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

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Human estimation of pricesF

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Normal distribution.Log-normal distribution.

Normalized price (linear scale)

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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

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Fixation500 ms

Sample800 ms

Delay1000 ms

Test 1200 msMatch

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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

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Adaptation vs dot number

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Baselines

Effect of number of adaptor dots

Adaptation: magnitude estimation

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Numerosity or texture?

Size of rectangular elements: paired comparisons

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Effect of the test contrast

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Effect of adaptor contrast

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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

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88% Yellow 88% Blue No Adapt

What are the neural mechanisms underlying numerosity adaptation?

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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

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“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

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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