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Digital Image Processing (2000)

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3.5 Color Space Conversion

The RGB (red, green, blue) color scheme is just one of many color representation methods used in practice. The three so-called primary colors are combined (added) in various proportions to produce a composite, full-color image. The RGB color model is universally used in color monitors and color video cameras and is implemented in the Mathematica graphics directive RGBColor. Also, the human visual system is tuned to perceive color as a variable combination of these primary colors. The primary colors added in equal amounts produce the secondary colors of light: cyan (C), magenta (M), and yellow (Y). These are the primary pigment colors used in the printing industry and thus the relevance of the CMY color model.
For image processing applications it is often useful to separate the color information from luminance. The HSV (hue, saturation, value) model has this property. Hue represents the dominant color as seen by an observer, saturation refers to the amount of dilution of the color with white light, and value defines the average brightness. The luminance component may, therefore, be processed independently of the image's color information. Here is an array of color specifications using the color directive Hue, with hue and saturation held constant and value ranging from zero to one.
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When processing color images it is sometimes desirable to change the color format of the image. Color format conversions are implemented as point operations. A single-channel monochrome format and seven multichannel color formats are supported by the Digital Image Processing package: Mathematica color spaces GrayLevel, RGBColor, Hue and CMYKColor, the CIE color spaces CIEXYZColor, CIELABColor, and CIELUVColor, and a generic color space.

Color format conversion functions.

This loads the package.
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This reads an example color image in RGB color format.
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Here we convert to a monochrome image.
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Here is the input form of the monochrome version of the example image.
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The grayscale values of an RGB color image, denoted , are computed using a weighted average of {r(x,y), g(x,y), b(x,y)} according to the following formula:
The weighting coefficients may be changed by the user. Here is an example of conversion to monochrome using a simple average of the three color values.
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Here we convert to the CMYK color format and show the input form of the result. Note that a CMYK color specification uses four channels. Also note that the color values are real numbers in the range 0≤c,m,y,k≤1.
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The CIE (International Commission on Illumination) color spaces L*u*v* and L*a*b* are device independent, colorimetric (i.e., perceptually equal colors are numerically equal), and perceptually uniform (i.e., color differences of a given magnitude are equally perceptible irrespective of the region of the color space being examined) [Poy03]. It should be noted that this is not the case with the common RGB color space. These properties make the CIE color spaces especially valuable for measuring and quantifying changes in color images. Channel L* represents lightness, while channels a* and b* (or u*, v*) roughly represent the color differences red minus green and green minus blue, respectively. It has been demonstrated [Kas92] that the L*a*b* color space separates color from luminance better than any other color model.
This iterates over the a* and b* channels with L*=75 to produce a CIELABColor image and converts to RGBColor for rendering purposes.
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This shows the three CIELABColor channels of the example beans color image. Since the CIE color spaces are not directly displayable as a composite image they are automatically rendered as three graylevel channels (i.e., in planar format).
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In Section 2.4 we introduced the function RawImageData, which is used to extract raw data from an ImageData expression. On occasion, it may be of interest to perform the inverse operation (i.e., construct an ImageData object given raw data in one of the supported formats, see Equations (2.2.1), (2.3.1), and (2.3.2)). Here we take raw image data in pixel-interleaved form and convert to a composite RGB color image.
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This displays the result.
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The point transformations between color values in the supported color domains are defined by the following functions.

Color value transformations.

Here we convert an RGB color specification to equivalent colors in HSV and CMYK formats.
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Here a range of HSV color values is converted to an RGB color specification. Note that as the hue value is increased, the colors change from red to green, blue, and back to red.
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