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Explore nonlinearity in Human Visual System, MacAdam ellipses, and uniform color spaces like CIE L*u*v* and L*a*b*. Learn about Weber's Law and color order systems. Discover the importance of uniformity, transformation, and perceptual relevance in color spaces.
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ECE 638: Principles ofDigital Color Imaging Systems Lecture 13: Uniform Color Spaces
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
Weber’s Law Stimulus Increment • Weber’s Law: • Vision • Source: D.E. Pearson, Transmission of Pictorial Information Total Stimulus constant Subject adjusts until they see a difference Threshold for a difference is ~ Luminance:
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
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
MacAdam Ellipses – Experimental Setup • 2) MacAdam Ellipses (1942) Source: W&S pp.306-313 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. 2° 42°
MacAdam Ellipses – Subject Task and Modeling • 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. fixed Subject adjusts color along this line to achieve a match
MacAdam ellipses in 1931 CIE xy chromaticity diagram • 1942 data from observer PGN • Axes of plotted ellipses are 10x their actual length
MacAdam Ellipses in 1931 CIE xy Chromaticity Diagram with Colors Shown
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.
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
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
Color Difference Formula for 1976 CIE L*u*v* Space • Color difference between & • corresponds to a just perceptible difference.
MacAdam ellipses in 1976 CIE u*v* chromaticity diagram • text
Comparision of MacAdam ellipses in xy and u*v* chromaticity diagrams • text
Farnsworth 1958 transformation of CIE xy chromaticity diagram • text
1976 CIE L*a*b* Uniform Color Space valid for • Chroma: Saturation: no definition Hue: Opponent Channels
Formulas for conversion for CIE XYZ to 1976 CIE L*a*b* From Wyszecki and Stiles, Color Science Concepts and Methods, Quantitative Data and Formulae, 2nd Ed., p. 167.
Graphical representations of CIE 1976 L*a*b* color space • text
Color Difference Formula for 1976 CIE L*a*b* Color Space • Color Difference is the JND (just noticeable difference) • For color imaging systems, L*a*b* seems to be preferred.
