D iffe r e n tia l th r e s h o ld in c o lo u r p e r c e p tio n
a c o n s e q u e n c e o f re tin a l p ro c e s s in g a n d p h o to re c e p to r n o n -lin e a ritie s D e s c r ip tio n o f m e a s u r e s L + M 300
300
200
200
60
S
M
S
40
L -M
20
40
80
120
100
100
0
0
80
160
W R JB
100
120
140
160
20
30
L
L L + M
120
400
80
M
S
M
40
50
60
400
300
300
200
S 200
100
100
0
0
40
L -M 0 0
100
200
G F
300
0
400
L
0.9
50
100
150
200
250
300
0
350
20
W R JB
L
0.7
40
60
80
100
M
d (L -M )
0.5
Y . L e G r a n d R e v .O p t. 1 9 4 9 T r a n s la te d b y K . K n o b la u c h C R A 1 9 9 4 . A .L N a g y J O S A 1 9 8 7
0.4 0.5 0.3
0.2 0.3 0.1
0.1
-10
L -M
0
10
L
20
L
M M
0
A
S
a
0
s C D
0
c
20
S
m
C
0
0
L -M
40
60
80
D
E u c lid ie n th re s h o ld
L M S sp a c e L a y e r 1
P h o to re c e p to r tra n s d u c tio n
lm s s p a c e L a y e r 2
R e tin a l c o lo r c o d in g
A C D sp a c e L a y e r 3
0
d
120
m
G a n g lio n c e ll c o n v e rs io n to im p u ls e tra in
a c d s p a c e
T h e M o d e l is c o m p o s e d o f tw o n o n lin e a r la y e rs a n d o n e lin e a r la y e r. In th e firs t la y e r, p h o to re c e p to r tra n s d u c tio n fo llo w s th e N a k a -R u s h to n la w x = X /(X + X 0 ) w h e re X 0 re p re s e n ts th e a d a p ta tio n s ta te o f th e p h o to re c e p to r. T h is la w is n o n -lin e a r, a n d th e n o n lin e a rity is m o d u la te d b y th e a d a p ta tio n s ta te . T h e v a ria tio n o f lig h t fa llin g o n th e p h o to re c e p to r is v e ry im p o rta n t (2 -3 lo g u n it). H o w e v e r, n e u ro n s c o d e o n ly s m a ll v a ria tio n . T h e a d a p ta tiv e n o n lin e a r la w c o m p re s s e s in p u t s ig n a l to m a tc h th e n e u ro n c a p a c ity In th e s e c o n d la y e r (lin e a r) th e tra n s d u c tio n o f p h o to re c p to r is c o d e d in lu m in a n c e a n d c o lo r o p p o s itio n (c h ro m in a n c e ). In th e th ird la y e r, w e m o d e l th e g a n g lio n c e lls c o n v e rs io n fro m b ip o la r c e lls a n a lo g u e s ig n a l to th e o p tic n e rv e p u ls e tra in . T h e n o n lin e a r g a n g lio n c o n v e rs io n la w is a p p ro x im a te d b y a n a rc ta n fu n c tio n w h ic h ta k e in to a c c o u n t O N & O F F p a th w a y s
100
180
80
160
M L
60 140
40 120
20
0
0
50
100
150
M
L
100 -100
200
250
300
350
-60
-20
L -M
400
0
20
60
100
v a ria tio n
P a r a m e te r e s tim a tio n
p a ra m e te r c o n v e rg e n c e 160
E llip s o id p a ra m e te rs
X
G iX = 1
T
= N
i
i
- 1
P '- 1 M
i
c o s t fu n c tio n
J = (H
G iM i
- 1
- I) i
P
- 1
(2 )
N i
L 0
100
80
- 1
0 0.1 -0.2 0.08
M 0
60
0.06
C 0 40
0
1000
2000
3000
4000
5000
(3 )
-0.6
0.04
0
1000
2000
Nb Iteration
3000
4000
5000 -0.5
Nb Iteration
1
0.4
L 0
D 0
0.25
0.2
90 0.2
80
M 0
70
T h e p a ra m e te rs a re c o m p u te d in o rd e r to m in im is e th e c o s t fu n c tio n .
0
d -0.2 0.15
60 -0.4
C 0
S 0
40
30
0
1000
3000
5000
7000
0.05 0
9000
2000
80
-0.6
4000
6000
8000
S iz e a n d o rie n ta tio n o f th e e llip s o id s a re a lm o s t id e n tic a l in th e a c d s p a c e .
