# Color conversions

See cv::cvtColor and cv::ColorConversionCodes Todo document other conversion modes

RGB 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.

RGB CIE XYZ.Rec 709 with D65 white point

$\begin{split}\begin{bmatrix} X \\ Y \\ Z \end{bmatrix} \leftarrow \begin{bmatrix} 0.412453 & 0.357580 & 0.180423 \\ 0.212671 & 0.715160 & 0.072169 \\ 0.019334 & 0.119193 & 0.950227 \end{bmatrix} \cdot \begin{bmatrix} R \\ G \\ B \end{bmatrix}\end{split}$
$\begin{split}\begin{bmatrix} R \\ G \\ B \end{bmatrix} \leftarrow \begin{bmatrix} 3.240479 & -1.53715 & -0.498535 \\ -0.969256 & 1.875991 & 0.041556 \\ 0.055648 & -0.204043 & 1.057311 \end{bmatrix} \cdot \begin{bmatrix} X \\ Y \\ Z \end{bmatrix}\end{split}$

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

RGB 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

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

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

RGB 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

RGB 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

RGB 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

RGB 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

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

Bayer 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:

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.