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Digital Color Management: Encoding Solutions, 2nd Edition by Michael A. Kriss, Thomas E. Madden, Edward J. Giorgianni

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Color-Primary Conversions

Procedures for deriving 3 × 3 matrices for converting color values expressed in terms of one set of primaries to colorimetrically equivalent color values expressed in terms of a different set of color primaries are described below. The procedures can be used to convert RGB color values to colorimetrically equivalent CIE XYZ color values, CIE XYZ color values to colorimetrically equivalent RGB color values, and RGB color values expressed in terms of a one set of red, green, and blue primaries to colorimetrically equivalent RGB color values expressed in terms of a second set of red, green, and blue primaries. Also described is a related procedure for determining the color-matching functions for a given set of red, green, and blue primaries.

Matrix notation

A 3 × 3 matrix is a shorthand expression for three simultaneous equations. For example, the matrix expression

image

is equivalent to the set of simultaneous equations

image

RGB to CIE XYZ

A matrix for converting RGB color values expressed in terms of a set of red, green, and blue primaries to colorimetrically equivalent CIE XYZ color values expressed in terms of CIE X, Y, and Z primaries can be derived from the chromaticities of the red, green, and blue primaries and the chromaticity of their white point, i.e., ...

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