In
colorimetry
Colorimetry is "the science and technology used to quantify and describe physically the human color perception".
It is similar to spectrophotometry, but is distinguished by its interest in reducing spectra to the physical correlates of color ...
the OSA-UCS (Optical Society of America Uniform Color Space) is a
color space
A color space is a specific organization of colors. In combination with color profiling supported by various physical devices, it supports reproducible representations of colorwhether such representation entails an analog or a digital represent ...
first published in 1947 and developed by the
Optical Society of America
Optica (formerly known as The Optical Society (OSA) and before that as the Optical Society of America) is a professional society of individuals and companies with an interest in optics and photonics. It publishes journals and organizes conference ...
’s Committee on Uniform Color Scales.
Previously created color order systems, such as the
Munsell color system
In colorimetry, the Munsell color system is a color space that specifies colors based on three properties of color: hue (basic color), chroma (color intensity), and value ( lightness). It was created by Professor Albert H. Munsell in the first ...
, 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
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Analytic geometry is used in physics and engineer ...
would need to be used.
History and development
The development of the OSA-UCS took place during many years, from 1947-1977. Not long after the first mathematical color model was developed by the CIE, David MacAdam
David Lewis MacAdam (July 1, 1910 – March 9, 1998) 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 televisi ...
showed that when selecting a color on the CIE chromaticity diagram
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 s ...
, it could not be guaranteed that colors of the same perceived color difference around this color were at the same color distance with respect to the reference color.[ More simply, the Euclidean distance between any two colors on the chromaticity diagram could not be used as a uniform measure of perceived color difference. Immediately following this discovery work began to create a space that would behave uniformly in all directions of color difference.
Starting with a sample of 59 colored tiles of non-uniform color differences, the OSA asked 72 observers to judge color differences between the different sample tiles.][ From the data collected, formulas were developed and parameters were defined to create the new uniform color space. They chose the reference 10 degree observer and ]Illuminant D65
CIE standard illuminant D65 (sometimes written D65) is a commonly used standard illuminant defined by the International Commission on Illumination (CIE). It is part of the D series of illuminants that try to portray standard illumination conditio ...
to characterize the uniform space and a neutral gray background of 30% reflectance. In the end, 558 color samples were produced - 424 full step and 54 half step - and distributed by the OSA.[
]
Design
Geometry
The ideal color solid with points all at an equal distance from a center point is a sphere - however a collection of spheres can not be packed to form a larger solid without gaps. The geometry that the OSA finally chose is a rhombohedral lattice based on a cuboctahedron
A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it ...
. Each of the 12 vertices of this solid are equal distance from the center, as well as from each of their neighbors. The last step to completing this geometry was in a rescaling of the vertical L axis, in order to achieve integer coordinate locations for color description. The color distance uniformity is maintained, as only the axis dimensions are scaled, and the scaling is accounted for in the color distance formula.[
]
Coordinate values
The three perpendicular dimensions of the OSA-UCS are the lightness
Lightness is a visual perception of the luminance (L) 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 stan ...
dimension L, the jaune dimension j (a yellow/blue opponent dimension) and the green
Green is the color between cyan and yellow on the visible spectrum. It is evoked by light which has a dominant wavelength of roughly 495570 Nanometre, nm. In subtractive color systems, used in painting and color printing, it is created by ...
dimension g (a green/red opponent dimension).
Lightness (L)
The lightness scale of the OSA-UCS color solid varies vertically from about -10 to 8. UCS lightness of 0 corresponds to the 30% reflective neutral background gray selected for their samples, while lighter shades have positive values and darker shades have negative values.
Jaune (j)
The jaune dimension of the OSA-UCS color solid runs horizontally and perpendicular to the L dimension. This is a yellow-blue chromatic dimension, varying from positive values appearing more yellowish to negative values appearing more blueish. A j value of 0 lies along the neutral axis.
Green (g)
The green dimension of the OSA-UCS runs horizontally perpendicular to both the L and j dimensions. This green-red chromatic axis varies from more greenish positive values to more pinkish negative values. Again, a g value of 0 lies along the neutral (L) axis.
Color groupings
The cuboctahedron structure of the OSA-UCS color solid can be geometrically divided into 9 planes, known as cleavage planes. These 9 cleavage planes are defined as:
* L - A plane of constant L (lightness) that runs perpendicular to the L axis, where j and g can take on any values.
* j - A plane of constant j (yellow-blueness) that runs perpendicular to the j axis, where L and g can take on any values.
* g - A plane of constant g (red-greenness) that runs perpendicular to the g axis, where L and j can take on any values.
* L+j - A plane of constant L+j that runs parallel to the g axis, at 35° from the L axis and 55° from the j axis.
* L−j - A plane of constant L-j that runs parallel to the g axis, at 35° from the L axis and 55° from the j axis.
* L+g - A plane of constant L+g that runs parallel to the j axis, at 35° from the L axis and 55° from the g axis.
* L−g - A plane of constant L-g that runs parallel to the g axis, at 35° from the L axis and 55° from the g axis.
* j+g - A plane of constant j+g that runs parallel to the L axis, at 45° from the j and g axes.
* j−g - A plane of constant j-g that runs parallel to the L axis, at 45° from the j and g axes.
Color difference
OSA-UCS color difference is defined by the simple Euclidean distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points.
It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefor ...
between two colors in the color space, that takes into account the scaling done to the L axis. The formula used to calculate color difference between color 1 and 2 is:
:
Due to the design of the system, the color difference between two neighbors in the OSA-UCS color space is always 2. Small color differences can be accurately calculated using this formula. Larger color differences, however, require a non-linear correction for accuracy.[
]
Color transformations
CIEXYZ to OSA-UCS
To perform an analytical conversion from a CIEXYZ value to OSA-UCS, the following steps should be followed. First, a factor representing the Helmholtz-Kohlrausch effect must be calculated from the x and y chromaticity coordinates:
:
Next determine the modified luminous reflectance:
:
Then calculate the lightness and chroma modification factor:
: (given as in the original paper)
:
:
Convert the XYZ values to RGB
The RGB color model is an additive color model in which the red, green and blue primary colors of light are added together in various ways to reproduce a broad array of colors. The name of the model comes from the initials of the three addi ...
using the linear matrix transformation:
:
Last, calculate a and b:
:
:
and multiply them by C to obtain OSA-UCS g and j:
:
:
OSA-UCS to CIEXYZ
Although no closed-form conversion from OSA-UCS to CIEXYZ
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 defin ...
exists, numerical solvers have been written, including one based on the Newton–Raphson method
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valu ...
and another based on an artificial neural network
Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains.
An ANN is based on a collection of connected unit ...
.
See also
*Color model
A color model is an abstract mathematical model describing the way colors can be represented as tuples of numbers, typically as three or four values or color components. When this model is associated with a precise description of how the compon ...
*The Optical Society
Optica (formerly known as The Optical Society (OSA) and before that as the Optical Society of America) is a professional society of individuals and companies with an interest in optics and photonics. It publishes journals and organizes conference ...
*CIEXYZ
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 defin ...
*CIELAB
The CIELAB color space, also referred to as ''L*a*b*'' , is a color space defined by the International Commission on Illumination (abbreviated CIE) in 1976. (Referring to CIELAB as "Lab" without asterisks should be avoided to prevent confusion ...
*CIELUV
In colorimetry, the CIE 1976 ''L''*, ''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 CI ...
*David MacAdam
David Lewis MacAdam (July 1, 1910 – March 9, 1998) 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 televisi ...
References
{{color space
Color space