motion smear/ sharpening fitzhugh-nagumo equation can
TRANSCRIPT
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FitzHugh-Nagumo equation can describe frequency responses
in human vision
Atsushi Osa, Masaru Suzuki, Koki Otaka,
Shoichi Kai, Hidetoshi Miike
Yamaguchi University
Motion smear/ Sharpening
• The visual system integrates signals over time.
Motion blur Motion blur Motion sharpening Motion sharpening
Motion sharpening
• When objects move fast they look sharper than when they are stationary. – Ramachandran et al.(1974), Bex et al. (1995), Hammett & Bex (1996)・・・
Brightness (stationary)
Perceived shape (moving)
Moving
A typical impulse response function can show the motion sharpening
(Pääkkönen & Morgan 2001)
An impulse response function of the human vision systemAn impulse response function of the human vision system
Steep slope
gradual slope
moving edge
brightness
position
moving edge
brightness
position
motion Sharpening motion Sharpening
motion smear motion smear
From frequency response of vision to impulse response
Sensitively to sin-wave flicker Sensitively to sin-wave flicker
Frequency (Hz)
Sen
siti
vely
Impulse response Impulse response
IFT IFT
model D. H. Kelly (1971)
Impulse responses depending on the average illuminance
• D. H. Kelly (1971)
frequency response frequency response
Impulse responses Impulse responses
Average illuminance
● 9300 td 〇 850 td △ 77 td ◇ 7.1 td □ 0.65 td ■ 0.06 td
Frequency (Hz)
Sen
siti
vely
retina model retina model
2
Frequency response of vision
Average illuminance
● 9300 td 〇 850 td △ 77 td ◇ 7.1 td □ 0.65 td ■ 0.06 td
Sen
siti
vely
Frequency (Hz)
low-pass low-pass
band-pass band-pass
dark stimulus dark stimulus
light stimulus light stimulus
In liner system
• RLC circuit
ftACdt
dqR
dt
qdL 2cos
12
2
The resonant frequency doesn’t depend on the inputThe resonant frequency doesn’t depend on the input
LC
10
Purpose
Liner Transfer function I O
Nonlinear transfer function
using FHN eq.
I O
FitzHugh-Nagumo equation
Spike generations in a neuron
u: activator v: inhibitor
abvudt
dv
IvuuCdt
duext
3
depolarization
hyperpolarization
u
v
Using equation
abvudt
dv
vuuCdt
du 3
CIaubbuCdt
dubuC
dt
ud 113 32
2
2Input Input
one variable
0113 32
2
2
aubbuCdt
dubuC
dt
ud
FHN eq. FHN eq.
Input : infinitesimal amplitude
• Input: I=I0+Aeit, I0: constant (average illuminant), A: infinitesimal amplitude
• Output: , u0: fixed point
• Power spectrum
bbuCCCubi
ACu
133
~2
0
2
0
2
22
0
2222
0
224
22*
13132
~~
bbuCuCCb
CAuuP
tuuu i
0 )e(~+=
3
Power spectrum
•
– D>=0 : Low-pass
– D<0: Band-pass
• p: peak frequency
22
0
22 132 uCCbD
2/Dp
22
0
2222
0
224
22*
13132
~~
bbuCuCCb
CAuuP
low-pass low-pass
band-pass band-pass
Pp)
2224
22
22 pp
p
bCC
CAP
b=0.8
C=5
Numerical analysis
abvudt
dv
vuuCdt
du 3
ftCACIaubbuCdt
dubuC
dt
ud2cos113 0
32
2
2
Input: I
