Color Conversion Algorithms
Contents
* RGB to HSV & HSV to RGB
* RGB to YIQ & YIQ to RGB
* RGB to XYZ & XYZ to RGB
* XYZ to CIE L*a*b* (CIELAB) & CIELAB to XYZ
* XYZ to CIELUV & CIELUV to XYZ
RGB to HSV & HSV to RGB
The Hue/Saturation/Value model was created by A. R. Smith in 1978. It is based on such intuitive color characteristics as tint, shade and tone (or family, purety and intensity). The coordinate system is cylindrical, and the colors are defined inside a hexcone. The hue value H runs from 0 to 360º. The saturation S is the degree of strength or purity and is from 0 to 1. Purity is how much white is added to the color, so S=1 makes the purest color (no white). Brightness V also ranges from 0 to 1, where 0 is the black.
// r,g,b values are from 0 to 1
// h = [0,360], s = [0,1], v = [0,1]
// if s == 0, then h = -1 (undefined)
void RGBtoHSV( float r, float g, float b, float *h, float *s, float *v )
{
float min, max, delta;
min = MIN( r, g, b );
max = MAX( r, g, b );
*v = max; // v
delta = max - min;
if( max != 0 )
*s = delta / max; // s
else
{
// r = g = b = 0 // s = 0, v is undefined
*s = 0;
*h = -1;
return;
}
if( r == max )
*h = ( g - b ) / delta; // between yellow & magenta
else if( g == max )
*h = 2 + ( b - r ) / delta; // between cyan & yellow
else
*h = 4 + ( r - g ) / delta; // between magenta & cyan
*h *= 60; // degrees
if( *h < 0 )
*h += 360;
}
void HSVtoRGB( float *r, float *g, float *b, float h, float s, float v )
{
int i;
float f, p, q, t;
if( s == 0 )
{
// achromatic (grey)
*r = *g = *b = v;
return;
}
h /= 60; // sector 0 to 5
i = floor( h );
f = h - i; // factorial part of h
p = v * ( 1 - s );
q = v * ( 1 - s * f );
t = v * ( 1 - s * ( 1 - f ) );
switch( i )
{
case 0:
*r = v;
*g = t;
*b = p;
break;
case 1:
*r = q;
*g = v;
*b = p;
break;
case 2:
*r = p;
*g = v;
*b = t;
break;
case 3:
*r = p;
*g = q;
*b = v;
break;
case 4:
*r = t;
*g = p;
*b = v;
break;
default: // case 5:
*r = v;
*g = p;
*b = q;
break;
}
}
When programming in Java, use the RGBtoHSB and HSBtoRGB functions from the java.awt.Color class.
RGB to YIQ & YIQ to RGB
The YIQ system is the color primary system adopted by National Television System Committee (NTSC) for color TV broadcasting. The YIQ color solid is made by a linear transformation of the RGB cube. Its purpose is to exploit certain characteristics of the human eye to maximize the utilization of a fixed bandwidth. The human visual system is more sensitive to changes in luminance than to changes in hue or saturation, and thus a wider bandwidth should be dedicated to luminance than to color information. Y is similar to perceived luminance, I and Q carry color information and some luminance information. The Y signal usually has 4.2 MHz bandwidth in a 525 line system. Originally, the I and Q had different bandwidths (1.5 and 0.6 MHz), but now they commonly have the same bandwidth of 1 MHz.
Here is the RGB ->
[ Y ] [ 0.299 0.587 0.114 ] [ R ]
[ I ] = [ 0.596 -0.275 -0.321 ] [ G ]
[ Q ] [ 0.212 -0.523 0.311 ] [ B ]
Here is the YIQ ->
[ R ] [ 1 0.956 0.621 ] [ Y ]
[ G ] = [ 1 -0.272 -0.647 ] [ I ]
[ B ] [ 1 -1.105 1.702 ] [ Q ]
RGB to XYZ & XYZ to RGB
RGB values in a particular set of primaries can be transformed to and from CIE XYZ via a 3x3 matrix transform. These transforms involve tristimulus values, that is a set of three linear-light components that conform to the CIE color-matching functions. CIE XYZ is a special set of tristimulus values. In XYZ, any color is represented as a set of positive values.
[ R ] [ 3.240479 -1.537150 -0.498535 ] [ X ]
[ G ] = [ -0.969256 1.875992 0.041556 ] * [ Y ]
[ B ] [ 0.055648 -0.204043 1.057311 ] [ Z ].
The range for valid R, G, B values is [0,1]. Note, this matrix has negative coefficients. Some XYZ color may be transformed to RGB values that are negative or greater than one. This means that not all visible colors can be produced using the RGB system.
