Optokinetic stimulation
Rotation Stop
Light Dark
Rotation in dark
0 10 20-1
0
1
0 10 200
0.5
1
Angelaki & al. 1996
τ = 0.1 s
Velocity storage
0 50 100-1
-0.5
0
0.5
1
0 20 40 60 800
0.5
1
Rotation Stop Light Dark
Stimultation velocity
Estimated velocity (Ω)^
Vest. signal
'Velocity storage' (Ωt0)
^
Optokinetic stimulationRotation in Dark
Raphan, Cohen
Conclusion
● Probabilistic modelling: noise on vestibular signal σ
= 10°/s
noise on visual signal σ = 7°/s A priori on velocity σ = 40°/s
Light Dark
0 20 40 60 80
0
0.5
1
3D model
Angularacceleration
∫ ∫
Otolithsignal
Canalsignal
Linearacceleration
Linearvelocity
∫ ∫
A priori40 - 30 °/s
Angularvelocity
Headorientation
A priori3 - 5 m/s²
Headposition
Double integration
Double integration
Noise η10 °/s
Implementation: particle filter
Somatogravic effect
AccelerationA
Y (
m/s
²)
-2 0 2 4 6 8 10
0
2
4
Tilt
roll
(°)
-2 0 2 4 6 8 10
0
10
20
30
G
-A
F
Somatogravic: canals plugged
AY
(m
/s²)
-2 0 2 4 6 8 10
0
2
4ro
ll (°
)
-2 0 2 4 6 8 10
0
10
20
30
G
-A
F
Acceleration
Tilt
Tilt/translation discrimination
Acceleration (m/s²)
0 5 10 15-4-2024
tilt (°)
temps (s)0 5 10 15
-20
0
20
Acceleration (m/s²)
0 5 10 15-4-2024
tilt (°)
0 5 10 15
-20
0
20
Normal
Angelaki, 1999
Tilt/translation discrimination
0 5 10 15-4-2024
time (s)0 5 10 15
-20
0
20
0 5 10 15-4-2024
0 5 10 15
-20
0
20
Canals plugged
Angelaki, 1999
Acceleration (m/s²)
tilt (°)
Acceleration (m/s²)
tilt (°)
Post-rotatory tilt
60 80 100 120-60-40-20
020
60 80 100 120
-20
0
20
time (s)60 80 100 120
-20
0
20
Angelaki, 1994
OVAR
Head tilt (°)
0 50 100 150 2000
100
time (s)0 50 100 150 200
0
100
200
α
180 °/s
0 50 100 150 200
020
4060
60 °/s
Angular velocity (°/s)
Angular velocity (°/s)
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 σΩ
6 σΩ
Acceleration (13 m/s²) 2.6 σA
2.6 σA
2.6 σA
Correia 1966,Lackner 1978,
Mittelstaedt 1989,Bos 2002 (90°/s)
Guedry 1965,Benson 1966,Correia 1966,
Wall 1990
OVAR
Denise, Darlot, Droulez, Berthoz 1989
Angular velocity (°/s)
0 50 100 150 200
0
20
40
60
Angular velocity (°/s)
time (s)0 50 100 150 200
0
20
40
60
Angelaki 2000, Kushiro 2002
Motion sickness
0 20 40 6010
-2
100
102
104
accélération linéaire
rotation
inclinaison post-rotatoire
time (s)
k.P(Sensory Signal)
Conclusion
● 3 hypothesis Sensory signals uncertainty A priori Bayesian inference
● Lesion modelling (observer theory)● Bayesian approach● Extensions● Predictions Laurens, Droulez, Biol. Cyber. 2006