S1S2

A1V1V2 MTKrubitzer & Kaas

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.

7º

22º

45º

45º10º0º..

visual field

Hubel 1982

0

12 3

receptive fields

cortex0 1 2 3 mm Hubel & Wiesel 1974

Hubel & Wiesel2 mm

after Hubel & Wiesel 1962

“Hypercolumn”

~2 mm

~2 mm

Re-routing experiments (ferret)

Sur et al.

visual auditory

Roe et al. 1990

5 mm

1 mm

Sur et al. 1988

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

Van Essen et al. 1984

1 cm2º

Tootell et al. 1982

Half of area V1 represents the central 10º (2% of the visual field)

S1S2

A1V1V2 MTKrubitzer & Kaas

?

Cortex unfolded

Lateral view of monkey brain

Medial view of monkey brain

Felleman and Van Essen 1991

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."

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)

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

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

Simoncelli & Olshausen 2001

Neighboring pixels tend to have similar values

Simoncelli & Olshausen 2001

Neighboring pixels tend to have similar values

natural image

1/f 2

barlow_filt3.m

“Whitened”: ∇2⋅G or what ctr-sur doesSophie in the Arctic

Harris 1980

Finding New Associations in Sensory Data(The yellow Volkswagen problem)

YellowVolkswagen?

Reward?Yes No

Yes

No

Harris 1980

Finding New Associations in Sensory Data(The yellow Volkswagen problem)

sparse dense

YV

“yellowVolkswagen”

cell “redFerrari”

cell

“combinatorial explosion”

Harris 1980

Finding New Associations in Sensory Data(The yellow Volkswagen problem)

sparse dense

Y“yellow”

cell“Volkswagen”

cellV

Harris 1980

Finding New Associations in Sensory Data(The yellow Volkswagen problem)

Yellow?

Reward?Yes No

Yes

No

Volkswagen?

Reward?Yes No

Yes

No

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

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

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”

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

The perfect map?

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

MBTA map

Linking Features: Orientation

Guzmann 1968

after Hubel & Wiesel 1962

Striate cortex contains a map of orientation.

“Hypercolumn”

“Space” “Feature”

Tootell et al. 1982

Bosking et al. 1997

Tootell et al. 1982

Linking Features: Orientation

Guzmann 1968

(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

Hough Transform

Horace Barlow 1986

Horace Barlow 1986

1 mm

MT*

5 mm

V1

*

* HM

VM

fovea

VisualField

Tootell & Born

fundus of STS

post. bank of STS

MT direction

map

1 mm

UpDown

d

m

Tootell & Born, unpub’d

fovea

periphery

inferior VF

superior VF