Color Space Conversion

Convert color information between color spaces

• Library:

• Computer Vision Toolbox / Conversions

• 

Description

The Color Space Conversion block converts color information between color spaces. Use the Conversion parameter to specify the color spaces you are converting between.

• R'G'B' to Y'CbCr

• Y'CbCr to R'G'B'

• R'G'B' to intensity

• R'G'B' to HSV

• HSV to R'G'B'

• sR'G'B' to XYZ

• XYZ to sR'G'B'

• sR'G'B' to L*a*b*

• L*a*b* to sR'G'B'

Ports

Input

Input — Input

M-by-N-by-P color matrix

Input color information, specified as an M-by-N-by-P color matrix of P color planes.

Data Types: single | double | int8 | uint8

R' — R plane

M-by-N matrix

R plane of the RGB color information, specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

G' — G plane

M-by-N matrix

G plane of the RGB color information, specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

B' — B plane

M-by-N matrix

B plane of the RGB color information, specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

Y' — Luma signal component

M-by-N matrix

Luma signal component, specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

Cb — Chrominance component

M-by-N matrix

Chrominance component, specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

Cr — Chrominance component

M-by-N matrix

Chrominance component, specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

I' — Intensity values

M-by-N-by-P color video

Intensity values specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

H — Hue component

M-by-N matrix

Hue component, specified as an M-by-N matrix.

Data Types: single | double

S — Saturation component

M-by-N matrix

Saturation component, specified as an M-by-N matrix.

Data Types: single | double

V — Brightness component

M-by-N matrix

Brightness component, specified as an M-by-N matrix.

Data Types: single | double

X — X component

M-by-N matrix

X component, specified as an M-by-N matrix.

Data Types: single | double

Y — Y component

M-by-N matrix

Y component, specified as an M-by-N matrix.

Data Types: single | double

Z — Z component

M-by-N matrix

Z component, specified as an M-by-N matrix.

Data Types: single | double

L* — Luminance portion

M-by-N matrix

Luminance component, specified as an M-by-N matrix.

Data Types: single | double

a* — a* component

M-by-N matrix

a* component, specified as an M-by-N matrix.

Data Types: single | double

b* — b* component

M-by-N matrix

b* component, specified as an M-by-N matrix.

Data Types: single | double

Output

Input — Input

M-by-N-by-P color matrix

Input color information, specified as an M-by-N-by-P color matrix of P color planes.

• If the input is uint8, then Y'CbCr is uint8, where Y is in the range [16 235], and Cb and Cr are in the range [16 240].

• If the input is a double, then Y' is in the range [16/255 235/255] and Cb and Cr are in the range [16/255 240/255].

Data Types: single | double | int8 | uint8

R' — R plane

M-by-N matrix

R plane of the RGB color information, specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

G' — G plane

M-by-N matrix

G plane of the RGB color information, specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

B' — B plane

M-by-N matrix

B plane of the RGB color information, specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

Y' — Luma signal component

M-by-N matrix

Luma signal component, specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

Cb — Chrominance component

M-by-N matrix

Chrominance component, specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

Cr — Chrominance component

M-by-N matrix

Chrominance component, specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

I' — Intensity values

M-by-N-by-P color video

Intensity values specified as an M-by-N matrix.

Data Types: single | double | int8 | uint8

H — Hue component

M-by-N matrix

Hue component, specified as an M-by-N matrix.

Data Types: single | double

S — Saturation component

M-by-N matrix

Saturation component, specified as an M-by-N matrix.

Data Types: single | double

V — Brightness component

M-by-N matrix

Brightness component, specified as an M-by-N matrix.

Data Types: single | double

X — X component

M-by-N matrix

X component, specified as an M-by-N matrix.

Data Types: single | double

Y — Y component

M-by-N matrix

Y component, specified as an M-by-N matrix.

Data Types: single | double

Z — Z component

M-by-N matrix

Z component, specified as an M-by-N matrix.

Data Types: single | double

L* — Luminance portion

M-by-N matrix

Luminance component, specified as an M-by-N matrix.

Data Types: single | double

a* — a* component

M-by-N matrix

a* component, specified as an M-by-N matrix.

Data Types: single | double

b* — b* component

M-by-N matrix

b* component, specified as an M-by-N matrix.

