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.

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.

XYZ / xyY

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

XYZ → xyY

Input: (Observer. = 2°, Illuminant = D65)
- X in [0, 0.95047]
- Y in [0, 1.00000]
- Z in [0, 1.08883]
Output: xyY in [0,1]

Y = Y
x = X / ( X + Y + Z )
y = Y / ( X + Y + Z )

xyY → XYZ

Input: xyY in [0,1]
Output: (Observer. = 2°, Illuminant = D65)
- X in [0, 0.95047]
- Y in [0, 1.00000]
- Z in [0, 1.08883]

X = x * ( Y / y )
Y = Y
Z = ( 1 - x - y ) * ( Y / y )

XYZ / Lab

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

Remember that CIE L*a*b* is device-independent but needs a white point reference nevertheless.

Here, the D65 illuminant is used.

XYZ → Lab*

Input: (Observer. = 2°, Illuminant = D65)
- X in [0, 0.95047]
- Y in [0, 1.00000]
- Z in [0, 1.08883]
Output:
- L* in [0,100]
- a*, b* in [-?,?]

var_X = X / ref_X          // ref_X = 0.95047   Observer= 2°, Illuminant= D65
var_Y = Y / ref_Y          // ref_Y = 1.000
var_Z = Z / ref_Z          // ref_Z = 1.08883

if ( var_X > 0.008856 ) var_X = var_X ^ ( 1/3 )
else                    var_X = ( 7.787 * var_X ) + ( 16 / 116 )
if ( var_Y > 0.008856 ) var_Y = var_Y ^ ( 1/3 )
else                    var_Y = ( 7.787 * var_Y ) + ( 16 / 116 )
if ( var_Z > 0.008856 ) var_Z = var_Z ^ ( 1/3 )
else                    var_Z = ( 7.787 * var_Z ) + ( 16 / 116 )

CIE-L* = ( 116 * var_Y ) - 16
CIE-a* = 500 * ( var_X - var_Y )
CIE-b* = 200 * ( var_Y - var_Z )

Lab* → XYZ

Input:
- L* in [0,100]
- a*, b* in [-?,?]
Output: (Observer. = 2°, Illuminant = D65)
- X in [0, 0.95047]
- Y in [0, 1.00000]
- Z in [0, 1.08883]

var_Y = ( CIE-L* + 16 ) / 116
var_X = CIE-a* / 500 + var_Y
var_Z = var_Y - CIE-b* / 200

if ( var_Y^3 > 0.008856 ) var_Y = var_Y^3
else                      var_Y = ( var_Y - 16 / 116 ) / 7.787
if ( var_X^3 > 0.008856 ) var_X = var_X^3
else                      var_X = ( var_X - 16 / 116 ) / 7.787
if ( var_Z^3 > 0.008856 ) var_Z = var_Z^3
else                      var_Z = ( var_Z - 16 / 116 ) / 7.787

X = ref_X * var_X     // ref_X = 0.95047     Observer= 2°, Illuminant= D65
Y = ref_Y * var_Y     // ref_Y = 1.00000
Z = ref_Z * var_Z     // ref_Z = 1.08883

Device-dependent / Device-independent Color Space Conversions

RGB (in sRGB) / XYZ

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

Please refer to the sRGB color profile specification to understand the pseudo-gamma correction in the following routines.

RGB → XYZ

Input: RGB in [0,1] with sRGB gamma profile
Output: (Observer. = 2°, Illuminant = D65)
- X in [0, 0.95047]
- Y in [0, 1.00000]
- Z in [0, 1.08883]

// Apply gamma correction (i.e. conversion to linear-space)
if ( R > 0.04045 ) R = ( ( R + 0.055 ) / 1.055 ) ^ 2.4
else               R = R / 12.92
if ( G > 0.04045 ) G = ( ( G + 0.055 ) / 1.055 ) ^ 2.4
else               G = G / 12.92
if ( B > 0.04045 ) B = ( ( B + 0.055 ) / 1.055 ) ^ 2.4
else               B = B / 12.92

// Observer. = 2°, Illuminant = D65
X = R * 0.4124 + G * 0.3576 + B * 0.1805
Y = R * 0.2126 + G * 0.7152 + B * 0.0722
Z = R * 0.0193 + G * 0.1192 + B * 0.9505

XYZ → RGB

Input: (Observer. = 2°, Illuminant = D65)
- X in [0, 0.95047]
- Y in [0, 1.00000]
- Z in [0, 1.08883]
Output: RGB in [0,1] with sRGB gamma profile

R = X *  3.2406 + Y * -1.5372 + Z * -0.4986
G = X * -0.9689 + Y *  1.8758 + Z *  0.0415
B = X *  0.0557 + Y * -0.2040 + Z *  1.0570

if ( R > 0.0031308 ) R = 1.055 * ( R ^ ( 1 / 2.4 ) ) - 0.055
else                 R = 12.92 * R
if ( G > 0.0031308 ) G = 1.055 * ( G ^ ( 1 / 2.4 ) ) - 0.055
else                 G = 12.92 * G
if ( B > 0.0031308 ) B = 1.055 * ( B ^ ( 1 / 2.4 ) ) - 0.055
else                 B = 12.92 * B

