今天我用javascript解决了一个类似的任务。 我已经确定了这个getPerceivedLightness(rgb)函数的HEX rgb颜色。 利用Fairchild和Perrotta公式对Helmholtz-Kohlrausch效应进行了亮度校正。

/**
 * Converts RGB color to CIE 1931 XYZ color space.
 * https://www.image-engineering.de/library/technotes/958-how-to-convert-between-srgb-and-ciexyz
 * @param  {string} hex
 * @return {number[]}
 */
export function rgbToXyz(hex) {
    const [r, g, b] = hexToRgb(hex).map(_ => _ / 255).map(sRGBtoLinearRGB)
    const X =  0.4124 * r + 0.3576 * g + 0.1805 * b
    const Y =  0.2126 * r + 0.7152 * g + 0.0722 * b
    const Z =  0.0193 * r + 0.1192 * g + 0.9505 * b
    // For some reason, X, Y and Z are multiplied by 100.
    return [X, Y, Z].map(_ => _ * 100)
}

/**
 * Undoes gamma-correction from an RGB-encoded color.
 * https://en.wikipedia.org/wiki/SRGB#Specification_of_the_transformation
 * https://stackoverflow.com/questions/596216/formula-to-determine-brightness-of-rgb-color
 * @param  {number}
 * @return {number}
 */
function sRGBtoLinearRGB(color) {
    // Send this function a decimal sRGB gamma encoded color value
    // between 0.0 and 1.0, and it returns a linearized value.
    if (color <= 0.04045) {
        return color / 12.92
    } else {
        return Math.pow((color + 0.055) / 1.055, 2.4)
    }
}

/**
 * Converts hex color to RGB.
 * https://stackoverflow.com/questions/5623838/rgb-to-hex-and-hex-to-rgb
 * @param  {string} hex
 * @return {number[]} [rgb]
 */
function hexToRgb(hex) {
    const match = /^#?([a-f\d]{2})([a-f\d]{2})([a-f\d]{2})$/i.exec(hex)
    if (match) {
        match.shift()
        return match.map(_ => parseInt(_, 16))
    }
}

/**
 * Converts CIE 1931 XYZ colors to CIE L*a*b*.
 * The conversion formula comes from <http://www.easyrgb.com/en/math.php>.
 * https://github.com/cangoektas/xyz-to-lab/blob/master/src/index.js
 * @param   {number[]} color The CIE 1931 XYZ color to convert which refers to
 *                           the D65/2° standard illuminant.
 * @returns {number[]}       The color in the CIE L*a*b* color space.
 */
// X, Y, Z of a "D65" light source.
// "D65" is a standard 6500K Daylight light source.
// https://en.wikipedia.org/wiki/Illuminant_D65
const D65 = [95.047, 100, 108.883]
export function xyzToLab([x, y, z]) {
  [x, y, z] = [x, y, z].map((v, i) => {
    v = v / D65[i]
    return v > 0.008856 ? Math.pow(v, 1 / 3) : v * 7.787 + 16 / 116
  })
  const l = 116 * y - 16
  const a = 500 * (x - y)
  const b = 200 * (y - z)
  return [l, a, b]
}

/**
 * Converts Lab color space to Luminance-Chroma-Hue color space.
 * http://www.brucelindbloom.com/index.html?Eqn_Lab_to_LCH.html
 * @param  {number[]}
 * @return {number[]}
 */
export function labToLch([l, a, b]) {
    const c = Math.sqrt(a * a + b * b)
    const h = abToHue(a, b)
    return [l, c, h]
}

/**
 * Converts a and b of Lab color space to Hue of LCH color space.
 * https://stackoverflow.com/questions/53733379/conversion-of-cielab-to-cielchab-not-yielding-correct-result
 * @param  {number} a
 * @param  {number} b
 * @return {number}
 */
function abToHue(a, b) {
    if (a >= 0 && b === 0) {
        return 0
    }
    if (a < 0 && b === 0) {
        return 180
    }
    if (a === 0 && b > 0) {
        return 90
    }
    if (a === 0 && b < 0) {
        return 270
    }
    let xBias
    if (a > 0 && b > 0) {
        xBias = 0
    } else if (a < 0) {
        xBias = 180
    } else if (a > 0 && b < 0) {
        xBias = 360
    }
    return radiansToDegrees(Math.atan(b / a)) + xBias
}

function radiansToDegrees(radians) {
    return radians * (180 / Math.PI)
}

function degreesToRadians(degrees) {
    return degrees * Math.PI / 180
}

/**
 * Saturated colors appear brighter to human eye.
 * That's called Helmholtz-Kohlrausch effect.
 * Fairchild and Pirrotta came up with a formula to
 * calculate a correction for that effect.
 * "Color Quality of Semiconductor and Conventional Light Sources":
 * https://books.google.ru/books?id=ptDJDQAAQBAJ&pg=PA45&lpg=PA45&dq=fairchild+pirrotta+correction&source=bl&ots=7gXR2MGJs7&sig=ACfU3U3uIHo0ZUdZB_Cz9F9NldKzBix0oQ&hl=ru&sa=X&ved=2ahUKEwi47LGivOvmAhUHEpoKHU_ICkIQ6AEwAXoECAkQAQ#v=onepage&q=fairchild%20pirrotta%20correction&f=false
 * @return {number}
 */
function getLightnessUsingFairchildPirrottaCorrection([l, c, h]) {
    const l_ = 2.5 - 0.025 * l
    const g = 0.116 * Math.abs(Math.sin(degreesToRadians((h - 90) / 2))) + 0.085
    return l + l_ * g * c
}

export function getPerceivedLightness(hex) {
    return getLightnessUsingFairchildPirrottaCorrection(labToLch(xyzToLab(rgbToXyz(hex))))
}

