Color Spaces

A color space is a mathematical representation of our visual perceptions.   It is visualized in a three-dimensional graphic of the colors that can be created using a certain color model or device.   There are literally hundreds of common color spaces in use.   There are several ways to classify them, some overlapping.  Some examples follow:

Classifications

Device Independent: These represent the average observers rather than any particular input or output device.  Describes a color space that can be defined using the full gamut of human vision, as defined by a standard observer, independent of the color rendering capabilities of any specific device.   These are the typical CIE (Commission International de L'Eclairage) spaces such as XYZ, xyY, Lab, and Luv.   Within these there are alternate versions of the same color space.   For example the CIE XYZ space can be based on the 2 observations or 10 observations.   CIE Lab also has L*a*b*, LAB94, LAB2000, and other variants.

Device Dependent: These represent a device or generic class of devices.   Most of the RGB and CMY spaces are device dependent.   They are typically defined in ICC (International Color Consortium) profiles.   These color spaces are limited by the gamut, or range of colors, that a particular device is capable of recording or producing.

Unrendered: Generally refers to a device independent color space.   Sometimes also used to reference unprocessed raw image data.

Rendered: The target of a color space conversion.   A rendered color space is generally gamma corrected.   This matches the non-linear luminosity characteristics of a device.   It is also typically gamut constrained.   These are your typical device dependent RGB and CMY spaces.

Reference Space: This is the color space used by an image processor for profile conversions.   They should always be device independent.   They are sometimes also called Profile Connection Spaces (PCS).

Photometric: These are based on spectral measurements and monochromatic photometric luminosity.   This is typically used to describe CIE XYZ and xyY spaces or the raw data from image sensors.

Colorimetric: Colorimetric refers to devices that measure and report color values directly.   So, these are based on color measurements.   This term is typically used to describe CIE lab and Luv spaces.

Color Matching: This term is used with reference to mathematic color matching functions.   These are based on monochromatic power stimuli throughout the spectrum.   They will match a color to a spectral wavelength.   Although this uniquely defines an object's color, it does not predict the human response to the color.   CIE XYZ and xyY are examples of color matching spaces.

Perceptual: These correlate the chromatic values to human visual response in a more linear fashion.   CIE Lab and Luv are examples.

Uniform Perceptual: These are improvements to perceptual values where the differences scale better with the ability of people to detect unique tones.   Thus a numeric difference more accurately predicts the ability of an observer to detect it.   These are also sometimes simply referred to as Uniform color spaces.   CIE L*a*b* and L*u*v* (sometime written as CIELAB or CIELUV) are examples.   CIELAB94 and CIEDE2000 are other examples.

Spectral: This designation is frequently used to describe the raw values produced by an image-sensing device.   It is sometimes used with CIE XYZ.

Summary

A brief summary and description of some of the most commonly used device independent color spaces follows:

XYZ  Y = Luminescence (cd/m2)   XZ = spectral weighting curves (spectral locus)
xyY  Y = Luminescence (cd/m2)   xy = chromaticity co-ordinates (spectral locus)
Lab  L = Luminescence (density)   a = red/green b = blue/yellow
Luv  L = Luminescence u = saturation v = hue angle
LCh  L = Luminescence C = chromacity h = hue angle
YCrCb  Y = Luminescence Cr = red/yellow Cb = blue/yellow
RGB  Color matching curves R=700 nm G=546.1 nm B=435.8 nm

CIE RGB is a set of CIE color-matching curves based on many experiments with average observers.   It is based on pure light sources at specific RGB wavelengths.   This is classified as a color matching space and should not be confused with more familiar RGB primaries or color spaces.   Red contains negative values.   The resulting spectral curves are called the CIE standard primaries.   Any spectral color is identified by a unique set of RGB values.

CIE RGB Matching Functionss

CIE XYZ and xyY are the foundation of most color spaces.   XYZ has color matching functions that use all positive values.   XYZ and xyY are closely related.   The values can be transformed between these with simple math that transforms spectral weights to chromatic co-ordinates.   Thus, two dimensional chromacity diagrams typically use xyY rather than XYZ.  
CIE xyY  x = X/(X+Y+Z)   y = Y/(X+Y+Z)   Y = Y
CIE XYZ  X = x/y * Y   Z = (1-x-y)/y * Y   Y = Y

Note that in the CIE color space diagrams the spectral locus is horseshoe shaped and the wavelengths are not linearly spaced around the locus.   The straight line that closes the horseshoe connects the endpoints of the visible spectrum.

CIE XYZ Matching Functions CIE xyY Chromacity

CIE Lab uses a red/green axis for the a value and a blue/yellow axis for the b value.   This is very close to how the human optic system works.   CIE Luv uses chromacity (saturation) for the u value and hue angle for the v value.

YCbCr has its roots in video imaging and broadcast television.   It is analogous to YIQ (NTCS) and YUV (PAL), but optimized for digital transmission.   These are all device independent. YCbCr is the basis for JPG and MPG compression routines.

Color Models

A Color Model is a color measurement scale or system that numerically specifies the perceived attributes of color.   A color model is a method of grouping numeric values by a set of primaries.   Most color models have three primary components.   Some application-specific color models use more components, for example, CMYK.   Munsel and Pantone are also color models, sometimes called color systems.

HSV, HSB, and HLS: The usual formulations of HSB and HLS are from RGB values.   But they make no reference to the linearity or nonlinearity of these underlying RGB values.   They also make no reference to the lightness perception of human vision.   The illuminent white point is unspecified.   The computations correlate poorly with the properties of color vision.   These are not generally useful for image computation or color mixing.   But they do describe color attributes with easily understood metrics.

References

Measuring Colour: Dr. R.W.G. Hunt ISBN 0863433871
Color Science: Wyszecki and Stiles ISBN 0471399183
Principles of Color Technology: Roy S. Berns ISBN 047119459X


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November 1, 2005

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