[ X ] [ 0.412453 0.357580 0.180423 ] [ R ] **
[ Y ] = [ 0.212671 0.715160 0.072169 ] * [ G ]
[ Z ] [ 0.019334 0.119193 0.950227 ] [ B ].
** February 20, 2000 - typo in this line of the matrix was corrected (0.189423 to 0.180423), thanks to Michal Karczmarek, University of Toronto
XYZ to CIE L*a*b* (CIELAB) & CIELAB to XYZ
CIE 1976 L*a*b* is based directly on CIE XYZ and is an attampt to linearize the perceptibility of color differences. The non-linear relations for L*, a*, and b* are intended to mimic the logarithmic response of the eye. Coloring information is referred to the color of the white point of the system, subforbidden n.
L* = 116 * (Y/Yn)1/3 - 16 for Y/Yn > 0.008856
L* = 903.3 * Y/Yn otherwise
a* = 500 * ( f(X/Xn) - f(Y/Yn) )
b* = 200 * ( f(Y/Yn) - f(Z/Zn) )
where f(t) = t1/3 for t > 0.008856
f(t) = 7.787 * t + 16/116 otherwise
Here Xn, Yn and Zn are the tristimulus values of the reference white.
The reverse transformation (for Y/Yn > 0.008856) is
X = Xn * ( P + a* / 500 ) 3
Y = Yn * P 3
Z = Zn * ( P - b* / 200 ) 3
where P = (L* + 16) / 116
XYZ to CIELUV & CIELUV to XYZ
CIE 1976 L*u*u* (CIELUV) is based directly on CIE XYZ and is another attampt to linearize the perceptibility of color differences. The non-linear relations for L*, u*, and v* are given below:
L* = 116 * (Y/Yn)1/3 - 16
u* = 13L* * ( u' - un' )
v* = 13L* * ( v' - vn' )
The quantities un' and vn' refer to the reference white or the light source; for the 2° observer and illuminant C, un' = 0.2009, vn' =
u' = 4X / (X + 15Y + 3Z) = 4x / ( -2x + 12y + 3 )
v' = 9Y / (X + 15Y + 3Z) = 9y / ( -2x + 12y + 3 ).
x = 27u' / ( 18u' - 48v' + 36 )
y = 12v' / ( 18u' - 48v' + 36 ).
u' = u / ( 13L*) + un
v' = v / ( 13L* ) + vn
Y = (( L* + 16 ) / 116 )3
X = - 9Yu' / (( u' - 4 ) v' - u'v' )
Z = ( 9Y - 15v'Y - v'X ) / 3v'
The following routines are written in C (with C++ comments HWB-RGB Transform Pair.
#define RETURN_HSV(h, w, b) {HSV.H = h; HSV.S = s; HSV.V = v; return HSV;}
#define RETURN_RGB(r, g, b) {RGB.R = r; RGB.G = g; RGB.B = b; return RGB;}
#define UNDEFINED -1
// Theoretically, hue 0 (pure red) is identical to hue 6 in these transforms. Pure
// red always maps to 6 in this implementation. Therefore UNDEFINED can be
// defined as 0 in situations where only unsigned numbers are desired.
typedef struct {float R, G, B;} RGBType;
typedef struct {float H, S, V;} HSVType;
HSVType
RGB_to_HSV( RGBType RGB ) {
// RGB are each on [0, 1]. S and V are returned on [0, 1] and H is
// returned on [0, 6]. Exception: H is returned UNDEFINED if S==0.
float R = RGB.R, G = RGB.G, B = RGB.B, v, x, f;
int i;
HSVType HSV;
x = min(R, G, B);
v = max(R, G, B);
if(v == x) RETURN_HSV(UNDEFINED, 0, v);
f = (R == x) ? G - B : ((G == x) ? B - R : R - G);
i = (R == x) ? 3 : ((G == x) ? 5 : 1);
RETURN_HSV(i - f /(v - x), (v - x)/v, v);
}
RGBType
HSV_to_RGB( HSVType HSV ) {
// H is given on [0, 6] or UNDEFINED. S and V are given on [0, 1].
// RGB are each returned on [0, 1].
float h = HSV.H, s = HSV.S, v = HSV.V, m, n, f;
int i;
RGBType RGB;
if(h == UNDEFINED) RETURN_RGB(v, v, v);
i = floor(h);
f = h - i;
if(!(i & 1)) f = 1 - f; // if i is even
m = v * (1 - s);
n = v * (1 - s * f);
switch (i) {
case 6:
case 0: RETURN_RGB(v, n, m);
case 1: RETURN_RGB(n, v, m);
case 2: RETURN_RGB(m, v, n)
case 3: RETURN_RGB(m, n, v);
case 4: RETURN_RGB(n, m, v);
case 5: RETURN_RGB(v, m, n);
}
}
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