1. ECE 638: Principles of Digital Color Imaging Systems
Lecture 13: Uniform Color Spaces

2. Synopsis Nonlinearity of the HVS – Weber’s Law Color Order systems
MacAdam ellipses
Requirements for a uniform color space
1976 CIE L*u*v* uniform color space
1976 CIE L*a*b* uniform color space

3. 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:

4. 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
Equal increments in brightness B correspond to logarithmically spaced increments in luminance L
Just perceivable
difference in brightness
constant

5. Color Order Systems HSV HSL Munsell Color System Pantone System
Colorsystem.com lists 59 different color order systems!
All systems share common attributes shown below, but are not uniform, and may not be well-defined in terms of HVS subspace

6. MacAdam Ellipses – Experimental Setup
2) MacAdam Ellipses (1942) Source: W&S pp
Addresses “uniformity”
test stimulus fixed (same primaries), adjust match stimulus
Background Y= 24 cd/m2, chromaticity = CIE Illuminant C
Match experiment: hold Y fixed, vary X and Z to move along a straight line in xy.
42° 2°

7. MacAdam Ellipses – Subject Task and Modeling
fixed
Subject adjusts color along this line to achieve a match
Model data as Gaussian
Estimate covariance matrix  parameters of an ellipse
Repeat for different values of
The contour of the ellipse therefore represents the just noticeable differences of chromaticity.

8. MacAdam ellipses in 1931 CIE xy chromaticity diagram
1942 data from observer PGN
Axes of plotted ellipses are 10x their actual length

9. MacAdam Ellipses in 1931 CIE xy Chromaticity Diagram with Colors Shown

10. Desired Properties for a Uniform Color Space
1) Uniformity  MacAdam ellipses should be circular with constant radius through out the color space.
2) Axes should correspond to perceptually relevant parameters (Perceptually relevant parameters should be easily identifiable).
3) There should be a well-defined transformation from a color space that spans the HVS subspace to the uniform color space.
4) The transformation should be invertible.

11. 1976 CIE L*u*v* Uniform Color Space
Reflects Weber's Law
--- luminance of nominally white stimulus
--- are calculated as a function of
for nominal white stimulus.
Accounts for adaptation

12. Properties of 1976 CIE L*u*v* Space
-- chromaticity of
Projective transformation:
Perceptual Attributes (correlates)
Lightness:
Hue:
Chroma:
Saturation:
Distance from white point in
(u’,v’) chromaticity diagram

13. Color Difference Formula for 1976 CIE L*u*v* Space
Color difference between &
corresponds to a just perceptible difference.

14. MacAdam ellipses in 1976 CIE u*v* chromaticity diagram
text

15. Comparision of MacAdam ellipses in xy and u*v* chromaticity diagrams
text

16. Farnsworth 1958 transformation of CIE xy chromaticity diagram
text

17. 1976 CIE L*a*b* Uniform Color Space
valid for
Chroma:
Saturation: no definition
Hue:
Opponent
Channels

18. Graphical representations of CIE 1976 L*a*b* color space
text

19. Color Difference Formula for 1976 CIE L*a*b* Color Space
is the JND (just noticeable difference)
For color imaging systems, L*a*b* seems to be preferred.

20. MacAdam Ellipses in the CIE 1976 a*b* diagram