Data Types: single | double

Parameters

Conversion — Conversion

R'G'B' to Y'CbCr (default) | Y'CbCr to R'G'B' | R'G'B' to intensity | R'G'B' to HSV | HSV to R'G'B' | sR'G'B' to XYZ | XYZ to sR'G'B' | sR'G'B' to L*a*b*

Specify the conversion color spaces as one of the following:

• R'G'B' to Y'CbCr

• Y'CbCr to R'G'B'

• R'G'B' to intensity

• R'G'B' to HSV

• HSV to R'G'B'

• sR'G'B' to XYZ

• XYZ to sR'G'B'

• sR'G'B' to L*a*b*

• L*a*b* to sR'G'B'

Use conversion specified by — Conversion standard

Rec. 601 (SDTV) (default) | Rec. 709 (HDTV)

Specify the standard to convert your values between the R'G'B' and Y'CbCr color spaces as either Rec. 601 (SDTV) or Rec. 709 (HDTV).

Dependencies

This parameter is visible when you set the Conversion to R'G'B' to Y'CbCr or Y'CbCr to R'G'B'.

Scanning standard — Scanning standard

1125/60/2:1 (default) | 1250/50/2:1

Specify the scanning standard to convert between the R'G'B' and Y'CbCr color spaces as either 1125/60/2:1 or 1250/50/2:1.

Dependencies

This parameter is visible when you set the Use conversion specified by parameter to Rec. 709 (HDTV).

White point — White point

D50 (default) | D55 | D65

Specify the reference white point.

Dependencies

This parameter is visible when you set the Conversion parameter to sR'G'B' to L*a*b* or L*a*b* to sR'G'B'.

Image signal — Image signal input

One multidimensional signal (default) | Separate color signals

Specify how to input and output a color signal. If you select One multidimensional signal, the block accepts an M-by-N-by-P color signal, where P is the number of color planes, at one port. If you select Separate color signals, additional ports appear on the block. Each port accepts one M-by-N plane of color signal stream.

Note

The prime notation indicates that the signals are gamma corrected.

Block Characteristics

Data Types	Boolean | double | integer | single
Multidimensional Signals	yes
Variable-Size Signals	yes

Algorithms

Conversion Between R'G'B' and Y'CbCr Color Spaces

The following equations define R'G'B' to Y'CbCr conversion and Y'CbCr to R'G'B' conversion:

$$\left[\begin{array}{c}{Y}^{\prime }\\ Cb\\ Cr\end{array}\right]=\left[\begin{array}{c}16\\ 128\\ 128\end{array}\right]+{\rm A}\times \left[\begin{array}{c}{R}^{\prime }\\ G^{\prime }\\ B^{\prime }\end{array}\right]$$

$$\left[\begin{array}{c}{R}^{\prime }\\ G^{\prime }\\ B^{\prime }\end{array}\right]={\rm B}\times \left(\left[\begin{array}{c}{Y}^{\prime }\\ Cb\\ Cr\end{array}\right]-\left[\begin{array}{c}16\\ 128\\ 128\end{array}\right]\right)$$

The values in matrices A and B are based on your choices for the Use conversion specified by and Scanning standard parameters.

Matrix	Use conversion specified by = Rec. 601 (SDTV)	Use conversion specified by = Rec. 709 (HDTV)
		Scanning standard = 1125/60/2:1	Scanning standard = 1250/50/2:1
A	$$\left[\begin{array}{ccc}0.25678824& 0.50412941& 0.09790588\\ -0.1482229& -0.29099279& 0.43921569\\ 0.43921569& -0.36778831& -0.07142737\end{array}\right]$$	$$\left[\begin{array}{l}\text{ 0}\text{.18258588 0}\text{.61423059 0}\text{.06200706}\\ \text{ -0}\text{.10064373 -0}\text{.33857195 0}\text{.43921569}\\ \text{ 0}\text{.43921569 -0}\text{.39894216 -0}\text{.04027352}\end{array}\right]$$	$$\left[\begin{array}{ccc}0.25678824& 0.50412941& 0.09790588\\ -0.1482229& -0.29099279& 0.43921569\\ 0.43921569& -0.36778831& -0.07142737\end{array}\right]$$
B	$$\left[\begin{array}{ccc}1.1643836& 0& 1.5960268\\ 1.1643836& -0.39176229& -0.81296765\\ 1.1643836& 2.0172321& 0\end{array}\right]$$	$$\left[\begin{array}{ccc}\text{1}\text{.16438356}& \text{0}& \text{1}\text{.79274107}\\ \text{1}\text{.16438356}& \text{-0}\text{.21324861}& \text{-0}\text{.53290933}\\ \text{1}\text{.16438356}& \text{2}\text{.11240179}& \text{0}\end{array}\right]$$	$$\left[\begin{array}{ccc}1.1643836& 0& 1.5960268\\ 1.1643836& -0.39176229& -0.81296765\\ 1.1643836& 2.0172321& 0\end{array}\right]$$

