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A visual sense of number

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.

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A visual sense of number

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  1. The University of Florence A visual sense of number David Burr & John Ross Burr & Ross Current Biology 2008

  2. Estimation of numerosity in rats

  3. Monkeys: same/different task

  4. C 30 4 20 Mean 2 SD 10 0 0 0,30 CV 0.15 0 Number of level presses Number production by key-press

  5. D 20 18 16 Log-normal distribution. Frequency (%) 14 Normal distribution. 12 10 8 6 4 2 0 0 1 2 3 Normalized price (linear scale) Human estimation of prices

  6. CS Left hemisphere Right hemisphere IPS A B bilateral horizontal segment of intraparietal sulcus (HIPS) left angular gyrus (AG) bilateral posterior superior parietal lobe (PSPL) Top view C L Brain imaging

  7. Test 1200 ms Match D A C P=0.50 2 0 Fixation Sample Delay 500 ms 800 ms 1000 ms 1 2 3 Test Test 1200 ms 1200 ms 4 Non-Match Match 5 P=0.25 Spike rate (Hz) 1 0 P=0.25 1 0 0 0 7 5 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 5 0 2 5 1 0 0 0 Time 7 5 5 0 B 2 5 ) 0 % 5 0 ( e 1 1 0 0 s 2 n 7 5 o 3 p 4 0 s 5 0 4 e r 5 2 5 d e z 0 i l 3 0 a 1 0 0 m r Spike rate (Hz) o 7 5 N 5 0 2 0 2 5 0 1 0 1 0 0 0 7 5 2 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 5 0 0 Time 5 1 5 2 3 4 N u m b e r o f i t e m s ( l o g s c a l e ) Neurons in monkey pre-frontal and parietal cortex Selectivity follows a log scale

  8. Number neurons cover a large range Nieder & Merten J Neuroscience 2007

  9. Could numerosity be a visual attribute? If so it should be subject to adaptation.

  10. Adaptation demo

  11. Adaptation demo

  12. Where did the other dots go? (We’ll come back to that)

  13. Adaptation: 45 sec + 8 sec top-up

  14. Test stimulus (500 ms)

  15. 0.5 sec pause

  16. Probe stimulus (500 ms)

  17. Psychometric functions with adaptation

  18. Adaptation vs dot number Adapt to 400 dots

  19. Effect of number of adaptor dots

  20. Adaptation: magnitude estimation Adapt 7 No adapt Adapt 120

  21. Numerosity or texture?

  22. Size of rectangular elements: paired comparisons

  23. Adapt Adaptation does not depend on element orientation

  24. Effect of the test contrast

  25. Effect of adaptor contrast

  26. Numerosity or texture Neither PSE nor Weber fractions depend on: • Size or shape of elements • Orientation of elements • Fourier sprectra of stimuli • Contrast, or contrast sign • Chromaticity

  27. Colour-contingency after-effect

  28. Colour-contingency after-effect

  29. Colour-contingency after-effect

  30. What are the neural mechanisms underlying numerosity adaptation?

  31. Test 1200 ms Match D A C P=0.50 2 0 Fixation Sample Delay 500 ms 800 ms 1000 ms 1 2 3 Test Test 1200 ms 1200 ms 4 Non-Match Match 5 P=0.25 Spike rate (Hz) 1 0 P=0.25 1 0 0 0 7 5 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 5 0 2 5 1 0 0 0 Time 7 5 5 0 B 2 5 ) 0 % 5 0 ( e 1 1 0 0 s 2 n 7 5 o 3 p 4 0 s 5 0 4 e r 5 2 5 d e z 0 i l 3 0 a 1 0 0 m r Spike rate (Hz) o 7 5 N 5 0 2 0 2 5 0 1 0 1 0 0 0 7 5 2 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 5 0 0 Time 5 1 5 2 3 4 N u m b e r o f i t e m s ( l o g s c a l e ) “Number-neurons” in monkey pre-frontal and parietal cortex

  32. LIP neurons respond in graded fashion to total number in RF Roitman, Brannon &Platt PLoS 2007

  33. Implications for adaptation LIP VIP

  34. Data

  35. 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

  36. Attention and subitizing

  37. Weber’s law for numerosity 25% Weber fraction explains the subitizing limit of 4 Ross, Perception, 2003

  38. The attentional blink: slow motionGiovanni Anobile

  39. Attention affects subitizing but not estimation

  40. Spatial attention: slow motion demoMarco Turi

  41. Attention affects subitizing but not estimation

  42. Attention affects subitizing but not estimation

  43. Mental abacus represents large exact numerosities using pre-existing visual resources Frank, M.C.., & Barner, D.

  44. Abacus

  45. Mental abacus

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