1. Visual computation of lightness in simple and complex images
Alan Gilchrist
National Science Foundation: BCS Public Health Service: GM

2. Perceived white, gray, or black shade of a surface.
What is Lightness?
Perceived white, gray, or black shade of a surface.

3. The problem of lightness constancy:
Adelson’s checkered shadow
These two squares are identical

4. Luminance is ambiguous
Any absolute luminance can appear as any shade of gray

5. Wallach’s solution:
Relative luminance

7. 1948 - Wallach’s solution: 1 5 50 10 Relative luminance
Disks appear equal when luminance ratios are equal

8. Near condition Far condition

10. without an anchoring rule,
But,
without an anchoring rule,
luminance ratios are also ambiguous
This local
luminance ratio. . .
. . . is consistent with any of these:

11. THE ANCHORING PROBLEM Given: the scale of A range of luminances
WHITE
GRAY
BLACK
SELF-
LUMINOUS
the scale of
perceived
gray shades
Given:
A range of
luminances
in the image
How to map these onto….

12. Two proposed anchoring rules
Wallach,
Land & McCann
SELF-
LUMINOUS
WHITE
Highest luminance Rule
Average luminance Rule
GRAY
Helson, Buchsbaum
Gray world assumption
BLACK

13. Which rule is correct? Another rule Bipolar anchoring Koffka,Rock
SELF-
LUMINOUS
Koffka,Rock
WHITE
Bipolar anchoring
GRAY
BLACK
Which rule is correct?

14. Challenge: pit these rules against each other
in the simplest possible image

15. Two surfaces of different gray that fill the entire visual field.
What is a simple image?
Heinemann: Disk/annulus in a dark room
Gilchrist: Disk/annulus is too complex
Simplest image:
Two surfaces of different gray that fill the entire visual field.
Wallach: "Opaque colors which deserve to be called white or gray, in other words ‘surface colors,’ will make their appearance only when two regions of different light intensity are in contact with each other..."

16. 1 2 3

17. Highest Luminance Rule wins
Anchoring under minimal conditions:
Two surfaces fill entire visual field
Physical Stimulus
5.5
2.5
4.5
9.5
Li & Gilchrist, 1999
Appearance
Highest Luminance Rule wins

18. Highest luminance rule:
The highest luminance
within a framework appears white
and darker regions are
computed relative to this value.

19. Three rules of anchoring in simple images:
Physical Stimulus Appearance
1. Highest Luminance Rule
Highest luminance appears white
Physical Stimulus Appearance
2. Area Rule.
The larger the lighter
3. Scale Normalization Rule.
The perceived range of grays tends
toward that between black and white.
(30:1)
Physical Stimulus Appearance

20. Two problems for the highest luminance rule
Self-luminosity perception
Upward induction/downward induction problem

21. What color is the ceiling?
Highest luminance rule fails

23. When the luminance difference between two adjacent regions increases:
Upward induction/downward induction problem
When the luminance difference
between two adjacent regions increases:
Does the darker one
appear to get darker?
Or does the lighter one
appear to get lighter still?
Downward induction
Upward induction

24. Downward induction
Upward induction

25. The answer lies in relative area

28. Method Nine stimulus domes:
Each viewed by a different group of 15 subjects
Matches made from
immediate memory
using a Munsell chart

29. Standard Deviations Perceived Log reflectance White Gray Black 1.89
1.69
1.49
Gray
1.29
1.09
0.89
0.69
Black
0.49

30. Degrees of dark gray Perceived Log reflectance White Gray Black 1.85
1.65
1.45
Gray
1.25
1.05
0.85
0.65
Black
0.45 50
100
150
200
250
300
350
Degrees of dark gray

31. lightens as it gets larger
The area rule:
The darker region
lightens as it gets larger
As the darker region becomes very large, the lighter region
appears first super-white, and then self-luminous..

33. 2 degree square
7 x 9 degree rectangle

34. WHITE GRAY BLACK 1 8 6 4 2 3 9 1 3 2 TARGET LUMINANCE (cd /m )2 4 6 8 1 3
TARGET LUMINANCE (cd /m )
% LUMINOSITY
REPORTS
50%
BACKGROUND LIGHTNESS 3 1 9 2
TARGET LUMINANCE (cd /m )
WHITE
GRAY
BLACK

35. Theoretical significance:
Inconsistent with inverse optics
Neurally plausible

36. Scale normalization rule:
The perceived range of grays
within a framework
tends toward that between black and white
If the range is truncated (less than 30:1), expansion occurs.
Coefficient of expansion proportional to the degree of truncation.
The expansion shows up at the bottom of the range,
not the top, which is anchored at white.
Similar to MacLeod and Brown’s gamut expansion

37. EXPANSION COMPRESSION Disk/Ganzfeld Percentage Rescaling 160 140 120
100
4.8 80 60 40 1 10 40
Stimulus:
Disk/Ganzfeld
Range
full
Gilchrist & Bonato (1995)

38. Three rules of anchoring in simple images:
Physical Stimulus Appearance
1. Highest Luminance Rule
Highest luminance appears white
Physical Stimulus Appearance
2. Area Rule.
The larger the lighter
3. Scale Normalization Rule.
The perceived range of grays tends
toward that between black and white.
(30:1)
Physical Stimulus Appearance

39. What about complex images?

40. What is the relationship between simple and complex images?
Contrast era:
Findings from simple images can be directly applied to complex images
Arend (1994):
Disk/annulus displays are too simple to tell us anything useful about lightness perception.
Gilchrist:
Simple and complex images are related in a systematic way.
Applicability assumption
Co-determination principle

41. The applicability assumption:
Rules of lightness computation in simple
images can be applied to frameworks embedded within complex images

42. The co-determination principle
Lightness is determined by computations both in the relevant framework and in adjacent and/or superordinate frameworks
Lajos Kardos
... brilliant but largely-unknown
Gestalt psychologist.

43. Applicability assumption:
Highest luminance rule
2. Area function
3. Scale normalization

44. A B
Corrugated Mondrian
(Adelson)

46. Now for a
Live Demo!

47. LOG T/H LOG PERCEIVED REFLECTANCE WHITE WHITE GRAY BLACK GLOBAL LOCAL2
WHITE
WHITE
GLOBAL
1.8
1.6
1.4
GRAY
1.2 1
LOCAL
0.8
BLACK
0.6
0.4
-1.6
-1.4
-1.2 -1
-0.8
-0.6
-0.4
-0.2
LOG T/H

48. Applicability assumption:
Highest luminance rule
2. Area function
3. Scale normalization

50. Applicability assumption:
Highest luminance rule
2. Area function
3. Scale normalization

51. Frameworks of illumination exist in the visual environment Photo:
Cartier-Bresson

52. Cartier-Bresson

54. Cartier-Bresson

55. We can explore frameworks using a probe disk of constant luminance:

77. Conclusions:
Lightness computation in simple images described by three rules:
3. Scale Normalization Rule.
2. Area Rule.
Physical Stimulus Appearance
1. Highest Luminance Rule

78. Conclusions:
These rules can be applied to frameworks embedded with complex images
(the applicability assumption)
GLOBAL
LOCAL
Lightness is co-determined by computations in multiple frameworks.

79. Thank You

82. Standard Deviations Perceived Log reflectance White Gray Black 1.89
PR=(100-Ad)/50 x (Lt/Lh x 90%)+(Ad-50)/50 x 90%
Ad - Area of darker region
Lt - Luminance of target
Lh - Highest luminance
1.69
1.49
Gray
1.29
1.09
0.89
0.69
Black
0.49

83. Visual Field