我正在寻找某种公式或算法来确定给定RGB值的颜色的亮度。我知道这不像把RGB值加在一起那么简单，更高的总和更亮，但我有点不知所措，不知道从哪里开始。
当前回答
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))))
}
其他回答
我已经在接受的答案中对三种算法做了比较。我循环生成颜色，大约每400个颜色使用一次。每种颜色由2x2像素表示，颜色从最深到最浅(从左到右，从上到下)排序。
第一张图片-亮度(相对)
0.2126 * R + 0.7152 * G + 0.0722 * B
第二张图片- http://www.w3.org/TR/AERT#color-contrast
0.299 * R + 0.587 * G + 0.114 * B
第三张图片- HSP颜色模型
sqrt(0.299 * R^2 + 0.587 * G^2 + 0.114 * B^2)
第4张图- WCAG 2.0 SC 1.4.3相对亮度和对比度公式(见@Synchro的答案在这里)
根据一行中的颜色数量，有时可以在第一张和第二张图片上发现图案。我从第3或第4算法的图片上没有发现任何模式。
如果我必须选择，我会选择算法3，因为它更容易实现，比4快33%。
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).
再加上其他人说的话:
所有这些方程在实践中都工作得很好，但如果你需要非常精确，你必须首先将颜色转换为线性颜色空间(应用逆图像-gamma)，对原色进行权重平均，如果你想显示颜色- 把亮度调回监控器伽马。
在深灰色中，忽略伽玛和正确伽玛之间的亮度差异高达20%。
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。
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