rgb2gray function converts RGB images to grayscale by eliminating the hue (色调) and saturation (饱和度) information while retaining the luminance (亮度).

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clc, clear, close all

figure("Units", "pixels", "Position", [280,251,1303,541])
tiledlayout(1,2)

% RGB figure
nexttile
RGB = imread('peppers.png');
imshow(RGB)

% Grayscale figure
nexttile
I = rgb2gray(RGB);
imshow(I)

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>> whos
  Name        Size                Bytes  Class    Attributes
  I         384x512              196608  uint8              
  RGB       384x512x3            589824  uint8     

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[X, map] = imread('corn.tif');

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>> whos
  Name        Size              Bytes  Class     Attributes

  X         415x312            129480  uint8               
  map       256x3                6144  double              

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figure("Units", "pixels", "Position", [215,276,761,352])
tiledlayout(1,2)
nexttile
imshow(X)
colorbar

nexttile
imshow(X, map)
colorbar

rgb2gray converts RGB values to grayscale values by forming a weighted sum of the $R$, $G$, and $B$ components: \(0.298936021293775 * R + 0.587043074451121 * G + 0.114020904255103 * B\notag\)

The coefficients used to calculate grayscale values in rgb2gray are identical to those used to calculate luminance (E’y) in Rec.ITU-R BT.601-7² after rounding to 3 decimal places. Rec.ITU-R BT.601-7 calculates E’y using this formula:

\[0.299 * R + 0.587 * G + 0.114 * B\notag\]

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YIQ = rgb2ntsc(RGB)

YIQ = rgb2ntsc(RGB) converts the red, green, and blue values of an RGB image to luminance (Y) and chrominance (I and Q) values of an NTSC image.

…

In the NTSC color space, the luminance is the grayscale signal used to display pictures on monochrome (black and white) televisions. The other components carry the hue and saturation information. The value 0 corresponds to the absence of the component, while the value 1 corresponds to full saturation of the component.

rgb2ntsc defines the NTSC components using

\[\begin{bmatrix} Y\\I\\Q \end{bmatrix}= \begin{bmatrix} 0.299 & 0.587 & 0.114\\ 0.596 & -0.274 & -0.322\\ 0.211 & -0.523 & 0.312\\ \end{bmatrix} \begin{bmatrix} R\\G\\B \end{bmatrix}\notag\]

• Y: Luma, or brightness of the image. Values are in the range [0, 1], where 0 specifies black and 1 specifies white. Colors increase in brightness as Y increases.
• I: In-phase, which is approximately the amount of blue or orange tones in the image. I in the range [-0.5959, 0.5959], where negative numbers indicate blue tones and positive numbers indicate orange tones. As the magnitude of I increases, the saturation of the color increases.
• Q: Quadrature, which is approximately the amount of green or purple tones in the image. Q in the range [-0.5229, 0.5229], where negative numbers indicate green tones and positive numbers indicate purple tones. As the magnitude of Q increases, the saturation of the color increases.

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RGB = imread('board.tif');
YIQ = rgb2ntsc(RGB);

% Three components in YIQ Color Space
figure("Units", "pixels", "Position", [369,141,1010,580])
nexttile
imshow(YIQ(:,:,1));
title('Luminance in YIQ Color Space');
nexttile
imshow(YIQ(:,:,2));
title('In-phase in YIQ Color Space');
nexttile
imshow(YIQ(:,:,3));
title('Quadrature in YIQ Color Space');

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% Constrast differenct conversion function
figure("Units", "pixels", "Position", [369,141,1010,580])
nexttile
imshow(RGB)
title('RGB Color Space')
nexttile
imshow(rgb2gray(RGB))
title('Converted by rgb2gray function')
nexttile
imshow(YIQ(:,:,1));
title('Luminance in YIQ Color Space');

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>> mean(double(rgb2gray(RGB))/255-YIQ(:, :, 1), "all")
ans =
   6.7028e-06

The RGB color space represents images as an m-by-n-by-3 numeric array whose elements specify the intensity values of the red, green, and blue color channels. The range of numeric values depends on the data type of the image.

• For single or double arrays, RGB values range from [0, 1].
• For uint8 arrays, RGB values range from [0, 255].
• For uint16 arrays, RGB values range from [0, 65535].

NTSC 1953 colorimetry

These formulas approximate the conversion between the original 1953 color NTSC specification and YIQ.

