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3.4.3. BRIGHTNESS CALCULATION

Lecture



The color coordinates define this color relative to the reference white color. Often, however, it is necessary to know not the relative, but the absolute intensities of the primary colors that reproduce the given color. This data can be obtained by calculating its brightness.

From expressions (3.4.5) it follows that the brightness   3.4.3.  BRIGHTNESS CALCULATION colors   3.4.3.  BRIGHTNESS CALCULATION equal to the sum of the brightness of its main components:

  3.4.3.  BRIGHTNESS CALCULATION . (3.4.17)

Integrals

  3.4.3.  BRIGHTNESS CALCULATION (3.4.18)

are called the luminance coefficients of the primary colors. These coefficients are the brightness of the primary colors that equalize the white reference color. Therefore, the brightness of the color   3.4.3.  BRIGHTNESS CALCULATION can be written as

  3.4.3.  BRIGHTNESS CALCULATION . (3.4.19)

Chromaticity color   3.4.3.  BRIGHTNESS CALCULATION defined as

  3.4.3.  BRIGHTNESS CALCULATION . (3.4.20)

Multiplying the left and right sides of expressions (3.4.19) and (3.4.20) respectively, after some transformations, we get

  3.4.3.  BRIGHTNESS CALCULATION (3.4.21a)

and similarly

  3.4.3.  BRIGHTNESS CALCULATION , (3.4.21b)

  3.4.3.  BRIGHTNESS CALCULATION . (3.4.21b)

Thus, color coordinates can be expressed in terms of luminance and chromaticity coordinates.


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Digital image processing

Terms: Digital image processing