OpenCV: Color conversions

| OpenCV 3.4.2 Open Source Computer Vision

Color conversions

See cv::cvtColor and cv::ColorConversionCodes

Todo:
  document other conversion modes

## RGB \(\leftrightarrow\) GRAY

Transformations within RGB space like adding/removing the alpha channel, reversing the channel order, conversion to/from 16-bit RGB color (R5:G6:B5 or R5:G5:B5), as well as conversion to/from grayscale using:

\[\text{RGB[A] to Gray:} \quad Y \leftarrow 0.299 \cdot R + 0.587 \cdot G + 0.114 \cdot B\]

and

\[\text{Gray to RGB[A]:} \quad R \leftarrow Y, G \leftarrow Y, B \leftarrow Y, A \leftarrow \max (ChannelRange)\]

The conversion from a RGB image to gray is done with:

cvtColor(src, bwsrc, cv::COLOR_RGB2GRAY);

More advanced channel reordering can also be done with cv::mixChannels.

See also
  cv::COLOR_BGR2GRAY, cv::COLOR_RGB2GRAY, cv::COLOR_GRAY2BGR, cv::COLOR_GRAY2RGB

## RGB \(\leftrightarrow\) CIE XYZ.Rec 709 with D65 white point

\[\begin{bmatrix} X \\ Y \\ Z \end{bmatrix} \leftarrow \begin{bmatrix} 0.412453 & 0.357580 & 0.180423 \\ 0.212671 & 0.715160 & 0.072169 \\ 0.019334 & 0.119193 & 0.950227 \end{bmatrix} \cdot \begin{bmatrix} R \\ G \\ B \end{bmatrix}\]

\[\begin{bmatrix} R \\ G \\ B \end{bmatrix} \leftarrow \begin{bmatrix} 3.240479 & -1.53715 & -0.498535 \\ -0.969256 & 1.875991 & 0.041556 \\ 0.055648 & -0.204043 & 1.057311 \end{bmatrix} \cdot \begin{bmatrix} X \\ Y \\ Z \end{bmatrix}\]

\(X\), \(Y\) and \(Z\) cover the whole value range (in case of floating-point images, \(Z\) may exceed 1).

See also
  cv::COLOR_BGR2XYZ, cv::COLOR_RGB2XYZ, cv::COLOR_XYZ2BGR, cv::COLOR_XYZ2RGB

## RGB \(\leftrightarrow\) YCrCb JPEG (or YCC)

\[Y \leftarrow 0.299 \cdot R + 0.587 \cdot G + 0.114 \cdot B\]

\[Cr \leftarrow (R-Y) \cdot 0.713 + delta\]

\[Cb \leftarrow (B-Y) \cdot 0.564 + delta\]

\[R \leftarrow Y + 1.403 \cdot (Cr - delta)\]

\[G \leftarrow Y - 0.714 \cdot (Cr - delta) - 0.344 \cdot (Cb - delta)\]

\[B \leftarrow Y + 1.773 \cdot (Cb - delta)\]

where

\[delta = \left \{ \begin{array}{l l} 128 & \mbox{for 8-bit images} \\ 32768 & \mbox{for 16-bit images} \\ 0.5 & \mbox{for floating-point images} \end{array} \right .\]

Y, Cr, and Cb cover the whole value range.

See also
  cv::COLOR_BGR2YCrCb, cv::COLOR_RGB2YCrCb, cv::COLOR_YCrCb2BGR, cv::COLOR_YCrCb2RGB

## RGB \(\leftrightarrow\) HSV

In case of 8-bit and 16-bit images, R, G, and B are converted to the floating-point format and scaled to fit the 0 to 1 range.

\[V \leftarrow max(R,G,B)\]

\[S \leftarrow \fork{\frac{V-min(R,G,B)}{V}}{if \(V \neq 0\)}{0}{otherwise}\]

\[H \leftarrow \forkthree{{60(G - B)}/{(V-min(R,G,B))}}{if \(V=R\)}{{120+60(B - R)}/{(V-min(R,G,B))}}{if \(V=G\)}{{240+60(R - G)}/{(V-min(R,G,B))}}{if \(V=B\)}\]

If \(H<0\) then \(H \leftarrow H+360\) . On output \(0 \leq V \leq 1\), \(0 \leq S \leq 1\), \(0 \leq H \leq 360\) .

The values are then converted to the destination data type:

- 8-bit images: \(V \leftarrow 255 V, S \leftarrow 255 S, H \leftarrow H/2 \text{(to fit to 0 to 255)}\)
- 16-bit images: (currently not supported) \(V <- 65535 V, S <- 65535 S, H <- H\)
- 32-bit images: H, S, and V are left as is

See also
  cv::COLOR_BGR2HSV, cv::COLOR_RGB2HSV, cv::COLOR_HSV2BGR, cv::COLOR_HSV2RGB

## RGB \(\leftrightarrow\) HLS

In case of 8-bit and 16-bit images, R, G, and B are converted to the floating-point format and scaled to fit the 0 to 1 range.

\[V_{max} \leftarrow {max}(R,G,B)\]

\[V_{min} \leftarrow {min}(R,G,B)\]

\[L \leftarrow \frac{V_{max} + V_{min}}{2}\]

\[S \leftarrow \fork { \frac{V_{max} - V_{min}}{V_{max} + V_{min}} }{if \(L < 0.5\) } { \frac{V_{max} - V_{min}}{2 - (V_{max} + V_{min})} }{if \(L \ge 0.5\) }\]

\[H \leftarrow \forkthree {{60(G - B)}/{(V_{max}-V_{min})}}{if \(V_{max}=R\) } {{120+60(B - R)}/{(V_{max}-V_{min})}}{if \(V_{max}=G\) } {{240+60(R - G)}/{(V_{max}-V_{min})}}{if \(V_{max}=B\) }\]

If \(H<0\) then \(H \leftarrow H+360\) . On output \(0 \leq L \leq 1\), \(0 \leq S \leq 1\), \(0 \leq H \leq 360\) .

