convert RGB to grayscale in C

Question

I used many formulas to convert from RGB to grayscale, but didn't get good results compared to GIMP.

I already tested the following formulas:

gray = (int)(0.299 * r + 0.587 * g + 0.144 * b);

gray = (int)(0.299 * r + 0.587 * g + 0.114 * b);

gray = (int)(0.2126 * r + 0.7152 * g + 0.0722 * b);

gray = (int) (0.35*r + 0.50*g + 0.15*b);

gray = ((r * 61) + (g * 174) + (b * 21)) / 256;

gray = (int)((4897 * r + 9617 * g + 1868 * b) >> 14);

gray = r; if(g > gray) gray = g; if(b > gray) gray = b;

Answer 1

In order to correctly convert RGB to grayscale, you should transform the gamma corrected R,G and B values into the linear color space, apply the conversion in the linear space, and then apply a gamma correction to the result.

The sRGB colorspace has a transform that only approximates a gamma curve. See the Wikipedia article for the particulars. Wikipedia also has a specific section on the subject of sRGB to grayscale.

Basically, to convert a sRGB component to linear format:

double sRGB_to_linear(double x) {
    if (x < 0.04045) return x/12.92;
    return pow((x+0.055)/1.055, 2.4);
}

Then, to convert sRGB to linear grayscale:

double R_linear = sRGB_to_linear(R/255.0);
double G_linear = sRGB_to_linear(G/255.0);
double B_linear = sRGB_to_linear(B/255.0);
double gray_linear = 0.2126 * R_linear + 0.7152 * G_linear + 0.0722 * B_linear;

Then, apply the sRGB gamma correction again:

double linear_to_sRGB(double y) {
    if (y <= 0.0031308) return 12.92 * y;
    return 1.055 * pow(y, 1/2.4) - 0.055;
}

I.e.

double gray_color = round(linear_to_sRGB(gray_linear) * 255);

Answer 2

There is a GIMP tutorial that describes several different ways that The GIMP can convert a color image to grayscale. One method is a weighted desaturation like you've tried already, and the article gives some weights that can be used to approximate The GIMP's conversion.

The GIMP's gegl library, which is the basis for all of its image operations, has a rather elaborate mechanism for converting color to greyscale, which takes into account the color of neighboring pixels and uses an iterative approach that seems to emulate the process of developing black and white photographs.

Answer 3

The gimp help for the desaturate tool states three available formulas corresponding to the options named "Lighness", "Luminosity" and "Average". Those would be:

Lightness: 0.5 * (max(R,G,B) + min(R,G,B))

Luminosity: (0.21 * R) + (0.72 * G) + (0.07 * B)

Average: (R + G + B)/3