1. ECE 638: Principles of Digital Color Imaging Systems
Lecture 12: Characterization of Illuminants and Nonlinear Response of Human Visual System

2. Synopsis Characterization of illuminants
Review of model for HVS and light interaction with surfaces
Development of black body radiator concept
Correlated color temperature
Artificial sources and CIE standard illuminants
Nonlinear Response of Human Visual System
Weber’s law
Gamma correction
CIE uniform color spaces

3. Review of HVS color model
Trichromatic Stage
Opponent Color Stage
Wandell’s
Model
Equivalent Representation for Trichromatic Stage:
CIE XYZ (standard space
for Colorimetry)

4. Review of Stimulus Model
Seeking a more compact parameterization of
Stimulus Model:

5. Development of black-body radiator*
Imagine an experiment in which you heat up various structures made of different materials to a fixed temperature to see which combination radiates the most energy.
Example:
Most efficient possible absorber is a small aperture in a hollow cylinder
When heated, this becomes a black body radiator (BBR) with spectral power distribution
Planck’s law describes power for a BBR at any given temperature (see W&S, p13)
* This material is taken from Wyzecki and Stiles

6. Spectral power distribution for black body radiator
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7. Relative spectral power distribution of black body radiator
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8. Example (cont.) -- Chromaticity for a BBR at some temperature T.
How to relate BBR to real-world stimulus?
For each temperature T, compute the CIE XYZ coordinates of a BBR emitting light when heated to temperature T.
-- Chromaticity for a BBR at some temperature T.
--Chromaticity for a phase of daylight.
Hypothetical arrangement of chromaticity points for BBR and daylight. The next slide shows what it actually looks like.
“Phases of daylight” refer to different conditions of sky (i.e. cloudy or not, shading of observer from direct sun, and time of day

9. Daylight locus
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11. Spectral power distribution of daylight
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These curves are based on a principal components expansion of a family of actual daylight power spectra. Two such power spectra are shown on next slide.

12. Two phases of real daylight

13. Spectral power distribution of tungsten
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14. Relative spectral power distribution of fluorescent sources
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15. Summary of Daylight Characteristics
Daylight behaves a lot like a BBR
Each phase of daylight can be correlated with a BBR operating at unique temperature.
More generally, this can be done for any illuminant.
examples:
1) sun+total sky (clear overcast) 5000k7000k
2) daylight from north sky >7000k
3) daylight from sun disk only <5000k

16. Artificial Sources and CIE Standard Illuminants
1) tungsten behaves like a BBR at lower T than daylight
2) flourescent only somewhat (See W&S)
CIE Standard Illuminants
Older A,B,C (not used much today)

17. Synopsis Characterization of illuminants
Review of model for HVS and light interaction with surfaces
Development of black body radiator concept
Correlated color temperature
Artificial sources and CIE standard illuminants
Nonlinear Response of Human Visual System
Weber’s law
Gamma correction
CIE uniform color spaces

18. Probit Analysis Overall HVS model thus far is linear
Psychometric function
Question: Does Bag in right hand weigh more than Bag in left hand? Yes or No?
Probit Analysis
0.5
Threshold level
stimulus
Slope measure of sensitivity
# of books in right hand
when # of books in left hand is fixed

19. Weber’s Law Weber’s Law: Vision
Stimulus Increment
Total Stimulus
constant
Weber’s Law:
Vision
Source: D.E. Pearson, Transmission of Pictorial Information
Threshold for
a difference is ~
Subject adjusts
until they see
a difference
Luminance:

20. Weber’s Law Application
Quantization – space quantization levels
non-uniformly as a function of luminance
What does Weber’s law suggest:
Integrating, we get
Suggests that we should quantize
L so that levels are farther apart as L increases
Just perceivable
difference in brightness
constant

21. Weber’s Law Application (cont.)
Two possible implementations:
1) non-uniform quantization directly
2) process with a non-uniform mapping then
quantize uniformly
How does this get used?
1) Gamma
2) CRT (Cathode Ray Tube)
D/A
Digital
Value DV
Voltage V
Electron Gun Y
DV~V
Phosphor

22. Gamma Correction and Limitations of Weber’s Law
DV = captured luminance
Limitations of Weber’s Law
“Happy Coincidence”

23. Summary of impact of gamma in imaging systems and image processing
According to trichromatic model for HVS, cone responses are linearly related to incident photon count:
This model is also applicable to image capture devices – scanners, cameras.
However, the output from these devices is generally gamma-corrected to account for Weber’s Law and in anticipation of the power-law behavior of output devices – displays and printers.

24. Gamma Correction Typical value (sRGB):
RGB captured image in linear space (linear RGB)
Gamma-corrected output from cameras and scanners (assuming 8 bits/channel) (This is the default.)
Typical value (sRGB):

25. Gamma Uncorrection
What displays and printers do (generally hidden from user)
Similar relationships hold for CIE X and CIE Z components
So gamma correction means raise to power
Gamma uncorrection* means raise to power
*This is also called degamma-ing the image

26. Implications for Image Processing
If you want to convert an image to CIE XYZ, and thence to a uniform color space, such as CIE L*a*b*, you must first gamma uncorrect it.
If you want to halftone an image, you must first gamma uncorrect it.
If you want to display or print an image that you have processed in a linear space (pixel values proportional to photon count), you must first gamma correct it.
Note that a binary halftone image would have values 0 or 255 only; so gamma correction of the halftone image has no effect.