The values are then converted to the destination data type:

- 8-bit images: \(V \leftarrow 255 \cdot V, S \leftarrow 255 \cdot S, H \leftarrow H/2 \; \text{(to fit to 0 to 255)}\)
- 16-bit images: (currently not supported) \(V <- 65535 \cdot V, S <- 65535 \cdot S, H <- H\)
- 32-bit images: H, S, V are left as is

See also
  cv::COLOR_BGR2HLS, cv::COLOR_RGB2HLS, cv::COLOR_HLS2BGR, cv::COLOR_HLS2RGB

## RGB \(\leftrightarrow\) CIE L*a*b*

In case of 8-bit and 16-bit images, R, G, and B are converted to the floating-point format and scaled to fit the 0 to 1 range.

\[\vecthree{X}{Y}{Z} \leftarrow \vecthreethree{0.412453}{0.357580}{0.180423}{0.212671}{0.715160}{0.072169}{0.019334}{0.119193}{0.950227} \cdot \vecthree{R}{G}{B}\]

\[X \leftarrow X/X_n, \text{where} X_n = 0.950456\]

\[Z \leftarrow Z/Z_n, \text{where} Z_n = 1.088754\]

\[L \leftarrow \fork{116*Y^{1/3}-16}{for \(Y>0.008856\)}{903.3*Y}{for \(Y \le 0.008856\)}\]

\[a \leftarrow 500 (f(X)-f(Y)) + delta\]

\[b \leftarrow 200 (f(Y)-f(Z)) + delta\]

where

\[f(t)= \fork{t^{1/3}}{for \(t>0.008856\)}{7.787 t+16/116}{for \(t\leq 0.008856\)}\]

and

\[delta = \fork{128}{for 8-bit images}{0}{for floating-point images}\]

This outputs \(0 \leq L \leq 100\), \(-127 \leq a \leq 127\), \(-127 \leq b \leq 127\) . The values are then converted to the destination data type:

- 8-bit images: \(L \leftarrow L*255/100, \; a \leftarrow a + 128, \; b \leftarrow b + 128\)
- 16-bit images: (currently not supported)
- 32-bit images: L, a, and b are left as is

See also
  cv::COLOR_BGR2Lab, cv::COLOR_RGB2Lab, cv::COLOR_Lab2BGR, cv::COLOR_Lab2RGB

## RGB \(\leftrightarrow\) CIE L*u*v*

In case of 8-bit and 16-bit images, R, G, and B are converted to the floating-point format and scaled to fit 0 to 1 range.

\[\vecthree{X}{Y}{Z} \leftarrow \vecthreethree{0.412453}{0.357580}{0.180423}{0.212671}{0.715160}{0.072169}{0.019334}{0.119193}{0.950227} \cdot \vecthree{R}{G}{B}\]

\[L \leftarrow \fork{116*Y^{1/3} - 16}{for \(Y>0.008856\)}{903.3 Y}{for \(Y\leq 0.008856\)}\]

\[u' \leftarrow 4*X/(X + 15*Y + 3 Z)\]

\[v' \leftarrow 9*Y/(X + 15*Y + 3 Z)\]

\[u \leftarrow 13*L*(u' - u_n) \quad \text{where} \quad u_n=0.19793943\]

\[v \leftarrow 13*L*(v' - v_n) \quad \text{where} \quad v_n=0.46831096\]

This outputs \(0 \leq L \leq 100\), \(-134 \leq u \leq 220\), \(-140 \leq v \leq 122\) .

The values are then converted to the destination data type:

- 8-bit images: \(L \leftarrow 255/100 L, \; u \leftarrow 255/354 (u + 134), \; v \leftarrow 255/262 (v + 140)\)
- 16-bit images: (currently not supported)
- 32-bit images: L, u, and v are left as is

Note that when converting integer Luv images to RGB the intermediate X, Y and Z values are truncated to \( [0, 2] \) range to fit white point limitations. It may lead to incorrect representation of colors with odd XYZ values.

The above formulae for converting RGB to/from various color spaces have been taken from multiple sources on the web, primarily from the Charles Poynton site http://www.poynton.com/ColorFAQ.html

See also
  cv::COLOR_BGR2Luv, cv::COLOR_RGB2Luv, cv::COLOR_Luv2BGR, cv::COLOR_Luv2RGB

## Bayer \(\rightarrow\) RGB

The Bayer pattern is widely used in CCD and CMOS cameras. It enables you to get color pictures from a single plane where R,G, and B pixels (sensors of a particular component) are interleaved as follows:

Bayer pattern

The output RGB components of a pixel are interpolated from 1, 2, or 4 neighbors of the pixel having the same color. There are several modifications of the above pattern that can be achieved by shifting the pattern one pixel left and/or one pixel up. The two letters \(C_1\) and \(C_2\) in the conversion constants CV_Bayer \(C_1 C_2\) 2BGR and CV_Bayer \(C_1 C_2\) 2RGB indicate the particular pattern type. These are components from the second row, second and third columns, respectively. For example, the above pattern has a very popular "BG" type.

See also
  cv::COLOR_BayerBG2BGR, cv::COLOR_BayerGB2BGR, cv::COLOR_BayerRG2BGR, cv::COLOR_BayerGR2BGR, cv::COLOR_BayerBG2RGB, cv::COLOR_BayerGB2RGB, cv::COLOR_BayerRG2RGB, cv::COLOR_BayerGR2RGB