From RGB to YIQ:

\[\begin{bmatrix} Y\\I\\Q \end{bmatrix}\approx \begin{bmatrix} 0.299 & 0.587 & 0.114\\ 0.5959 & -0.2746 & -0.3213\\ 0.2115 & -0.5227 & 0.3112\\ \end{bmatrix} \begin{bmatrix} R\\G\\B \end{bmatrix}\notag\]

From YIQ to RGB:

\[\begin{bmatrix} R\\G\\B \end{bmatrix}\approx \begin{bmatrix} 1 & 0.956 & 0.619\\ 1 & -0.272 & -0.647\\ 1 & -1.106 & 1.703\\ \end{bmatrix} \begin{bmatrix} Y\\I\\Q \end{bmatrix}\notag\]

Note that the top row is identical to that of the YUV color space

\[\begin{bmatrix} R\\G\\B \end{bmatrix}= \begin{bmatrix} 1\\1\\1 \end{bmatrix}\Rightarrow \begin{bmatrix} Y\\I\\Q \end{bmatrix}= \begin{bmatrix} 1\\0\\0 \end{bmatrix}\notag\]

The scope of the terms Y′UV, YUV, YCbCr, YPbPr, etc., is sometimes ambiguous and overlapping.⁷

(1) RGB

The RGB color space represents images as an m-by-n-by-3 numeric array whose elements specify the intensity values of the red, green, and blue color channels. The range of numeric values depends on the data type of the image.

• Linear RGB: Linear RGB values are raw data obtained from a camera sensor. The value of R, G, and B are directly proportional to the amount of light that illuminates the sensor. Preprocessing of raw image data, such as white balance, color balance, and chromatic aberration compensation, are performed on linear RGB values.
• sRGB: sRGB values apply a nonlinear function, called gamma correction, to linear RGB values. Images are frequently displayed in the sRGB color space because they appear brighter and colors are easier to distinguish.
• Adobe RGB (1998)： Adobe RGB (1998) RGB values apply gamma correction to linear RGB values using a simple power function.

(2) HSV

The HSV (Hue, Saturation, Value) color space corresponds better to how people experience color than the RGB color space does. For example, this color space is often used by people who are selecting colors, such as paint or ink color, from a color wheel or palette.

• H: Hue, which corresponds to the color’s position on a color wheel. H is in the range [0, 1]. As H increases, colors transition from red to orange, yellow, green, cyan, blue, magenta, and finally back to red. Both 0 and 1 indicate red.
• S: Saturation, which is the amount of hue or departure from neutral. S is in the range [0, 1]. As S increases, colors vary from unsaturated (shades of gray) to fully saturated (no white component).
• V: Value, which is the maximum value among the red, green, and blue components of a specific color. V is in the range [0, 1]. As V increases, the corresponding colors become increasingly brighter.

(3) Deviced-independent Color Spaces⁹

CIE 1976 XYZ and CIE 1976 L*a*b* are device-independent color spaces developed by the International Commission on Illumination, known by the acronym CIE. These color spaces model colors according to the typical sensitivity of the three types of cone cells in the human eye.

• The XYZ color space is the original model developed by the CIE. The Y channel represents the luminance of a color. The Z channel approximately relates to the amount of blue in an image, but the value of Z in the XYZ color space is not identical to the value of B in the RGB color space. The X channel does not have a clear color analogy. However, if you consider the XYZ color space as a 3-D coordinate system, then X values lie along the axis that is orthogonal to the Y (luminance) axis and the Z axis.¹⁰

• The L*a*b* color space provides a more perceptually uniform color space than the XYZ model. Colors in the L*a*b* color space can exist outside the RGB gamut (the valid set of RGB colors). For example, when you convert the L*a*b* value [100, 100, 100] to the RGB color space, the returned value is [1.7682, 0.5746, 0.1940], which is not a valid RGB color. For more information, see Determine If L*a*b* Value Is in RGB Gamut.¹¹

(4) YCbCr¹²

The YCbCr color space is widely used for digital video. In this format, luminance information is stored as a single component (Y) and chrominance information is stored as two color-difference components (Cb and Cr). Cb and Cr represent the difference between a reference value and the blue or red component, respectively.

YUV, another color space widely used for digital video, is very similar to YCbCr but not identical.

(5) YIQ

The National Television Systems Committee (NTSC) defines a color space known as YIQ. This color space is used in televisions in the United States. This color space separates grayscale information from color data, so the same signal can be used for both color and black and white television sets.

… because they present color information in ways that make certain calculations more convenient

… or because they provide a way to identify colors that is more intuitive. For example, the RGB color space defines a color as the percentages of red, green, and blue hues mixed together. Other color models describe colors by their hue (shade of color), saturation (amount of gray or pure color), and luminance (intensity, or overall brightness).

The YIQ system is intended to take advantage of human color-response characteristics. The eye is more sensitive to changes in the orange-blue (I) range than in the purple-green range (Q)—therefore less bandwidth is required for Q than for I.

The YIQ representation is sometimes employed in color image processing transformations. For example, applying a histogram equalization directly to the channels in an RGB image would alter the color balance of the image. Instead, the histogram equalization is applied to the Y channel of the YIQ or YUV representation of the image, which only normalizes the brightness levels of the image.