CIEXYZ转CIELUV中u'、v'、u'ₙ、v'ₙ、Yₙ的含义及与白点的关系

Hey there! Let me break down those white point-related variables for you since you're diving into CIEXYZ and CIELUV conversions—this stuff can feel tangled at first, but it's all anchored to the "white reference" idea.

First, let's ground this: all these variables revolve around the white point—the defined "ideal white" reference for your color space. Different standards (like D65, D50) and viewing angles (2° vs 10°) have unique white point parameters, which are the backbone of these calculations.

Core Variables & Their White Point Links #

• Yₙ: This is the Y component of the white point in the CIEXYZ color space. Since Y represents luminance in CIEXYZ, Yₙ is simply the luminance value of your reference white. For most standard white points (like D65), Yₙ is normalized to 100 (this is a common convention to keep luminance values in a intuitive 0-100 range).
• u'ₙ, v'ₙ: These are the chromaticity coordinates (u'v' coordinates) of the white point, converted from its XYZ values using these formulas:

  u' = (4X) / (X + 15Y + 3Z)
  v' = (9Y) / (X + 15Y + 3Z)
  

  Plug the white point's Xₙ, Yₙ, Zₙ values into these equations, and you get u'ₙ and v'ₙ. These act as the "anchor" for white in CIELUV—all other colors' u'v' coordinates are compared against this to measure color shift.
• u', v': These are the u'v' chromaticity coordinates of the color you're converting. You calculate them using the exact same formula above, but with the target color's X, Y, Z values instead of the white point's. They're used alongside u'ₙ and v'ₙ to compute the u* and v* components in CIELUV (which represent red-green and yellow-blue color shifts).

Example: 2° Field of View White Point #

For example, the D65 white point (2° field of view) has XYZ values: Xₙ=95.047, Yₙ=100, Zₙ=108.883. Plugging these into the u'v' formula gives u'ₙ≈0.1978 and v'ₙ≈0.4683—this is the standard white reference you'll see in most CIELUV conversion tools.

The Full Logic Flow #

To tie it all together:

1. Pick your white point standard (e.g., 2° D65) and look up its Xₙ, Yₙ, Zₙ parameters.
2. Calculate u'ₙ and v'ₙ from those XYZ values to set your CIELUV white baseline.
3. Convert your target color's XYZ values to u' and v'.
4. Combine Y (target color's luminance), Yₙ, u', v', u'ₙ, and v'ₙ to compute the final CIELUV values: L* (luminance), u* (red-green axis), v* (yellow-blue axis).

Hope this clears up the confusion—feel free to dig into the math deeper if you're tweaking conversions for specific use cases!

内容的提问来源于stack exchange，提问作者Steven