s1 v1 a1 krubitzer & kaas v2 mt s2 · brain weight (grams) 0.1 1 10 100 1,000 10,000 0.001 0.01...
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S1S2
A1V1V2 MTKrubitzer & Kaas
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Rockel AJ, Hiorns RW & Powell TP (1980) “The basic uniformity in structure of the neocortex,” Brain 103:221-44.
30 μm
pia
white matter
Somato- Mean ofMotor sensory Frontal Temporal Parietal Visual means
Mouse 109.2 ± 6.7 111.9 ±6.9 110.8 ±7.1 110.5 ±6.5 104.7 ±7.2 112.2 ±6.0 109.9 ±6.8Rat 108.2 ±5.8 107.0 ±6.7 104.3 ±7.2 107.7 ±9.2 105.2 ±6.8 107.8 ±7.9 106.7 ±7.4Cat 103.9 ±7.6 106.6 ±7.2 108.0 ±6.2 113.8 ±7.3 110.6 ±7.4 109.8 ±9.9 108.8 ±7.7Monkey 110.2 ±9.4 109.4 ±9.4 112.0 ±11.1 109.8 ±10.3 114.6 ±9.9 267.9 ±13.7 ----Man 102.3 ±9.5 103.7 ±5.8 103.3 ±8.6 107.7 ±7.5 104.1 ±12.5 258.9 ±15.8 ----
mean ± s.d.
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7º
22º
45º
45º10º0º..
visual field
Hubel 1982
0
12 3
receptive fields
cortex0 1 2 3 mm Hubel & Wiesel 1974
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Hubel & Wiesel2 mm
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after Hubel & Wiesel 1962
“Hypercolumn”
~2 mm
~2 mm
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Re-routing experiments (ferret)
Sur et al.
visual auditory
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Roe et al. 1990
5 mm
1 mm
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Sur et al. 1988
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Body weight (Kilograms)
Bra
in w
eigh
t (gr
ams)
0.1
1
10
100
1,000
10,000
0.001 0.01 0.1 1 10 100 1,000 10,000 100,000
Primates
Mammals
Birds
Bony Fish
Reptiles
modernhuman
porpoise
bluewhale
elephant
eel
alligatorcrow
goldfish
humming-bird
Crile & Quiring
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Van Essen et al. 1984
1 cm2º
Tootell et al. 1982
Half of area V1 represents the central 10º (2% of the visual field)
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S1S2
A1V1V2 MTKrubitzer & Kaas
?
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Cortex unfolded
Lateral view of monkey brain
Medial view of monkey brain
Felleman and Van Essen 1991
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Barlow 1994
"Thus the hypothesis is that the cerebral cortex confers skill in deriving useful knowledge about the material and social world from the uncertain evidence of our senses, it stores this knowledge, and gives access to it when required."
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Barlow 1994
Finding New Associations in Sensory Data
1. Remove evidence of associations you already know about . . .
. . . to facilitate detecting new ones.
2. Make available the probabilities of the features currently present . . .
. . . to determine chance expectations.
3. Choose features that occur independentlyof each other in the normal environment . . .
. . . to determine chance expectations or combinations of them.
4. Choose “suspicious coincidences” as features . . .
. . . to reduce redundancy and ensure appropriate generalization.
(1/f2 and center-surround)
(-logp, adaptation)
(orientation selectivity)
(lateral inhibition)
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Barlow 1994, fig. 1.3
Sensorymessages
Model ofcurrent scene
New associativeknowledge
Stored knowledgeabout environment
New informationabout environment
Compareand remove
matches
Context:Previous sense dataTask prioritiesUnsatisfied appetites
What weactually
see
This cycle can be repeated
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Welch & Bishop, fig. 1.2
1−kx) 1−kPInitial estimates for and
Time Update (“Predict”)
(1) Project the state ahead
(2) Project the error covariance ahead
11 −+−=−kBukxAkx ))
QAkAPkP T +−=−1
⎟⎠⎞⎜
⎝⎛ −−+−= kxHzkKkxkx k
)))
−⎟⎠⎞
⎜⎝⎛ −= kPHkKkP 1
1−
⎟⎠⎞⎜
⎝⎛ +−−= RHkHPHkPkK TT
Measurement Update (“Correct”)
(1) Compute the Kalman gain
(2) Update estimate with measurement zk
(3) Update the error covariance
Schematic of a Kalman Filter
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Simoncelli & Olshausen 2001
Neighboring pixels tend to have similar values
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Simoncelli & Olshausen 2001
Neighboring pixels tend to have similar values
natural image
1/f 2
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barlow_filt3.m
“Whitened”: ∇2⋅G or what ctr-sur doesSophie in the Arctic
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Harris 1980
Finding New Associations in Sensory Data(The yellow Volkswagen problem)
YellowVolkswagen?
