ECE 638: Principles of Digital 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 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:

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. 42° 2°

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.

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

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

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.

MacAdam Ellipses in the CIE 1976 a*b* diagram