MacAdam ellipse

Last updated

In the study of color vision, a MacAdam ellipse is roughly a region on a chromaticity diagram which contains all colors which are indistinguishable, to the average human eye, from the color at the center of the ellipse. Specifically, it is the standard deviation of a number of experimental color matches to the central color. Assuming a bivariate normal distribution of these match points, a MacAdam ellipse thus contains about 39% of the color match points. A 2X MacAdam ellipse will contain about 86% of the match points, and a 3X MacAdam ellipse will contain about 99% of the match points. The just-noticeable differences of chromaticity is generally taken to be a 3X MacAdam ellipse. [1] Standard Deviation Color Matching in LED lighting uses deviations relative to MacAdam ellipses to describe color precision of a light source. [2]

Contents

MacAdam ellipses for one of MacAdam's test participants, Perley G. Nutting (observer "PGN"), plotted on the CIE 1931 xy chromaticity diagram. The ellipses are ten times their actual size, as depicted in MacAdam's paper . CIExy1931 MacAdam.png
MacAdam ellipses for one of MacAdam's test participants, Perley G. Nutting (observer "PGN"), plotted on the CIE 1931 xy chromaticity diagram. The ellipses are ten times their actual size, as depicted in MacAdam's paper .

History

In the study of color perception, it is essential to develop a method of specifying a particular color such that it can be differentiated from all other colors. It has been found that three quantities are needed to specify a particular color. The relative amounts of red, green and blue in a color will serve to specify that color completely. This question was first approached by a number of researchers in the 1930s, and their results were formalized in the specification of the CIE XYZ color space.

The concept of a color space can similarly be used to determine how distant one color is from another. This particular question was considered by researchers dating back to Helmholtz and Schrödinger, [3] and later in industrial applications, [4] but experiments by Wright and Pitt, [5] and David MacAdam provided much-needed empirical support.

Procedure

MacAdam set up an experiment in which a trained observer viewed two different colors, at a fixed luminance of about 48 cd/m2. One of the colors (the "test" color) was fixed, but the other was adjustable by the observer, and the observer was asked to adjust that color until it matched the test color. This match was, of course, not perfect, since the human eye, like any other instrument, has limited accuracy. It was found by MacAdam, however, that the standard deviation of the matches made by the observer fell into an ellipse on the CIE 1931 chromaticity diagram. The measurements were made at 25 points on the chromaticity diagram, and it was found that the size and orientation of the ellipses on the diagram varied widely depending on the test color. [6] These 25 ellipses measured by MacAdam, for a particular observer, are shown on the chromaticity diagram above.

Extension to three dimensions

A more general concept is that of "discrimination ellipsoids" in the entire three-dimensional color space, which would include the ability of an observer to discriminate between two different luminances of the same color. [7] Such measurements were carried out, among others, by Brown and MacAdam in 1949, [8] Davidson in 1951, [9] Brown in 1957, [10] and by Wyszecki and Fielder in 1971. [11] It was found that the discrimination ellipsoids yielded relatively unchanging discrimination ellipses in chromaticity space for luminances between 3 and 30 cd/m2. [8]

Eccentricity dependency

The original experiment carried out by MacAdam limited the field of view to be 2°, [1] essentially giving the ellipse estimations at the foveal vision. A recent work examined the eccentricity dependency of color discrimination using a virtual reality device. [12] Unsurprisingly, the discrimination ellipses grow in size as the eccentricity increases, because the human visual acuity drops sharply with eccentricity. The study also builds a computational model that predicts the ellipse shape given the test color and the eccentricity. The computational model is then used to wisely adjust pixel colors in the rendering pipeline to save display power, given that OLEDs power is strongly correlated with color. It is shown that one can save up to 20% of the display dynamic power without affecting the perceptual quality.

Effects in colour theory

MacAdam's results confirmed earlier suspicions that colour difference could be measured using a metric in a chromaticity space. A number of attempts have been made to define a color space which is not as distorted as the CIE XYZ space. [13] The most notable of these are the CIELUV and CIELAB color spaces. Although both of these spaces are less distorted than the CIE XYZ space, they are not completely free of distortion. This means that the MacAdam ellipses become nearly (but not exactly) circular in these spaces.

Using a Fisher information metric, da Fonseca et al. [14] investigated the degree to which MacAdam ellipses can be derived from the response functions of the retinal photoreceptors. It was demonstrated that photoreceptor absorption properties explain ≈ 87% of the variance of human color discrimination ability, as tested by previous behavioral experiments.

See also

Related Research Articles

<span class="mw-page-title-main">Chromaticity</span> Specification of color hue and saturation

Chromaticity is an objective specification of the quality of a color regardless of its luminance. Chromaticity consists of two independent parameters, often specified as hue (h) and colorfulness (s), where the latter is alternatively called saturation, chroma, intensity, or excitation purity. This number of parameters follows from trichromacy of vision of most humans, which is assumed by most models in color science.

