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I want to convert the RGB color space to LUV
How to do that

Many thanks!

Accepted Answer from ho_alan
Date: 12/30/2004 08:43AM PST
Grade: A

RGB -> CIE XYZitu (D65): |X| |0.430574 0.341550 0.178325| |Red | |Y| = |0.222015 0.706655 0.071330| * |Green| |Z| |0.020183 0.129553 0.939180| |Blue | This provides the formula to transform RGB to CIE XYZitu and vice-versa: RGB -> CIE XYZitu (D65) | CIE XYZitu (D65) -> RGB X = 0.431*Red+0.342*Green+0.178*Blue | Red = 3.063*X-1.393*Y-0.476*Z Y = 0.222*Red+0.707*Green+0.071*Blue | Green = -0.969*X+1.876*Y+0.042*Z Z = 0.020*Red+0.130*Green+0.939*Blue | Blue = 0.068*X-0.229*Y+1.069*Z CIE XYZ -> CIE Lab { L* = 116*((Y/Yn)^(1/3)) whether Y/Yn>0.008856 { L* = 903.3*Y/Yn whether Y/Yn<=0.008856 u* = 13*(L*)*(u'-u'n) v* = 13*(L*)*(v'-v'n) where u'=4*X/(X+15*Y*+3*Z) and v'=9*Y/(X+15*Y+3*Z) and u'n and v'n have the same definitions for u' and v' but applied to the white point reference. So, you have: u'n=4*Xn/(Xn+15*Yn*+3*Zn) and v'n=9*Yn/(Xn+15*Yn+3*Zn)
Comment from ho_alan Date: 12/30/2004 08:44AM PST	Comment
hope it helps:-)
Comment from grg99 Date: 12/30/2004 02:05PM PST	Comment
First I'd check whatever graphics package you are using to display your images. 97.795% of them have built-in functions for converting between the different color representations. Many of those are a lot faster than any code you coul dwrite, as they use video hardware assistance to convert a whole image in a flash.

Silly questions

http://www1.tip.nl/~t876506/ColorDesign.html#sil

Why did you write color instead of colour?
Many more people looking for pages on the internet know the American spelling color better than the British spelling colour. But in the meta-tags of this document also a 'colour' keyword has been incorporated.

Transformavimo formules: http://www.easyrgb.com/math.html

Yxy —> XYZ

//Y = From 0 to 100
//x = From 0 to 1
//y = From 0 to 1

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

XYZ —> RGB

ref_X = 95.047 //Observer = 2°, Illuminant = D65
ref_Y = 100.000
ref_Z = 108.883

var_X = X / 100 //X = From 0 to ref_X
var_Y = Y / 100 //Y = From 0 to ref_Y
var_Z = Z / 100 //Z = From 0 to ref_Y

var_R = var_X * 3.2406 + var_Y * -1.5372 + var_Z * -0.4986
var_G = var_X * -0.9689 + var_Y * 1.8758 + var_Z * 0.0415
var_B = var_X * 0.0557 + var_Y * -0.2040 + var_Z * 1.0570

if (var_R > 0.0031308) var_R = 1.055 * (var_R ^ (1 / 2.4)) - 0.055
else var_R = 12.92 * var_R
if (var_G > 0.0031308) var_G = 1.055 * (var_G ^ (1 / 2.4)) - 0.055
else var_G = 12.92 * var_G
if (var_B > 0.0031308) var_B = 1.055 * (var_B ^ (1 / 2.4)) - 0.055
else var_B = 12.92 * var_B

R = var_R * 255
G = var_G * 255
B = var_B * 255

RGB —> XYZ

var_R = (R / 255) //R = From 0 to 255
var_G = (G / 255) //G = From 0 to 255
var_B = (B / 255) //B = From 0 to 255

if (var_R > 0.04045) var_R = ((var_R + 0.055) / 1.055) ^ 2.4
else var_R = var_R / 12.92
if (var_G > 0.04045) var_G = ((var_G + 0.055) / 1.055) ^ 2.4
else var_G = var_G / 12.92
if (var_B > 0.04045) var_B = ((var_B + 0.055) / 1.055) ^ 2.4
else var_B = var_B / 12.92

var_R = var_R * 100
var_G = var_G * 100
var_B = var_B * 100

//Observer. = 2°, Illuminant = D65
X = var_R * 0.4124 + var_G * 0.3576 + var_B * 0.1805
Y = var_R * 0.2126 + var_G * 0.7152 + var_B * 0.0722
Z = var_R * 0.0193 + var_G * 0.1192 + var_B * 0.9505

