ECE 638: Principles of Digital Color Imaging Systems Lecture 6: CIE Standards

Synopsis Brief review of primaries Chromaticity diagram for primaries Overview of CIE Photometry and relative luminous efficiency function CIE 1931 standard observer RGB form XYZ form

Review: Primary mixture and sensor response

Review: Match equation Response to test stimulus Match amounts of primaries

Review: Color matching functions Given primaries , let denote the amount of these primaries required to match the stimulus for each fixed wavelength . Thus, we have where , the matrix is given as before, and Combining these results, we obtain

Review: Computation of match amounts for an arbitrary stimulus Consider arbitrary stimulus Match amounts are given by This looks like a sensor

Chromaticity coordinates for primaries In same way that we did for the sensor response, we can define chromaticities corresponding to primary amounts required to match a given stimulus as viewed by a given sensor

Spectral locus in primary chromaticity space For the special case of a monochromatic stimulus with wavelength , the primary amounts are given by the color matching functions evaluated at that wavelength. In this case, when plotted as a function of , the chromaticity coordinates yield the spectral locus.

Example: three channel overlap sensor and monochromatic primaries Sensor response functions Primaries Primary response matrix

Color matching functions

Spectral locus Note coordinates (1,0,0), (0,1,0), and (0,0,1) that occur at wavelengths 650, 550, and 450 nm, respectively.

Compare to common CIE chromaticity diagram

What is the CIE? International standards organization Commission Internationale de l'Eclairage (International Commission on Illumination) an organization devoted to international cooperation and exchange of information among its member countries on all matters relating to the science and art of lighting. Formed in 1913. Predecessor organization formed in 1903. http://members.eunet.at/cie/

Photometry Matching of brightness Difficulties Color matching involves complete match between two stimuli, i.e. under match condition, test stimulus and match stimulus look exactly the same. Brightness matching involves matching one attribute (brightness or lightness) of two stimuli which will generally differ in other attributes (hue and saturation). Several approaches may be used to overcome this limitation.

Flicker photometry Consider the apparatus shown below which presents a stimulus that periodically switches between two different stimuli.

Flicker photometry (cont.) A match occurs when the observer fails to see temporal variation (flicker) in the stimulus. For the HVS, the temporal frequency response to a time-varying chromatic stimulus has a lower cut-off frequency than the temporal frequency response to a time-varying achromatic stimulus. For flicker frequencies between 10 Hz and 40 Hz, the two stimuli will appear to have the same hue and saturation, but may differ in brightness until the matching stimulus is adjusted to achieve a match.

Summary of flicker photometry observations Luminance Match? Chrominance Match? Flicker Frequency Observation No f0 < 10 Hz Flicker in lightness and hue or saturation Yes Flicker in hue or saturation 10 Hz < f0 < 40 Hz Flicker in lightness No flicker 60 Hz < f0 This is the regime that is useful for flicker photometry

Relative luminous efficiency An achromatic sensor with response function is called the standard photometric observer.

Definition of luminance cd – candela lm – lumen

CIE 1931 standard RGB observer Observer consists of color matching functions corresponding to monochromatic primaries Primaries R – 700 nm G – 546.1 nm B – 435.8 nm Ratio of radiances Chosen to place chromaticity of equal energy stimulus E at center of (r-g) chromaticity diagram, i.e. at (0.333,0.333) that areas under color matching functions are identical. Based on observations in a 2 degree field of view using color matching method discussed earlier.

Color matching functions for 1931 CIE standard RGB observer

Chromaticity diagram for 1931 CIE standard RGB observer

CIE 1931 standard XYZ observer The CIE also defined a second standard observer based on a linear transformation from the 1931 RGB color matching functions. The XYZ observer has the following properties: The color matching functions are non-negative at all wavelengths. The chromaticity coordinates of all realizable stimuli are non-negative. The color matching function is equal to the relative luminous efficiency function To achieve these properties, it was necessary to use primaries that are not realizable. The chromaticities of the primaries lie outside the spectral locus. What does it mean for a primary to not be realizable?

Why non-negative color matching functions? The 30-ton ENIAC computer with 19,000 vacuum tubes and 1,500 relays was placed in service in 1945. IBM introduced the 5150 PC in 1981. Color scientists were worried about calculation errors, especially those due to working with negative numbers.

Color matching functions for 1931 CIE standard XYZ observer

Chromaticity diagram for 1931 CIE standard XYZ observer

Fundamental spectral components of 1931 CIE XYZ primaries From Wolski, “A Review of Linear Color Descriptors and their Applications.” 1994