Reward?Yes No
Yes
No
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Harris 1980
Finding New Associations in Sensory Data(The yellow Volkswagen problem)
sparse dense
YV
“yellowVolkswagen”
cell “redFerrari”
cell
“combinatorial explosion”
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Harris 1980
Finding New Associations in Sensory Data(The yellow Volkswagen problem)
sparse dense
Y“yellow”
cell“Volkswagen”
cellV
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Harris 1980
Finding New Associations in Sensory Data(The yellow Volkswagen problem)
Yellow?
Reward?Yes No
Yes
No
Volkswagen?
Reward?Yes No
Yes
No
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Harris 1980
Finding New Associations in Sensory Data(The yellow Volkswagen problem)
sparse dense
“y”cell
“v”cell
e
v
w
k s
a
y
l
o
gn
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Gardner-Medwin & Barlow 2001
The curve shows how statistical efficiency for detecting associations with a feature X varies with the value of a parameter defined as follows:
Γx=αxpxZ / ⟨α⟩
where αx , ⟨α⟩ are the activity ratio for feature X and the average activity ratio, px is the probability of X, and Z is the number of neurons in the subset under consideration. For instance, one could identify an association with any one of the 45 possible pairs of active neurons in a subset of 10 with an efficiency of 50% provided that the neurons were active independently, the pair caused two neurons to be active, the probability of the pair occurring was 0.1, and the average fraction active was 0.2. (From Gardner-Medwin and Barlow 1994)
“sparseness”
Y
V
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Gardner-Medwin & Barlow 2001
What are the desirable properties of directly represented features?
“. . . primitive conjunctions of active elements that actually occur often, but would be expected to occur only infrequently by chance,” that is,
“curious coincidences”
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2 3 4 5 6 7 80
2
4
6
Line
sum of 9 pixels
log 1
0(#)
barlow_filt3.m
“Whitened”: ∇2⋅G or what ctr-sur does
2 3 4 5 6 7 80
2
4
6
Random
log 1
0(#)
Suspicious Coincidences
Sophie in the Arctic
p < 0.0100
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The perfect map?
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StreetsAberdeen Rd …….….C7Academy St …….…...D9Acorn Pk ……….…....F9Acton St ……….…….C7Adamian Pk …....……C9Adams St ……….…...D9Addison St ……..……D9Aerial St ……….…....C8Albermarle St ….……D8Alfred Rd …………....E9Allen St ……………...D9Alpine St ………...…..C7
.
.
.
.
.
.
.
.
.
.
.
.
.Longwood Ave …….L12
K
L
M
1211 13
T
T
A more useful map
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MBTA map
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Linking Features: Orientation
Guzmann 1968
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after Hubel & Wiesel 1962
Striate cortex contains a map of orientation.
“Hypercolumn”
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“Space” “Feature”
Tootell et al. 1982
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Bosking et al. 1997
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Tootell et al. 1982
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Linking Features: Orientation
Guzmann 1968
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(1024 * 768)pixels * 24 bits/pixel = 18,874,368 bits
38 points * 2 words/point * 16 bits/word = 1,216 bits
compression ratio = 15,522
edge detection
invariancea) positionb) sign of contrast
curvature
gain adjustment
hierarchy
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Hough Transform
Horace Barlow 1986
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Horace Barlow 1986
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1 mm
MT*
5 mm
V1
*
* HM
VM
fovea
VisualField
Tootell & Born
fundus of STS
post. bank of STS
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MT direction
map
1 mm
UpDown
d
m
Tootell & Born, unpub’d
fovea
periphery
inferior VF
superior VF