XYZ —> Yxy

//X = From 0 to 95.047 Observer. = 2°, Illuminant = D65
//Y = From 0 to 100.000
//Z = From 0 to 108.883

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

Yxy —> XYZ

//Y = From 0 to 100
//x = From 0 to 1
//y = From 0 to 1

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

XYZ —> Hunter-Lab

H)L = 10 * sqrt(Y)
(H)a = 17.5 * (((1.02 * X) - Y) / sqrt(Y))
(H)b = 7 * ((Y - (0.847 * Z)) / sqrt(Y))

Hunter-Lab —> XYZ

var_Y = (H)L / 10
var_X = (H)a / 17.5 * (H)L / 10
var_Z = (H)b / 7 * (H)L / 10

Y = var_Y ^ 2
X = (var_X + out_Y) / 1.02
Z = -(var_Z - out_Y) / 0.847

XYZ —> CIE-L*ab

var_X = X / 95.047 //Observer = 2°, Illuminant = D65
var_Y = Y / 100.000
var_Z = Z / 108.883

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)

CIE-L*ab —> XYZ

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 = 95.047 Observer= 2°, Illuminant= D65
Y = ref_Y * var_Y //ref_Y = 100.000
Z = ref_Z * var_Z //ref_Z = 108.883

CIE-L*ab —> CIE-L*CH°

var_H = arc_tangent(CIE-b*, CIE-a*) //Quadrant by signs

if (var_H > 0) var_H = (var_H / PI) * 180
else var_H = 360 - (abs(var_H) / PI) * 180

CIE-L* = CIE-L*
CIE-C* = sqrt(CIE-a* ^ 2 + CIE-b* ^ 2)
CIE-H° = var_H

CIE-L*CH° —> CIE-L*ab

//CIE-H° = From 0 to 360°

CIE-L* = CIE-L*
CIE-a* = cos(degree_2_radian(CIE-H°)) * CIE-C*
CIE-b* = sin(degree_2_radian(CIE-H°)) * CIE-C*

XYZ —> CIE-L*uv

var_U = (4 * X) / (X + (15 * Y) + (3 * Z))
var_V = (9 * Y) / (X + (15 * Y) + (3 * Z))

var_Y = Y / 100
if (var_Y > 0.008856) var_Y = var_Y ^ (1/3)
else var_Y = (7.787 * var_Y) + (16 / 116)

ref_X = 95.047 //Observer= 2°, Illuminant= D65
ref_Y = 100.000
ref_Z = 108.883

ref_U = (4 * ref_X) / (ref_X + (15 * ref_Y) + (3 * ref_Z))
ref_V = (9 * ref_Y) / (ref_X + (15 * ref_Y) + (3 * ref_Z))

CIE-L* = (116 * var_Y) - 16
CIE-u* = 13 * CIE-L* * (var_U - ref_U)
CIE-v* = 13 * CIE-L* * (var_V - ref_V)

CIE-L*uv —> XYZ

var_Y = (CIE-L* + 16) / 116
if (var_Y^3 > 0.008856) var_Y = var_Y^3
else var_Y = (var_Y - 16 / 116) / 7.787

ref_X = 95.047 //Observer= 2°, Illuminant= D65
ref_Y = 100.000
ref_Z = 108.883

ref_U = (4 * ref_X) / (ref_X + (15 * ref_Y) + (3 * ref_Z))
ref_V = (9 * ref_Y) / (ref_X + (15 * ref_Y) + (3 * ref_Z))

var_U = CIE-u* / (13 * CIE-L*) + ref_U
var_V = CIE-v* / (13 * CIE-L*) + ref_V

Y = var_Y * 100
X = - (9 * Y * var_U) / ((var_U - 4) * var_V - var_U * var_V)
Z = (9 * Y - (15 * var_V * Y) - (var_V * X)) / (3 * var_V)