<span class="mw-page-title-main">CIELAB color space</span> Standard color space with color-opponent values

The CIELAB color space, also referred to as L*a*b*, is a color space defined by the International Commission on Illumination in 1976. It expresses color as three values: L* for perceptual lightness and a* and b* for the four unique colors of human vision: red, green, blue and yellow. CIELAB was intended as a perceptually uniform space, where a given numerical change corresponds to a similar perceived change in color. While the LAB space is not truly perceptually uniform, it nevertheless is useful in industry for detecting small differences in color.

<span class="mw-page-title-main">Adobe RGB color space</span> Color space developed by Adobe

The Adobe RGB (1998) color space or opRGB is a color space developed by Adobe Inc. in 1998. It was designed to encompass most of the colors achievable on CMYK color printers, but by using RGB primary colors on a device such as a computer display. The Adobe RGB (1998) color space encompasses roughly 30% of the visible colors specified by the CIELAB color space – improving upon the gamut of the sRGB color space, primarily in cyan-green hues. It was subsequently standardized by the IEC as IEC 61966-2-5:1999 with a name opRGB and is used in HDMI.

<span class="mw-page-title-main">Color rendering index</span> Measure of ability of a light source to reproduce colors in comparison with a standard light source

A color rendering index (CRI) is a quantitative measure of the ability of a light source to reveal the colors of various objects faithfully in comparison with a natural or standard light source. Light sources with a high CRI are desirable in color-critical applications such as neonatal care and art restoration.

<span class="mw-page-title-main">Planckian locus</span> Locus of colors of incandescent black bodies within a color space

In physics and color science, the Planckian locus or black body locus is the path or locus that the color of an incandescent black body would take in a particular chromaticity space as the blackbody temperature changes. It goes from deep red at low temperatures through orange, yellowish, white, and finally bluish white at very high temperatures.

<span class="mw-page-title-main">Correlated color temperature</span> Property of light based on human perception

The correlated color temperature is defined as "the temperature of the Planckian radiator whose perceived color most closely resembles that of a given stimulus at the same brightness and under specified viewing conditions."

<span class="mw-page-title-main">CIE 1931 color space</span> Color space defined by the CIE in 1931

The CIE 1931 color spaces are the first defined quantitative links between distributions of wavelengths in the electromagnetic visible spectrum, and physiologically perceived colors in human color vision. The mathematical relationships that define these color spaces are essential tools for color management, important when dealing with color inks, illuminated displays, and recording devices such as digital cameras. The system was designed in 1931 by the "Commission Internationale de l'éclairage", known in English as the International Commission on Illumination.

<span class="mw-page-title-main">Color solid</span> Three-dimensional representation of a color space

A color solid is the three-dimensional representation of a color space or model and can be thought as an analog of, for example, the one-dimensional color wheel, which depicts the variable of hue ; or the two-dimensional chromaticity diagram, which depicts the variables of hue and spectral purity. The added spatial dimension allows a color solid to depict the three dimensions of color: lightness, hue, and colorfulness, allowing the solid to depict all conceivable colors in an organized three-dimensional structure.

<span class="mw-page-title-main">Standard illuminant</span> Theoretical source of visible light

A standard illuminant is a theoretical source of visible light with a spectral power distribution that is published. Standard illuminants provide a basis for comparing images or colors recorded under different lighting.

<span class="mw-page-title-main">Lightness</span> Property of a color

Lightness is a visual perception of the luminance of an object. It is often judged relative to a similarly lit object. In colorimetry and color appearance models, lightness is a prediction of how an illuminated color will appear to a standard observer. While luminance is a linear measurement of light, lightness is a linear prediction of the human perception of that light.

<span class="mw-page-title-main">David MacAdam</span> American physicist and color scientist

David Lewis MacAdam was an American physicist and color scientist who made important contributions to color science and technology in the fields of colorimetry, color discrimination, color photography and television, and color order.

In colorimetry, the CIE 1976L*, u*, v*color space, commonly known by its abbreviation CIELUV, is a color space adopted by the International Commission on Illumination (CIE) in 1976, as a simple-to-compute transformation of the 1931 CIE XYZ color space, but which attempted perceptual uniformity. It is extensively used for applications such as computer graphics which deal with colored lights. Although additive mixtures of different colored lights will fall on a line in CIELUV's uniform chromaticity diagram, such additive mixtures will not, contrary to popular belief, fall along a line in the CIELUV color space unless the mixtures are constant in lightness.

<span class="mw-page-title-main">CIE 1960 color space</span>

The CIE 1960 color space ("CIE 1960 UCS", variously expanded Uniform Color Space, Uniform Color Scale, Uniform Chromaticity Scale, Uniform Chromaticity Space) is another name for the (u, v) chromaticity space devised by David MacAdam.

The CIE 1964 (U*, V*, W*) color space, also known as CIEUVW, is based on the CIE 1960 UCS:

In colorimetry the OSA-UCS is a color space first published in 1947 and developed by the Optical Society of America’s Committee on Uniform Color Scales. Previously created color order systems, such as the Munsell color system, failed to represent perceptual uniformity in all directions. The committee decided that, in order to accurately represent uniform color differences in each direction, a new shape of three dimensional Cartesian geometry would need to be used.