RGB (in Adobe RGB) / XYZ

(Source: http://www.adobe.com/digitalimag/pdfs/AdobeRGB1998.pdf)

RGB → XYZ

Input: RGB in [0,1] with Adobe RGB gamma profile
Output: (Observer. = 2°, Illuminant = D65)
- X in [0, 0.95047]
- Y in [0, 1.00000]
- Z in [0, 1.08883]

// Gamma correction of ~2.2
R = R ^ 2.19921875
G = G ^ 2.19921875
B = B ^ 2.19921875

// Observer. = 2°, Illuminant = D65
X =  0.57667 * R + 0.18556 * G + 0.18823 * B
Y =  0.29734 * R + 0.62736 * G + 0.07529 * B
Z =  0.02703 * R + 0.07069 * G + 0.99134 * B

XYZ → RGB

Input: (Observer. = 2°, Illuminant = D65)
- X in [0, 0.95047]
- Y in [0, 1.00000]
- Z in [0, 1.08883]
Output: RGB in [0,1] with Adobe RGB gamma profile

R =  2.04159 * X - 0.56501 * Y - 0.34473 * Z
G = -0.96924 * X + 1.87597 * Y + 0.04156 * Z
B =  0.01344 * X - 0.11836 * Y + 1.01517 * Z

// Gamma correction
R = R ^ (1.0 / 2.19921875)
G = G ^ (1.0 / 2.19921875)
B = B ^ (1.0 / 2.19921875)

RGB (in Adobe RGB ICC Profile v2.4) / XYZ

(Source: http://www.adobe.com/digitalimag/pdfs/AdobeRGB1998.pdf)

RGB → XYZ

Input: RGB in [0,1] with Adobe RGB gamma profile
Output: (Observer. = 2°, Illuminant = D50)
- X in [0, 0.9642]
- Y in [0, 1.0000]
- Z in [0, 0.8249]

// Gamma correction of ~2.2
R = R ^ 2.19921875
G = G ^ 2.19921875
B = B ^ 2.19921875

// Observer. = 2°, Illuminant = D50
X = 0.60974 * R + 0.20528 * G + 0.14919 * B
Y = 0.31111 * R + 0.62567 * G + 0.06322 * B
Z = 0.01947 * R + 0.06087 * G + 0.74457 * B

XYZ → RGB

Input: (Observer. = 2°, Illuminant = D50)
- X in [0, 0.9642]
- Y in [0, 1.0000]
- Z in [0, 0.8249]
Output: RGB in [0,1] with Adobe RGB gamma profile

R =  1.96253 * X - 0.61068 * Y - 0.34137 * Z
G = -0.97876 * X + 1.91615 * Y + 0.03342 * Z
B =  0.02869 * X - 0.14067 * Y + 1.34926 * Z

// Gamma correction
R = R ^ (1.0 / 2.19921875)
G = G ^ (1.0 / 2.19921875)
B = B ^ (1.0 / 2.19921875)

RGB (in ProPhoto RGB) / XYZ

(Source: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.202.294)

RGB → XYZ

Input: RGB in [0,1] with ProPhoto RGB gamma profile
Output: (Observer. = 2°, Illuminant = D50)
- X in [0, 0.96421]
- Y in [0, 1.00000]
- Z in [0, 0.82519]

// Gamma correction
if ( R > 16 * 0.001953 ) R = R ^ 1.8
else                     R = R / 16
if ( G > 16 * 0.001953 ) G = G ^ 1.8
else                     G = G / 16
if ( B > 16 * 0.001953 ) B = B ^ 1.8
else                     B = B / 16

// Observer. = 2°, Illuminant = D50
X = 0.7977 * R + 0.1352 * G + 0.0313 * B
Y = 0.2880 * R + 0.7119 * G + 0.0001 * B
Z = 0.0000 * R + 0.0000 * G + 0.8249 * B

XYZ → RGB

Input: (Observer. = 2°, Illuminant = D50)
- X in [0, 0.96421]
- Y in [0, 1.00000]
- Z in [0, 0.82519]
Output: RGB in [0,1] with ProPhoto RGB gamma profile

R =  1.3460 * X - 0.2556 * Y - 0.0511 * Z
G = -0.5446 * X + 1.5082 * Y + 0.0205 * Z
B =  0.0000 * X + 0.0000 * Y + 1.2123 * Z

// Gamma correction
if ( R > 0.001953 ) R = R ^ ( 1 / 1.8 )
else                R = 16.0 * R
if ( G > 0.001953 ) G = G ^ ( 1 / 1.8 )
else                G = 16.0 * G
if ( B > 0.001953 ) B = B ^ ( 1 / 1.8 )
else                B = 16.0 * B

Dealing with Generic Color Profiles

XYZ Matrices

When dealing with standard profiles like sRGB, Adobe RGB or ProPhoto RGB you are given the chromaticities of Red, Green, Blue and the one for the White Point.

