Formula to determine brightness of RGB color

Question

I'm looking for some kind of formula or algorithm to determine the brightness of a color given the RGB values. I know it can't be as simple as adding the RGB values together and having higher sums be brighter, but I'm kind of at a loss as to where to start.

Answer 1

The 'V' of HSV is probably what you're looking for. MATLAB has an rgb2hsv function and the previously cited wikipedia article is full of pseudocode. If an RGB2HSV conversion is not feasible, a less accurate model would be the grayscale version of the image.

Answer 2

The HSV colorspace should do the trick, see the wikipedia article depending on the language you're working in you may get a library conversion .

H is hue which is a numerical value for the color (i.e. red, green...)

S is the saturation of the color, i.e. how 'intense' it is

V is the 'brightness' of the color.

Answer 3

I wonder how those rgb coefficients were determined. I did an experiment myself and I ended up with the following:

Y = 0.267 R + 0.642 G + 0.091 B

Close but but obviously different than the long established ITU coefficients. I wonder if those coefficients could be different for each and every observer, because we all may have a different amount of cones and rods on the retina in our eyes, and especially the ratio between the different types of cones may differ.

For reference:

ITU BT.709:

Y = 0.2126 R + 0.7152 G + 0.0722 B

ITU BT.601:

Y = 0.299 R + 0.587 G + 0.114 B

I did the test by quickly moving a small gray bar on a bright red, bright green and bright blue background, and adjusting the gray until it blended in just as much as possible. I also repeated that test with other shades. I repeated the test on different displays, even one with a fixed gamma factor of 3.0, but it all looks the same to me. More over, the ITU coefficients literally are wrong for my eyes.

And yes, I presumably have a normal color vision.

Answer 4

Rather than getting lost amongst the random selection of formulae mentioned here, I suggest you go for the formula recommended by W3C standards.

Here's a straightforward but exact PHP implementation of the WCAG 2.0 SC 1.4.3 relative luminance and contrast ratio formulae. It produces values that are appropriate for evaluating the ratios required for WCAG compliance, as on this page, and as such is suitable and appropriate for any web app. This is trivial to port to other languages.

/**
 * Calculate relative luminance in sRGB colour space for use in WCAG 2.0 compliance
 * @link http://www.w3.org/TR/WCAG20/#relativeluminancedef
 * @param string $col A 3 or 6-digit hex colour string
 * @return float
 * @author Marcus Bointon <[e-mail]>
 */
function relativeluminance($col) {
    //Remove any leading #
    $col = trim($col, '#');
    //Convert 3-digit to 6-digit
    if (strlen($col) == 3) {
        $col = $col[0] . $col[0] . $col[1] . $col[1] . $col[2] . $col[2];
    }
    //Convert hex to 0-1 scale
    $components = array(
        'r' => hexdec(substr($col, 0, 2)) / 255,
        'g' => hexdec(substr($col, 2, 2)) / 255,
        'b' => hexdec(substr($col, 4, 2)) / 255
    );
    //Correct for sRGB
    foreach($components as $c => $v) {
        if ($v <= 0.03928) {
            $components[$c] = $v / 12.92;
        } else {
            $components[$c] = pow((($v + 0.055) / 1.055), 2.4);
        }
    }
    //Calculate relative luminance using ITU-R BT. 709 coefficients
    return ($components['r'] * 0.2126) + ($components['g'] * 0.7152) + ($components['b'] * 0.0722);
}

/**
 * Calculate contrast ratio acording to WCAG 2.0 formula
 * Will return a value between 1 (no contrast) and 21 (max contrast)
 * @link http://www.w3.org/TR/WCAG20/#contrast-ratiodef
 * @param string $c1 A 3 or 6-digit hex colour string
 * @param string $c2 A 3 or 6-digit hex colour string
 * @return float
 * @author Marcus Bointon <[e-mail]>
 */
function contrastratio($c1, $c2) {
    $y1 = relativeluminance($c1);
    $y2 = relativeluminance($c2);
    //Arrange so $y1 is lightest
    if ($y1 < $y2) {
        $y3 = $y1;
        $y1 = $y2;
        $y2 = $y3;
    }
    return ($y1 + 0.05) / ($y2 + 0.05);
}

Answer 5

RGB Luminance value = 0.3 R + 0.59 G + 0.11 B

http://www.scantips.com/lumin.html

If you're looking for how close to white the color is you can use Euclidean Distance from (255, 255, 255)

I think RGB color space is perceptively non-uniform with respect to the L2 euclidian distance. Uniform spaces include CIE LAB and LUV.

Answer 6

I found this code (written in C#) that does an excellent job of calculating the "brightness" of a color. In this scenario, the code is trying to determine whether to put white or black text over the color.