The inverse-gamma formula by Jive Dadson needs to have the half-adjust removed when implemented in Javascript, i.e. the return from function gam_sRGB needs to be return int(v*255); not return int(v*255+.5); Half-adjust rounds up, and this can cause a value one too high on a R=G=B i.e. grey colour triad. Greyscale conversion on a R=G=B triad should produce a value equal to R; it's one proof that the formula is valid. See Nine Shades of Greyscale for the formula in action (without the half-adjust).

下面是将sRGB图像转换为灰度的唯一正确算法，如在浏览器等中使用。

在计算内积之前，有必要对颜色空间应用伽玛函数的逆。然后你把函数应用到减少的值上。未能合并gamma函数可能导致高达20%的误差。

对于典型的计算机，颜色空间是sRGB。sRGB的正确数字约为。0.21 0.72 0.07。sRGB的Gamma是一个复合函数，近似取幂1/(2.2)。这是c++的全部内容。

// sRGB luminance(Y) values
const double rY = 0.212655;
const double gY = 0.715158;
const double bY = 0.072187;

// Inverse of sRGB "gamma" function. (approx 2.2)
double inv_gam_sRGB(int ic) {
    double c = ic/255.0;
    if ( c <= 0.04045 )
        return c/12.92;
    else 
        return pow(((c+0.055)/(1.055)),2.4);
}

// sRGB "gamma" function (approx 2.2)
int gam_sRGB(double v) {
    if(v<=0.0031308)
      v *= 12.92;
    else 
      v = 1.055*pow(v,1.0/2.4)-0.055;
    return int(v*255+0.5); // This is correct in C++. Other languages may not
                           // require +0.5
}

// GRAY VALUE ("brightness")
int gray(int r, int g, int b) {
    return gam_sRGB(
            rY*inv_gam_sRGB(r) +
            gY*inv_gam_sRGB(g) +
            bY*inv_gam_sRGB(b)
    );
}

方法可以根据您的需要而有所不同。以下是计算亮度的3种方法:

亮度(某些颜色空间的标准):(0.2126*R + 0.7152*G + 0.0722*B)光源 亮度(感知选项1):(0.299*R + 0.587*G + 0.114*B)光源 亮度(感知选项2，计算较慢):根号(0.241*R^2 + 0.691*G^2 + 0.068*B^2)→根号(0.299*R^2 + 0.587*G^2 + 0.114*B^2)(感谢@MatthewHerbst)来源

[编辑:添加了使用命名css颜色的例子，按每种方法排序。]

我想知道这些rgb系数是如何确定的。我自己做了一个实验，得出了以下结论:

Y = 0.267 R + 0.642 G + 0.091 B

接近，但与长期建立的ITU系数明显不同。我想知道这些系数是否对每个观察者来说都是不同的，因为我们眼睛视网膜上的视锥细胞和视杆细胞的数量都是不同的，尤其是不同类型的视锥细胞之间的比例可能是不同的。

供参考:

这是BT . 709:

Y = 0.2126 R + 0.7152 G + 0.0722 B

这是BT . 601:

Y = 0.299 R + 0.587 G + 0.114 B

我在亮红色、亮绿色和亮蓝色的背景上快速移动一个小灰色条，并调整灰色，直到它尽可能地融合在一起。我还用其他色调重复了这个测试。我在不同的显示器上重复了测试，即使是gamma因子固定为3.0的显示器，但在我看来都是一样的。更重要的是，ITU系数对我的眼睛来说是错误的。

是的，我对颜色的视觉应该是正常的。

与其迷失在这里提到的随机选择的公式中，我建议您使用W3C标准推荐的公式。

下面是WCAG 2.0 SC 1.4.3相对亮度和对比度公式的简单而精确的PHP实现。它生成的值适合于评估符合WCAG要求的比率，就像在这个页面上一样，因此适用于任何web应用程序。这对于移植到其他语言来说是微不足道的。

/**
 * Calculate relative luminance in sRGB colour space for use in WCAG 2.0 compliance
 * @link http://www.w3.org/TR/WCAG20/#relativeluminancedef
 * @param string $col A 3 or 6-digit hex colour string
 * @return float
 * @author Marcus Bointon <marcus@synchromedia.co.uk>
 */
function relativeluminance($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 <= 0.04045) {
            $components[$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 $c2 A 3 or 6-digit hex colour string
 * @return float
 * @author Marcus Bointon <marcus@synchromedia.co.uk>
 */
function contrastratio($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);
}