<span class="mw-page-title-main">Deane B. Judd</span> American color scientist (1900–1972)

Deane Brewster Judd was an American physicist who made important contributions to the fields of colorimetry, color discrimination, color order, and color vision.

<span class="mw-page-title-main">Impossible color</span> Color that cannot be perceived under ordinary viewing conditions

Impossible colors are colors that do not appear in ordinary visual functioning. Different color theories suggest different hypothetical colors that humans are incapable of perceiving for one reason or another, and fictional colors are routinely created in popular culture. While some such colors have no basis in reality, phenomena such as cone cell fatigue enable colors to be perceived in certain circumstances that would not be otherwise.

<span class="mw-page-title-main">Günter Wyszecki</span>

Günter Wolfgang Wyszecki was a German-Canadian physicist who made important contributions to the fields of colorimetry, color discrimination, color order, and color vision.

A color appearance model (CAM) is a mathematical model that seeks to describe the perceptual aspects of human color vision, i.e. viewing conditions under which the appearance of a color does not tally with the corresponding physical measurement of the stimulus source.

Data visualization involves presenting data and information using visual elements like charts, graphs, and maps. It simplifies complex data, making patterns and trends more apparent, and aiding in better understanding and decision-making. And color coding in data visualization is implemented to help users of data to easily read, understand, and categorize the different facets of information that a given set data is trying to explain.

References

  1. 1 2 3 MacAdam, David Lewis (May 1942). "Visual sensitivities to color differences in daylight" (abstract). JOSA . 32 (5): 247–274. Bibcode:1942JOSA...32..247M. doi:10.1364/JOSA.32.000247.
  2. ↑ "Talking Photometry - Colour Difference". Photometric Testing. Retrieved 26 March 2017.
  3. ↑ Kühni, Rolf G. (March 2003). "6. Historical Development of Color Space and Color Difference Formulas". Color Space and Its Divisions. New York: Wiley. pp. 204–270. doi:10.1002/0471432261.ch6. ISBN   978-0-471-32670-0.
  4. ↑ Judd, Deane B. (July 1939). "Specification of Color Tolerances at the National Bureau of Standards". The American Journal of Psychology. 52 (3). The American Journal of Psychology, Vol. 52, No. 3: 418–428. doi:10.2307/1416753. JSTOR   1416753.
  5. ↑ Wright, William David; Pitt, F.H.G. (May 1934). "Hue-discrimination in normal colour-vision". Proceedings of the Physical Society . 46 (3): 459–473. Bibcode:1934PPS....46..459W. doi:10.1088/0959-5309/46/3/317.
  6. ↑ Wood, Mike (2010). "MacAdam ellipses" (PDF). Out of the Wood by Mike Wood. Retrieved April 30, 2024.
  7. ↑ Günter Wyszecki and Walter Stanley Stiles, Color Science: Concepts and Methods, Quantitative Data and Formula (2nd edition), Wiley-Interscience. (July 28, 2000). ISBN   0-471-39918-3
  8. 1 2 Brown, Walter R.J.; MacAdam, David L. (October 1949). "Visual sensitivities to combined chromaticity and luminance differences" (abstract). JOSA . 39 (10): 808–834. Bibcode:1949JOSA...39..808B. doi:10.1364/JOSA.39.000808. PMID   18142394.
  9. ↑ Davidson, Hugh R. (December 1951). "Calculation of Color Differences from Visual Sensitivity Ellipsoids" (abstract). JOSA . 41 (12): 1052–1056. Bibcode:1951JOSA...41.1052D. doi:10.1364/JOSA.41.001052.
  10. ↑ Brown, Walter R.J. (February 1957). "Color Discrimination of Twelve Observers" (abstract). JOSA . 47 (2): 137–143. Bibcode:1957JOSA...47..137B. doi:10.1364/JOSA.47.000137. PMID   13406654.
  11. ↑ Wyszecki, Günter; Fielder, G. H. (September 1971). "New Color-Matching Ellipses" (abstract). JOSA . 61 (9): 1135–1152. Bibcode:1971JOSA...61.1135W. doi:10.1364/JOSA.61.001135. PMID   5121883.
  12. ↑ Duinkharjav, Budmonde; Chen, Kenneth; Tyagi, Abhishek; He, Jiayi; Zhu, Yuhao; Sun, Qi (2022). "Color-Perception-Guided Display Power Reduction for Virtual Reality". ACM Transactions on Graphics . 41 (6): 1–16. arXiv: 2209.07610 . doi:10.1145/3550454.3555473. S2CID   252355104.
  13. ↑ Gravesen, Jens (November 2015). "The Metric of Color Space" (PDF). Graphical Models. 82: 77–86. doi:10.1016/j.gmod.2015.06.005 . Retrieved 28 November 2023.
  14. ↑ da Fonseca, Maria; Samengo, In´es (1 December 2016). "Derivation of human chromatic discrimination ability from an information-theoretical notion of distance in color space". Neural Computation. 28 (12): 2628–2655. arXiv: 1611.07272 . doi:10.1162/NECO_a_00903. PMID   27764598.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.