Color Transforms

As seen in the Colorimetry page, it's important to understand the difference between Absolute (or device-independent) Color Space (.e.g. CIEXYZ, CIExyY, CIELAB) and device-dependent colors spaces (e.g. RGB, HSL, HSB, HSV).

For example, it makes sense to convert from a device-dependent RGB space to a HSL space since, even though they are both device-dependent, they are defined in the same "dependent space".

Also, it makes sense to convert from 2 device-independent spaces like CIEXYZ and CIELAB.

Most importantly, the conversions between device-dependent color spaces and device-independent color spaces must always be accompanied by a Color Profile that appropriately describes the dependence to the device.

NOTE: All conversions assume HDR color values, meaning no boundary in luminance except where indicated.

Device-Dependent Color Space Conversions

Here, we will list the different conversions between device-dependent color spaces.

RGB / HSL

(Source: http://www.easyrgb.com)

RGB → HSL

• Input: RGB in [0,1]
• Output: HSL in [0,1]

var_Min = min( R, G, B )    // Min. value of RGB
var_Max = max( R, G, B )    // Max. value of RGB
del_Max = var_Max - var_Min // Delta RGB value

L = ( var_Max + var_Min ) / 2

if ( del_Max == 0 )                     // This is a gray, no chroma...
{
   H = 0                                // HSL results from 0 to 1
   S = 0
}
else                                    // Chromatic data...
{
   if ( L < 0.5 ) S = del_Max / ( var_Max + var_Min )
   else           S = del_Max / ( 2 - var_Max - var_Min )

   del_R = ( ( ( var_Max - var_R ) / 6 ) + ( del_Max / 2 ) ) / del_Max
   del_G = ( ( ( var_Max - var_G ) / 6 ) + ( del_Max / 2 ) ) / del_Max
   del_B = ( ( ( var_Max - var_B ) / 6 ) + ( del_Max / 2 ) ) / del_Max

   if      ( var_R == var_Max ) H = del_B - del_G
   else if ( var_G == var_Max ) H = ( 1 / 3 ) + del_R - del_B
   else if ( var_B == var_Max ) H = ( 2 / 3 ) + del_G - del_R

   if ( H < 0 ) H += 1
   if ( H > 1 ) H -= 1
}

HSL → RGB

• Input: HSL in [0,1]
• Output: RGB in [0,1]

if ( S == 0 )
{
   (R,G,B) = L;
}
else
{
   if ( L < 0.5 ) var_2 = L * ( 1 + S )
   else           var_2 = ( L + S ) - ( S * L )

   var_1 = 2 * L - var_2

   R = Hue_2_RGB( var_1, var_2, H + ( 1 / 3 ) ) 
   G = Hue_2_RGB( var_1, var_2, H )
   B = Hue_2_RGB( var_1, var_2, H - ( 1 / 3 ) )
}

Hue_2_RGB( v1, v2, vH )
{
   if ( vH < 0 ) vH += 1
   if ( vH > 1 ) vH -= 1
   if ( ( 6 * vH ) < 1 ) return ( v1 + ( v2 - v1 ) * 6 * vH )
   if ( ( 2 * vH ) < 1 ) return ( v2 )
   if ( ( 3 * vH ) < 2 ) return ( v1 + ( v2 - v1 ) * ( ( 2 / 3 ) - vH ) * 6 )
   return ( v1 )
}

RGB / HSV

(Source: http://www.easyrgb.com)

RGB → HSV

• Input: RGB in [0,1]
• Output: HSV in [0,1]

var_Min = min( R, G, B )    // Min. value of RGB
var_Max = max( R, G, B )    // Max. value of RGB
del_Max = var_Max - var_Min // Delta RGB value 

V = var_Max

if ( del_Max == 0 )                     // This is a gray, no chroma...
{
   H = 0                                // HSV results from 0 to 1
   S = 0
}
else                                    // Chromatic data...
{
   S = del_Max / var_Max

   del_R = ( ( ( var_Max - var_R ) / 6 ) + ( del_Max / 2 ) ) / del_Max
   del_G = ( ( ( var_Max - var_G ) / 6 ) + ( del_Max / 2 ) ) / del_Max
   del_B = ( ( ( var_Max - var_B ) / 6 ) + ( del_Max / 2 ) ) / del_Max

   if      ( var_R == var_Max ) H = del_B - del_G
   else if ( var_G == var_Max ) H = ( 1 / 3 ) + del_R - del_B
   else if ( var_B == var_Max ) H = ( 2 / 3 ) + del_G - del_R

   if ( H < 0 ) H += 1
   if ( H > 1 ) H -= 1
}

HSV → RGB

• Input: HSV in [0,1]
• Output: RGB in [0,1]

if ( S == 0 )                       //HSV from 0 to 1
{
   (R,G,B) = V
}
else
{
   var_h = H * 6
   if ( var_h == 6 ) var_h = 0      //H must be < 1
   var_i = int( var_h )             //Or ... var_i = floor( var_h )
   var_1 = V * ( 1 - S )
   var_2 = V * ( 1 - S * ( var_h - var_i ) )
   var_3 = V * ( 1 - S * ( 1 - ( var_h - var_i ) ) )

   if      ( var_i == 0 ) { R = V     ; G = var_3 ; B = var_1 }
   else if ( var_i == 1 ) { R = var_2 ; G = V     ; B = var_1 }
   else if ( var_i == 2 ) { R = var_1 ; G = V     ; B = var_3 }
   else if ( var_i == 3 ) { R = var_1 ; G = var_2 ; B = V     }
   else if ( var_i == 4 ) { R = var_3 ; G = var_1 ; B = V     }
   else                   { R = V     ; G = var_1 ; B = var_2 }
}

Device-Independent Color Space Conversions

Here, we will list the different conversions between device-independent color spaces.