350
300
300
250
250
S
S 200
200
150
150
100
100
50
50
0
0
40
20
80
100
120
140
160
-50 70
80
90
100
110
L
120
130
140
150
160
-50 15
500
500
100
400
400
200
200
40
100
100
35
40
-100
0
L
250
300
350
400
M
45
50
55
60
65
-100 0
50
100
150
200
L
250
300
350
0
T o th e c o m sp a
e s tim a te th e re s u lt, w e re p la c e a ll th e e llip s o id s in a c d s p a c e b y th e a v e ra g e e llip s o id a n d th e n p u te th e c o rre s p o n d in g e llip s o id s in th e L M S c e .
W e o b s e rv e d th a t o n ly o n e e llip s o id ty p e (th e a v e ra g e ) g iv e s ris e to a la rg e v a rie ty in s iz e a n d o rie n ta tio n in L M S s p a c e , a c c o rd in g to th e e x p e rim e n ta l d a ta .
T h e m o d e l p e rfe c tly m a tc h e s th e " V " s h a p e c u rv e a n d c o n firm s th a t a tw o n o n lin e a r la y e rs a rc h ite c tu re e x p la in s lo w le v e l c o lo r v is io n .
0
0
20
200
30
S
S 60
150
25
300
300
80
100
20
L
120
M
1
400
350
30
0.5
450
400
50
0
R e s u lt a n d c o n c lu s io n
450
M
-0.8 -0.5
c
70
60
10000
Nb Iteration
Nb Iteration
W e u s e a c la s s ic a l a lg o rith m (g ra d ie n t d e s c e n t) to a p p ro x im a te th e id e a l p a ra m e te rs T h e c o s t fu n c tio n is th e d iffe re n c e b e tw e e n e llip s o id in a c d s p a c e a n d sp h e re .
0.6 0.3
100
0.1
50
0.5
110
50
0
0
c
120
¶J = L ¶L 0
10 60
O n c e , th e th re e la y e rs m o d e l m a y b e a p p ro x im a te b y m a trix tra n s fo rm a tio n (2 ).
0.2 0.12
d
- 1
- I)T ( H
i
P a ra m e te rs o f e llip s o id in L M S s p a c e m a y b e w ritte n in m a trix fo rm (1 ).
D 0
0.14
120
M o d e l tra n s fo rm a tio n
H
e llip s o id in a c d s p a c e
0.6
0.16
S 0
140
(1 )
P a ra m e te r u p g ra d e
B io lo g ic a l m o d e l
0
l
A
0 -20
30
A - T h e firs t n o n lin e a rity la w tra n s fo rm s th e d ire c tio n a n d th e s iz e o f a s tim u lu s . F o r e x a m p le a c irle b e c o m e s a n e llip s e . B - Its o rie n ta tio n a n d s iz e d e p e n d s o n th e lo c a tio n o f th e c o n s id e re d s tim u lu s . T h is la s t p ro p e rty a llo w s to fo llo w th e p rin c ip a l d ire c tio n o f e x p e rim e n ta l d a ta . T h e e ffe c t o f c o lo r c o d in g (L a y e r 2 ) is to tu rn th e s p a c e in o rd e r to m a tc h w ith c h o m a tic d ire c tio n . C - T h e s e c o n d n o n -lin e a rity p ro v id e s th e " V " s h a p e d fu n c tio n .
C - E ffe c t o f s e c o n d n o n -lin e a rity o n v a ria tio n o f c h ro m in a n c e (L a y e r 3 ) 200
ra n d , th e a n c e fo llo w s a ra c te ris tic P G N , G F ,A R , a n d W R JB
T h is p ro p e rty a ls o e x is ts fo r th e 2 la s t c a s e s , m e a s u re s m a d e d o n o t e m p h a s is e d it.