RGB —> HSL

var_R = (R / 255) //RGB values = From 0 to 255
var_G = (G / 255)
var_B = (B / 255)

var_Min = min(var_R, var_G, var_B) //Min. value of RGB
var_Max = max(var_R, var_G, var_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

if (S == 0) //HSL values = From 0 to 1
{
R = L * 255 //RGB results = From 0 to 255
G = L * 255
B = L * 255
}
else
{
if (L < 0.5) var_2 = L * (1 + S)
else var_2 = (L + S) - (S * L)

var_1 = 2 * L - var_2

R = 255 * Hue_2_RGB(var_1, var_2, H + (1 / 3))
G = 255 * Hue_2_RGB(var_1, var_2, H)
B = 255 * Hue_2_RGB(var_1, var_2, H - (1 / 3))
}

Hue_2_RGB(v1, v2, vH) //Function Hue_2_RGB
{
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

var_R = (R / 255) //RGB values = From 0 to 255
var_G = (G / 255)
var_B = (B / 255)

var_Min = min(var_R, var_G, var_B) //Min. value of RGB
var_Max = max(var_R, var_G, var_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

if (S == 0) //HSV values = From 0 to 1
{
R = V * 255 //RGB results = From 0 to 255
G = V * 255
B = V * 255
}
else
{
var_h = H * 6
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) { var_r = V; var_g = var_3; var_b = var_1 }
else if (var_i == 1) { var_r = var_2; var_g = V; var_b = var_1 }
else if (var_i == 2) { var_r = var_1; var_g = V; var_b = var_3 }
else if (var_i == 3) { var_r = var_1; var_g = var_2; var_b = V }
else if (var_i == 4) { var_r = var_3; var_g = var_1; var_b = V }
else { var_r = V; var_g = var_1; var_b = var_2 }

R = var_r * 255 //RGB results = From 0 to 255
G = var_g * 255
B = var_b * 255
}
}

Range of HSL, HSB and HSV in popular applications

Applications	Space	H Range	S Range	L/V/B Range
Paint Shop Pro	HSL	0 - 255	0 - 255	L	0 - 255
Gimp	HSV	0 - 360°	0 - 100	V	0 - 100
Photoshop	HSV	0 - 360°	0 - 100%	B	0 - 100%
Windows	HSL	0 - 240	0 - 240	L	0 - 240
Linux / KDE	HSV	0 - 360°	0 - 255	V	0 - 255
GTK	HSV	0 - 360°	0 - 1.0	V	0 - 1.0
Java (awt.Color)	HSV	0 - 1.0	0 - 1.0	B	0 - 1.0
Apple	HSV	0 - 360°	0 - 100%	L	0 - 100%

RGB —> CMY

//RGB values = From 0 to 255

C = 1 - (R / 255)
M = 1 - (G / 255)
Y = 1 - (B / 255)

CMY —> RGB

//CMY values = From 0 to 1

R = (1 - C) * 255
G = (1 - M) * 255
B = (1 - Y) * 255

CMY —> CMYK

//CMY values = From 0 to 1

var_K = 1

if (C < var_K) var_K = C
if (M < var_K) var_K = M
if (Y < var_K) var_K = Y

C = (C - var_K) / (1 - var_K)
M = (M - var_K) / (1 - var_K)
Y = (Y - var_K) / (1 - var_K)
K = var_K

CMYK —> CMY

//CMYK values = From 0 to 1

C = (C * (1 - K) + K)
M = (M * (1 - K) + K)
Y = (Y * (1 - K) + K)

XYZ (Tristimulus) Reference values of a perfect reflecting diffuser

Observer	2° (CIE 1931)	10° (CIE 1964)
Illuminant	X2	Y2	Z2	X10	Y10	Z10
A (Incandescent)	109.850		35.585	111.144		35.200
C	98.074		118.232	97.285		116.145
D50	96.422		82.521	96.720		81.427
D55	95.682		92.149	95.799		90.926
D65 (Daylight)	95.047		108.883	94.811		107.304
D75	94.972		122.638	94.416		120.641
F2 (Fluorescent)	99.187		67.395	103.280		69.026
F7	95.044		108.755	95.792		107.687
F11	100.966		64.370	103.866		65.627

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