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The University of Florence. A visual sense of number. David Burr & John Ross. Burr & Ross Current Biology 2008. Estimation of numerosity in rats. Monkeys: same/different task. C. 30. 4. 20. Mean. 2. SD. 10. 0. 0. 0,30. CV. 0.15. 0. Number of level presses. - PowerPoint PPT Presentation
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A visual sense of number
David Burr & John Ross
Burr & RossCurrent Biology 2008
The University of Florence
Estimation of numerosity in rats
Monkeys: same/different task
Number production by key-pressC
0
0.15
0,30
CV
10
20
30
0
Mea
n
SD
0
2
4
Number of level presses
Human estimation of pricesF
requ
ency
(%
)
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3
Normal distribution.Log-normal distribution.
Normalized price (linear scale)
D
Brain imagingCS
IPS
Right hemisphereLeft hemisphere
left angular gyrus (AG)
bilateral posterior superior parietal lobe (PSPL)
bilateral horizontal segment of intraparietal sulcus (HIPS)
Top view
A
L
C
B
BTime
N u m b e r o f ite m s
( lo g s c a le )
0
2 5
5 0
7 5
10 0
0
2 5
5 0
7 5
1 0 0
0
2 5
5 0
7 5
1 0 0
No
rma
liz
ed
re
sp
on
se
(%
)
0
2 5
5 0
7 5
1 0 0
0
2 5
5 0
7 5
1 0 0
1 2 3 4 5
A C D
Fixation500 ms
Sample800 ms
Delay1000 ms
Test 1200 msMatch
Test 1200 msMatch
Test 1200 msNon-Match
P=0.25
P=0.25
P=0.50
0 500 1000 1500 20000
10
20
30
40
50 1 2 3 4 5
Time
Spi
ke r
ate
(Hz)
0 500 1000 1500 20000
10
20 1 2 3 4 5
Spi
ke r
ate
(Hz)
Neurons in monkey pre-frontal and parietal cortex
Selectivity follows a log scale
Nieder & MertenJ Neuroscience 2007
Number neurons cover a large range
Could numerosity be a visual attribute?
If so it should be subject to adaptation.
Adaptation demo
Adaptation demo
Where did the other dots go? (We’ll come back to that)
Adaptation: 45 sec + 8 sec top-up
Test stimulus (500 ms)
0.5 sec pause
Probe stimulus (500 ms)
Psychometric functions with adaptation
10 100 400
0.0
0.2
0.4
0.6
0.8
1.0
P(g
reat
er)
Matched dot number
ControlAdapt to400 dots
Probe
Adaptation vs dot number
3 10 100 3000.5
1.0
1.5
2.0
2.5
3.0
10 1000.5
1.0
1.5
2.0
2.5
3.0
Pro
port
ion
incr
ease
Probe dot number
DB
JRAdapt to 400 dots
10 1000.3
1
2 DB PB
Pro
po
rtio
n in
cre
ase
Adapt Dot Number
Baselines
Effect of number of adaptor dots
Adaptation: magnitude estimation
0 20 40 60
0
20
40
60
Est
ima
te
Dot Number
JR
0 20 40 60 80
0
20
40
60
80
Est
ima
teDot Number
DB
Adapt 7No adaptAdapt 120
Numerosity or texture?
Size of rectangular elements: paired comparisons
10 100
0.0
0.5
1.0
P(m
ore)
Dot number
Small-small Big-big Big-small Small-big
JB
Adaptation does not depend on element orientation
Control Parallel Orthog0
20
40
60
Mat
ched
dot
num
ber
DB ED PB
Adapt
Effect of the test contrast
2 10 100
1
10P
rop
ort
ion
incr
ea
se
Contrast of test (%)
UnadaptedThreshold
Adaptedthreshold
Effect of adaptor contrast
10 1000.3
1
6 DB PB
Pro
po
rtio
n in
cre
se
Adaptor contrast (%)
No adaptation baselines
detectionthresholds
Numerosity or textureNeither PSE nor Weber fractions depend on:
• Size or shape of elements
• Orientation of elements
• Fourier sprectra of stimuli
• Contrast, or contrast sign
• Chromaticity
Colour-contingency after-effect
Colour-contingency after-effect
Colour-contingency after-effect
0.0 0.5 1.0
0.0
0.5
1.0
Pro
port
ion
"mor
e bl
ue"
Ratio (Blue/Total)
88% Yellow 88% Blue No Adapt
What are the neural mechanisms underlying numerosity adaptation?
BTime
N u m b e r o f ite m s
( lo g s c a le )
0
2 5
5 0
7 5
10 0
0
2 5
5 0
7 5
1 0 0
0
2 5
5 0
7 5
1 0 0
No
rma
liz
ed
re
sp
on
se
(%
)
0
2 5
5 0
7 5
1 0 0
0
2 5
5 0
7 5
1 0 0
1 2 3 4 5
A C D
Fixation500 ms
Sample800 ms
Delay1000 ms
Test 1200 msMatch
Test 1200 msMatch
Test 1200 msNon-Match
P=0.25
P=0.25
P=0.50
0 500 1000 1500 20000
10
20
30
40
50 1 2 3 4 5
Time
Spi
ke r
ate
(Hz)
0 500 1000 1500 20000
10
20 1 2 3 4 5
Spi
ke r
ate
(Hz)
“Number-neurons” in monkey pre-frontal and parietal cortex
LIP neurons respond in graded fashion to total number in RF
Roitman, Brannon &PlattPLoS 2007
Implications for adaptation
LIP VIP
10 1000.1
1
10
Pre
dict
ed p
ropo
rtio
n in
crea
se
Adapt dot number
Probe 50
VIP
LIP
Data
10 1000.3
1
2 DB PB
Pro
po
rtio
n in
cre
ase
Adapt Dot Number
Baselines
10 1000.1
1
10
Pre
dict
ed p
ropo
rtio
n in
crea
se
Adapt dot number
Probe 50
VIP
LIP
Interim conclusions• The capacity to estimate number is
built into vision. • Numerosity is a primary visual
attribute: a dozen ripe cherries look twelvish, just as they look reddish.
• Like other visual attributes, numerosity obeys Weber’s Law, is subject to spatially local adaptation and contingency aftereffects.
See Burr & Ross Curr Biol 2008 And Butterworth Curr. Biol. 2008
Attention and subitizing
Weber’s law for numerosity
Ross, Perception, 2003
25% Weber fraction explains the subitizing limit of 4
25.0
N
NW
The attentional blink: slow motionGiovanni Anobile
Attention affects subitizing but not estimation
Spatial attention: slow motion demoMarco Turi
Attention affects subitizing but not estimation
Attention affects subitizing but not estimation
Mental abacus represents large exact numerosities using pre-
existing visual resources Frank, M.C.., & Barner, D.
Abacus
Mental abacus
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