Input: I0: average illuminance、 A: amplitude of stimulus
ftCACI 2cos0
one variable
0113 32
2
2
aubbuCdt
dubuC
dt
ud
Impulse f=0.1Hz f=0.25Hz
f=0.5Hz f=0.75Hz f=1.0Hz
f=2.5Hz f=5.0Hz f=7.5Hz
Output in various frequency u v
a=0.8
b=0.8
C=5
A=1
sec sec sec
sec sec sec
sec sec sec
A=0.01
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
0.01 0.1 1
Pow
er
Frequency (Hz)
0
0.22
0.44
0.49
0.53
Pp) Pp)
Analysis Analysis Numerical analysis Numerical analysis I I0
Light stimulus Light stimulus
dark stimulus dark stimulus
Difference
Variation range of the peak frequency p
narrow narrow
wide wide
FHN model Human vision
Bigger amplitude
0.000001
0.00001
0.0001
0.001
0.01
0.1
1
0.05 0.5
Po
wer
Frequency (Hz)
0 0.22
0.44 0.49
0.53
0.000001
0.00001
0.0001
0.001
0.01
0.1
1
0.05 0.5
Po
we
r
Frequency (Hz)
0 0.22
0.44 0.49
0.53 0.000001
0.00001
0.0001
0.001
0.01
0.1
1
0.05 0.5
Po
we
r
Frequency (Hz)
0 0.22
0.44 0.49
0.53
Input: I
Input: I0: average illuminance、 A: amplitude of stimulus
ftCACI 2cos0
I I0 I I0
I I0
A=0.01 A=0.01 A=0.1 A=0.1 A=0.4 A=0.4
4
0.0001
0.001
0.01
0.1
1
0.05 0.5
Pow
er
Frequency (Hz)
0 0.1
0.16 0.26
0.34 0.44
0.49 0.53
I I0
A=0.5 A=0.5
Frequency response Frequency response of vision
Frequency response Frequency response of FHN eq.
FHN with noise
avtbudt
dv
vuuCdt
du
)(
3
+
abvudt
dv
vuuCdt
du 3
noise
Effect of multiplicative noise
0.05 0.5
0 0.1
0.16 0.26
0.38 0.44
0.53
0.05 0.5
0 0.1
0.16 0.18
0.26 0.38
0.44 0.53 0.001
0.01
0.1
1
0.05 0.5
Pow
er
0 0.1 0.16 0.26 0.3 0.34 0.38 0.44 0.53
=0 =0 :0 ~ 0.4 (uniform distribution) :0 ~ 0.4 (uniform distribution)
:0 ~ 1 (uniform distribution) :0 ~ 1 (uniform distribution)
I I0 I I0 I I0
The most similar result
0.001
0.01
0.1
1
0.05 0.5
Pow
er
Frequency (Hz)
0 0.1
0.16 0.18
0.26 0.38
0.44
avtbudt
dv
vuuCdt
du
)(
3
+
a=0.8
b=0.8
C=5
:0 ~ 0.4 (uniform distribution)
I I0
Conclusions
• FitzHugh-Nagumo equation can describe frequency responses in human vision.
– Dynamical noise stabilizes the response.
FHN eq. I O
avtbudt
dv
vuuCdt
du
)(
3
+0.001
0.01
0.1
1
0.05 0.5
Po
we
r
Frequency (Hz)
0 0.1 0.16 0.18 0.26 0.38 0.44
Future work1
• More accurate simulation of human vision.
• D.H.Kelly’s retina model + Our model
0.001
0.01
0.1
1
0.05 0.5
Po
we
r
Frequency (Hz)
0 0.1 0.16 0.18 0.26
5
Future work 2
• Simulation of motion sharpening
FHN eq.
avtbudt
dv
vuuCdt
du
)(
3
+
Motion sharpening Motion sharpening
Future work 3
• Decrease in the flicker fusion rate relates to mental fatigue. • Flicker fusion rate : the frequency at which
an flicker light stimulus appears to be completely steady
• The mechanism has not been revealed yet. • The multiplicative noise in our model works to
decrease the sensitively of flicker. Dynamical noise in brainDynamical noise in brain
Mental fatigue Mental fatigue
relationship ? relationship ?
Thank you for your kind attention