Editing Colorfulness (section)

=== CIELUV and CIELAB ===

In [[CIELUV]], saturation is equal to the ''chroma'' normalized by the ''lightness'':
<math display=block>s_{uv} = \frac{C^*_{uv}}{L^*} = 13 \sqrt{(u' - u'_n)^2 + (v' - v'_n)^2}</math>
where <math>\left(u_n, v_n\right)</math> is the chromaticity of the white point, and chroma is defined below.<ref>{{Cite book|last=Schanda|first=János|title=Colorimetry: Understanding the CIE System|publisher=[[Wiley Interscience]]|year=2007|isbn=978-0-470-04904-4|url=https://books.google.com/books?id=g8VDAgAACAAJ|url-status=live|archive-url=https://web.archive.org/web/20170117120237/https://books.google.com/books?id=g8VDAgAACAAJ&dq=intitle:Colorimetry+intitle:Understanding+intitle:the+intitle:CIE+intitle:System|archive-date=2017-01-17}}, page 88.</ref>

By analogy, in [[CIELAB]] this would yield:
<math display=block>s_{ab} = \frac{C^*_{ab}}{L^*} = \frac{\sqrt{{a^*}^2 + {b^*}^2}}{L^*}</math>

The CIE has not formally recommended this equation since CIELAB has no chromaticity diagram, and this definition therefore lacks direct connection with older concepts of saturation.<ref>{{cite book|url=https://archive.org/details/focalencyclopedi00lesl|url-access=registration|title=The Focal Encyclopedia of Photography|publisher=Focal Press|editor=Leslie D. Stroebel, Richard D. Zakia|isbn=0-240-51417-3|year=1993|page=[https://archive.org/details/focalencyclopedi00lesl/page/124 124]|first=Robert William Gainer|last=Hunt}}</ref> Nevertheless, this equation provides a reasonable predictor of saturation, and demonstrates that adjusting the lightness in CIELAB while holding {{nobr|(''a''*, ''b''*)}} fixed does affect the saturation.

But the following verbal definition of Manfred Richter and the corresponding formula proposed by Eva Lübbe are in agreement with the human perception of saturation:
Saturation is the proportion of pure chromatic color in the total color sensation.<ref>{{Cite book|last=Lübbe|first=Eva|title=Colours in the Mind - Colour Systems in Reality- A formula for colour saturation|publisher=[Book on Demand]|year=2010|isbn=978-3-7881-4057-1 }}</ref>
<math display=block>S_{ab} = \frac{C^*_{ab}}{\sqrt{{C^*_{ab} }^2 + {L^*}^2}} 100\%</math>
where <math>S_{ab}</math> is the saturation, <math>L^*</math> the  lightness and <math>C^*_{ab}</math> is the chroma of the color.