1. What is vision
Aristotle - vision is knowing what is where by looking

2. What is vision Aristotle - vision is knowing what is where by looking
Helmholtz - vision is an act of unconscious inference
Our percepts are inferences about properties of the world from sensory data

4. What is vision Aristotle - vision is knowing what is where by looking
Helmholtz - vision is an act of unconscious inference
Our percepts are inferences about properties of the world from sensory data
Vision is (neural) computation

7. Processes of vision

8. What is vision Aristotle - vision is knowing what is where by looking
Helmholtz - vision is an act of unconscious inference
Our percepts are inferences about properties of the world from sensory data
Vision is (neural) computation
Vision controls action

9. The swinging room

10. Processes of vision II

11. Lecture outline Image transduction Neural coding in the retina
Neural coding in visual cortex
Visual pathways in the brain

13. The Optic Array: pattern of light intensity arriving
at a point as a function of direction (q, W), time (t) and wavelength(l)
I = f(q, W, t, l)

14. Goals of eye design Form high spatial resolution image
Accurately represent light intensities coming from different directions.
E.g. minimize blur in a camera
Maximize sensitivity
Trigger neural responses at very low light levels.
Particle nature of light places fundamental limit on sensitivity.

16. Visual angle

21. Point spread

22. Point spread function

24. Resolution (acuity)
Optics of eye and physics of light pace fundamental limit on acuity
Width of blur circle in fovea = 1’
Blur increases with eccentricity
Optical aberrations
Depth variation in the environment

26. Focus - the lens equation

27. Accommodation - bringing objects into focus
Focused on
Focused on

28. Some numbers Refractive power of cornea Refractive power of lens
43 diopters
Refractive power of lens
17 (relaxed) - 25 diopters
Other eyes
Diving ducks - 80 diopter accommodation range
Anableps - four eyes with different focusing power

33. Sampling in the fovea
Receptor sampling in fovea matches the width of point spread function (blur circle)
Effective width of blur circle ~ 1 minute of arc
Spacing of receptors ~ .5 minutes of arc (theoretical requirement for optimal resolution)

34. Relationship between sampling and blur
Two test images
60 cycle / degree grating
120 cycle / degree grating

35. Relationship between sampling and blur
Two test images
60 cycle / degree grating
120 cycle / degree grating
Receptor sampling = .5 minutes

36. Relationship between sampling and blur
Two test images
60 cycle / degree grating
120 cycle / degree grating
Receptor sampling = .5 minutes
Receptor Output

37. Peripheral sampling More rods than cones in periphery
Coarser sampling in periphery

38. Tricks for maximizing resolution

39. High resolution coding of intensity information
Problem:
High resolution coding of intensity information

40. Example
Computer monitors typically use 8 bits to encode the intensity of each pixel.
256 distinct light levels
Old monitors only provided 4 bits per pixel.
16 distinct light levels
Number of light levels encoded = intensity resolution of the system.
Human visual system can only distinguish ~ light levels.

41. Code wide range of light intensities
Range of light intensities receptors can encode
Dynamic range of receptors and of ganglion cells limits # of distinguishable light levels.
Problem
How does system represent large range of intensities while maintaining high intensity resolution?

42. Some typical intensity values

43. Solution Dynamic range of receptors (cones)
photons absorbed per 10 msec.
Range of intensities in a typical scene
cd / m2 in starlight
cd / m2 in sunlight
100:1 range of light intensities
Only need to code 100:1 range of intensities within a scene
Solution - Adaptation adjusts dynamic range of receptors to match range of intensities in a scene.

44. Increase Illumination Adaptation
# photons hitting
receptor
% photons
absorbed
# photons
absorbed
Scene 1
10 - 1,000
100%
10 - 1,000
Increase Illumination
Adaptation
10%
10 - 1,000
Scene 2
1, ,000

45. Sunlight Starlight Moonlight Indoor lighting 10-4 10-2 10 102 104 106
10-6
Window of visibility

46. (e.g. % photons absorbed = .1)
Adapt to the dark
(e.g. % photons absorbed = .1)
Starlight
Moonlight
Indoor lighting
Sunlight
10-6
10-4
10-2 10
102
104
106
Window of visibility

47. (e.g. % photons absorbed = .000000001)
Adapt to the bright
(e.g. % photons absorbed = )
Starlight
Moonlight
Indoor lighting
Sunlight
10-2 10
102
10-4
104
106
10-6
Window of visibility

48. Hartline Experiment
Limulus eye has ommotidia containing one receptor each.
Each receptor sends a large axon to the brain.
Output of one receptor was inhibited by light shining on a neighboring receptor (lateral inhibition).

51. Ganglion cell receptive fields
Receptive field - region of visual field that cell responds to.
Center-surround receptive field
On-center, off-surround
Off-center, on-surround - - - + + - - - - + + - + - + - + - - - + + + - - + - + - - + + - - + - - - + - - - + - - - + +

53. Ganglion cells as computational devices
Write a mathematical function that calculates firing rate of cell from luminance pattern.
1st guess
Increase in firing rate = weighted sum of intensities within receptive field.
Problem 1 - Adaptation
Problem 2 - dark regions in inhibitory region actually excite cell

54. Ganglion cells as computational devices
Solution
Increase in firing rate = weighted sum of local contrast values within receptive field.
Local contrast
C(x,y) = I(x,y) / M - 1

55. Ganglion cells as computational devices
Solution
Increase in firing rate = weighted sum of local contrast values within receptive field.
Local contrast
C(x,y) = I(x,y) / M - 1
Intensity

56. Ganglion cells as computational devices
Solution
Increase in firing rate = weighted sum of local contrast values within receptive field.
Local contrast
C(x,y) = I(x,y) / M - 1
Mean intensity
Intensity

57. Ganglion cells as computational devices
Solution
Increase in firing rate = weighted sum of local contrast values within receptive field.
Local contrast
C(x,y) = I(x,y) / M - 1
Mean intensity
Local contrast
Intensity

62. Ganglion Cells
Simple Cells

64. Cells in V1 Simple cells Complex cells orientation selective
scale selective (cells have different size receptive fields)
some are motion selective
some are end-stopped
Complex cells
same properties as simple cells, BUT ...
insensitive to position of stimulus within RF

75. Cortical pathways V2 MT
MST
Parietal
Lobe V1 V3 V4
Temporal
Lobe