Color Models

Based on the discussion on color perception, we know that a color can always be specified by three variables.

• RGB/YCM model

  The three additive primaries: Red, Green, Blue and the three secondary or subtractive primaries: Yellow, Cyan, Magenta.

  

  Each side of the RGB cube is 1 with its eight vertices located at $(0,0,0)$ (black), $(1,0,0)$ (red), $(0,1,0)$ (green), $(0,0,1)$ (blue), $(1,1,0)$ (yellow) $(1,0,1)$ (magenta), $(0,1,1)$ (cyan), $(1,1,1)$ (white). The length of the diagonal is $\sqrt{1+1+1}=\sqrt{3}$.

  The RGB plane shown in the figure can be specified by the equation
  

  $$R+G+B=1$$
  
  
  A RGB triangle is formed by the three vertices are $P_r=(0,0,1)$, $P_g=(0,1,0)$ and $P_b=(0,0,1)$, the lengths of its three sides are $\sqrt{2}$, and the center point of the triangle is $w=(1/3,1/3,1/3)$. The distance from the center to any of the vertices is $\sqrt{2/3}$, and the distance from the center to the closet side is $\sqrt{1/6}$.

  

  The YCM plane is specified by the equation
  

  $$Y+C+M=2$$
  
  
  with the center at $(2/3,2/3,2/3)$. Note that in this color cube, the primaries RGB are not on the same plane as the secondary primaries YCM.

• Additive and subtractive colors

  The primary colors R,G,B are additive colors used to describe the mixture of lights. In the background of black color (no light), the light corresponding to each of these primary colors will give us the color sensation of red, green or blue. Moreover, the mixture of any two of the three primary colors will give use the color sensation of yellow (R+G), magenta (R+B) and cyan (B+G). Finally the mixture of all three primaries (R+G+B) will give us the sensation of white color.
  

  $$R+G=Y,\;\;\;\;\;\;R+B=M,\;\;\;\;\;\;\;B+G=C$$
  
  
  and
  
  $$R+G+B=R+C=G+M=B+Y=W$$
  
  
  Note that here addition means mixture of lights.

  The secondary colors Y,C,M are subtractive colors used to describe the mixture of pigments or paints. In the background of white color (white paper), the pigments corresponding to each of Y, C, M will absorb one primary color: cyan absorbs (subtracts) red (C=W-R), magenta absorbs (subtracts) green (M=W-G), and yellow absorbs (subtracts) blue (Y=W-B). Moreover, the mixture of pigments of two secondary colors will also absorb more colors: mixture of C and M appears blue as both R and G are absorbed (W-R-G=B), mixture of C and Y appears green as both R and B are absorbed (W-R-B=G), and mixture of Y and M appears red as both Y and G are absorbed (W-Y-G=R). Finally, the mixture of all three secondaries appeers black as all R, G and B are absorbed.
  

  $$C=W-R,\;\;\;\;\;M=W-G,\;\;\;\;\;Y=W-B$$
  
  
  
  
  $$C+M=W-R-G=B,\;\;\;\;C+Y=W-R-B=G,\;\;\;\;\;M+Y=W-Y-G=R$$
  
  
  
  
  $$C+M+Y=W-R-G-B=0 \;\;\;\;\mbox{(black)}$$
  
  
  Note that here addition means mixture of pigments.

  

• HSV/HSI model

  Alternatively, a color can be specified by a set of three different variables: the Hue (H), Saturation (S), and value (V) or intensity (I).

  

  These two models are called HSV and HSI models, respectively. Any color is represented by a 3D point in the solid, with its hue represented by the angle with respect to red, its value or intensity represented by the vertical distance from zero representing black, and its saturation represented by the horizontal distance to the closest side.