0.6 0.7
d (L -M )
120
A c c o rd in g to Y . L e G v a ria tio n o f c h ro m in a " V " s h a p e . T h is c h a p p e a rs fo r o b se rv e r G W b u t n o t fo r D L M
B - P rin c ip a l d ire c tio n o f 2 D n o n lin e a rity (L a y e r 1 )
l
Valeur
400
tra n s fo rm a tio n o n a c irc u la r s tim u lu s
Valeur
G F
400
M o d e l a p p lic a tio n
A - E ffe c t o f th e 2 D n o n -lin e a r (L a y e r 1 ) 6 o b se rv e rs : P G N (2 D ), W R JB , D L M , G F , A R , G W (c o n s ta n t lu m in o s ity ) D .L . M a c A d a m J O S A 1 9 4 2 W .R .J . B r o w n J O S A 1 9 4 9 G . W y s ze c k i J O S A 1 9 7 1 W e c o n v e rt o rig in a l d a ta fro m th e C IE X Y Z s p a c e to th e L M S s p a c e In L M S , e llip s o id s c o rre s p o n d to th e d iffe re n tia l th re s h o ld o f e a c h p h o to re c e p to r In th e L M p ro je c tio n , e llip s o id s a re o rie n te d in L + M a n d L -M d ire c tio n . In th e L S o r M S p ro je c tio n , e llip s o id a re o rie n te d in fa n -s h a p e d .
Valeur
80
F -3 8 0 3 1 G re n o b le C e d e x F r a n c e h ttp ://w w w - tir f .in p g .f r /
J .H é r a u lt ( a lle y s s o ,h e r a u lt@ tir f .in p g .f r )
Valeur
D .A lle y s s o n &
L IS -IN P G L a b o ra to ire d e s im a g e s e t d e s s ig n a u x 4 6 , A v e . F é lix V ia lle t
50
100
150
200
L
250
300
350
F u rth e rm o re , th e s e c o n d la y e r in fo rm s u s a b o u t th e o p p o n e n t c o lo r c o d in g .
Repeat on the opposite side, being careful to not let the model unfold as you do so. This is a blow-up of the creasing pattern between steps 12 & 13, note that a.
Oblique lines result from travelling waves of activation (pigment production). Branches .... Stripes Parallel to the Direction of Growth: Formation of Stable Periodic.
purpose of the present paper is to test the usefulness of LSF information as compared to HSF ... emotional stimuli in his blind visual hemifield (de Gelder,. Vroomen, Pourtois ..... Machine Intelligence, 15(10), 1042-1052. Cottrell, G.W. (1990).
As analogy to the mosaic of cone, it may possible that in the cortex, the low frequency achromatic spatial information of the magnocellular pathway helps the ...
To perceive the surrounding world, its beauty and subtlety, we not only move eyes but our visual system ... camera processing. This last part allows us to .... Interesting lights in this context is those who are related to animal evolution, such as .
Most of digital cameras today use a color filter array and a single sensor to acquire ... these methods are optimized for Bayer CFA they are not very useful for ... In the case of demosaicing we suppose that the mosaiced image ... With these two matr
May 16, 2012 - derstand how the response of photoreceptor cells lead to ... in the following sections, neurogeometry could be a key to .... dences for such a renormalization process in Section 2. In ..... ers imply a change in processing when energy
Abstractâ We present a computationally efficient demosaicing algorithm ..... ing by accurate luminance estimation,â in IEEE International Conference on Image ...
network or the algorithm for convergence could be improved. We also show that the global level of luminosity is not exactly reconstructed. This is certainly ...
Jun 15, 2010 - equivalently placed on a triangular grid) and the cone types form ..... My acknowledgments also to Seitz Phototechnik A.G. Zurich for their .... Color naming, unique hues, and hue cancellation predicted from singularities.
two pathways and the mode of presentation of stimuli changes depending on the channel, M or P, to preferentially stimulate. This rules out ... pathway. In our group analysis this does not result in differential brain activation. ... Matlab 6 software
A very very brief introduction . . . The realization x, of a spatial point process defined on S and observed in a bounded domain is a finite set of objects xi â S.
Single-Sensor Imaging: Methods and Applications for Digital Cameras .... variables are linearly dependent and the intrinsic dimension is thus only two.
random arrangement of colors and quasi equal proportion of RGB provide best reconstruction ... color filter array (CFA) to provide several color components ..... emosaicing.html. 41 N.-X. Lian, ... 24/supplementarymaterial.pdf . J. Imaging Sci.
ABSTRACT. We present a new algorithm that performs demosaicing and super-resolution jointly from a set of raw images sampled with a color filter array.
CNRS, a grant from the French National Research Agency (ANR Grant .... Orban, G. A. (1984), Neuronal operations in the visual cortex, Studies in brain function, Vol. ... Winston, J. S., Vuilleumier, P., and Dolan, R. J. (2003), âEffects of ...