Also, when opening PNG file you can encounter the cHRM chunk that describes the same chromaticities. You then need to transform these 4 2D values into a 3x3 matrix to convert the RGB value to and from the XYZ master space.

First of all, remembering our basic CIEXYZ and CIExyY conversions, let's enumerate what we know:

<math>xyz_R = \frac{XYZ_R}{X_R+Y_R+Z_R} = \frac{XYZ_R}{\Sigma_R}</math> from the chromaticities for Red

<math>xyz_G = \frac{XYZ_G}{X_G+Y_G+Z_G} = \frac{XYZ_G}{\Sigma_G}</math> from the chromaticities for Green

<math>xyz_B = \frac{XYZ_B}{X_B+Y_B+Z_B} = \frac{XYZ_B}{\Sigma_B}</math> from the chromaticities for Blue

<math>xyz_W</math> from the chromaticities for White

<math>Y_W = 1</math> standard luminance for White

<math>XYZ_W</math> (since we have a completely defined <math>xyY_W</math>, we can thus easily convert to <math>XYZ_W</math>, see CIE XYZ color space)

Note that we don't know the <math>XYZ_R</math>, <math>XYZ_G</math> and <math>XYZ_B</math> vectors.

So we are looking for <math>M_{XYZ}</math> so that:

<math>

XYZ = RGB . M_{XYZ} = RGB . \begin{bmatrix} XYZ_R \\ XYZ_G \\ XYZ_B \end{bmatrix} = RGB . \begin{bmatrix} \Sigma_R.xyz_R \\ \Sigma_G.xyz_G \\ \Sigma_B.xyz_B \end{bmatrix} </math>

Using <math>RGB_W = [1,1,1]</math> we can write:

<math>XYZ_W = [1,1,1] . M_{XYZ} = \Sigma_R.xyz_R + \Sigma_G.xyz_G + \Sigma_B.xyz_B</math>

Or, in matrix form again:

<math>XYZ_W = \Sigma_{RGB} .

\begin{bmatrix} xyz_R \\ xyz_G \\ xyz_B \end{bmatrix} = \Sigma_{RGB} . M_{xyz} </math>

Solving by right composing with <math>M_{xyz}^{-1}</math>:

<math>

\Sigma_{RGB} = XYZ_W . M_{xyz}^{-1} </math>

we thus obtain <math>\Sigma_{RGB}</math> and since:

<math>

\begin{bmatrix} \Sigma_R . xyz_R \\ \Sigma_G . xyz_G \\ \Sigma_B . xyz_B \end{bmatrix} = \begin{bmatrix} XYZ_R \\ XYZ_G \\ XYZ_B \end{bmatrix} = M_{XYZ} </math>

we finally obtain <math>M_{XYZ}</math> that converts a RGB color into an XYZ color (obviously, you need to use the inverse <math>M_{XYZ}^{-1}</math> to convert from XYZ back into RGB).

Custom Profiles

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Color Transforms

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Contents

Device-Dependent Color Space Conversions

RGB / HSL

RGB → HSL

HSL → RGB

RGB / HSV

RGB → HSV

HSV → RGB

Device-Independent Color Space Conversions

XYZ / xyY

XYZ → xyY

xyY → XYZ

XYZ / Lab

XYZ → Lab*

Lab* → XYZ

Device-dependent / Device-independent Color Space Conversions

RGB (in sRGB) / XYZ

RGB → XYZ

XYZ → RGB

RGB (in Adobe RGB) / XYZ

RGB → XYZ

XYZ → RGB

RGB (in Adobe RGB ICC Profile v2.4) / XYZ

RGB → XYZ

XYZ → RGB

RGB (in ProPhoto RGB) / XYZ

RGB → XYZ

XYZ → RGB

Dealing with Generic Color Profiles

XYZ Matrices

Custom Profiles

The ICC/ICM file format

HDR Images

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Navigation

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Tools

Personal tools

Color Transforms

Contents

Device-Dependent Color Space Conversions

RGB / HSL

RGB → HSL

HSL → RGB

RGB / HSV

RGB → HSV

HSV → RGB

Device-Independent Color Space Conversions

XYZ / xyY

XYZ → xyY

xyY → XYZ

XYZ / Lab

XYZ → L*a*b*

L*a*b* → XYZ

Device-dependent / Device-independent Color Space Conversions

RGB (in sRGB) / XYZ

RGB → XYZ

XYZ → RGB

RGB (in Adobe RGB) / XYZ

RGB → XYZ

XYZ → RGB

RGB (in Adobe RGB ICC Profile v2.4) / XYZ

RGB → XYZ

XYZ → RGB

RGB (in ProPhoto RGB) / XYZ

RGB → XYZ

XYZ → RGB

Dealing with Generic Color Profiles

XYZ Matrices

Custom Profiles

The ICC/ICM file format

HDR Images

Navigation menu

Search

XYZ → Lab*

Lab* → XYZ