Conversion from R'G'B' to Intensity

The following equation defines conversion from the R'G'B' color space to intensity:

$$\text{intensity}=\left[\begin{array}{ccc}0.299& 0.587& 0.114\end{array}\right]\left[\begin{array}{c}{R}^{\prime }\\ G^{\prime }\\ B^{\prime }\end{array}\right]$$

Conversion Between R'G'B' and HSV Color Spaces

The R'G'B' to HSV conversion is defined by the following equations. In these equations, MAX and MIN represent the maximum and minimum values of each R'G'B' triplet, respectively. H, S, and V vary from 0 to 1, where 1 represents the greatest saturation and value.

$$\begin{array}{l}H=\{\begin{array}{c}\left(\frac{G^{\prime }-B^{\prime }}{MAX-MIN}\right)/6,\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}& \text{if}\end{array}& R^{\prime }=MAX\end{array}& \end{array}\\ \left(2+\frac{B^{\prime }-R^{\prime }}{MAX-MIN}\right)/6,\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}& \text{if}\end{array}& G^{\prime }=MAX\end{array}& \end{array}\\ \left(4+\frac{R^{\prime }-G^{\prime }}{MAX-MIN}\right)/6,\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}& \text{if}\end{array}& B^{\prime }=MAX\end{array}& \end{array}\end{array}\\ S=\frac{MAX-MIN}{MAX}\\ V=MAX\end{array}$$

The HSV to R'G'B' conversion is defined by the following equations:

$$\begin{array}{l}{H}_i=\lfloor 6H\rfloor \\ f=6H-H_i\\ p=1-S\\ q=1-fS\\ t=1-(1-f)S\\ \begin{array}{cc}\text{if}& H_i=0,\begin{array}{cccc}& R_{tmp}=1,& G_{tmp}=t,& B_{tmp}=p\end{array}\end{array}\\ \begin{array}{cc}\text{if}& H_i=1,\begin{array}{cccc}& R_{tmp}=q,& G_{tmp}=1,& B_{tmp}=p\end{array}\end{array}\\ \begin{array}{cc}\text{if}& H_i=2,\begin{array}{cccc}& R_{tmp}=p,& G_{tmp}=1,& B_{tmp}=t\end{array}\end{array}\\ \begin{array}{cc}\text{if}& H_i=3,\begin{array}{cccc}& R_{tmp}=p,& G_{tmp}=q,& B_{tmp}=1\end{array}\end{array}\\ \begin{array}{cc}\text{if}& H_i=4,\begin{array}{cccc}& R_{tmp}=t,& G_{tmp}=p,& B_{tmp}=1\end{array}\end{array}\\ \begin{array}{cc}\text{if}& H_i=5,\begin{array}{cccc}& R_{tmp}=1,& G_{tmp}=p,& B_{tmp}=q\end{array}\end{array}\\ u=V/\max (R_{tmp},G_{tmp},B_{tmp})\\ R^{\prime }=u{R}_{tmp}\\ G^{\prime }=u{G}_{tmp}\\ B^{\prime }=u{B}_{tmp}\end{array}$$

Conversion Between sR'G'B' and XYZ Color Spaces

The sR'G'B' to XYZ conversion is a two-step process. First, the block converts the gamma-corrected sR'G'B' values to linear sRGB values using the following equations:

$$\begin{array}{l}\text{If}\begin{array}{cc}& {R^{\prime }}_{sRGB},{G^{\prime }}_{sRGB},{B^{\prime }}_{sRGB}\le 0.03928\end{array}\\ R_{sRGB}={R^{\prime }}_{sRGB}/12.92\\ G_{sRGB}={G^{\prime }}_{sRGB}/12.92\\ B_{sRGB}={B^{\prime }}_{sRGB}/12.92\\ \text{otherwise,}\begin{array}{cc}& \begin{array}{cc}\text{if}& {R^{\prime }}_{sRGB},{G^{\prime }}_{sRGB},{B^{\prime }}_{sRGB}>0.03928\end{array}\end{array}\\ R_{sRGB}={\left[\raisebox{1ex}{$({R^{\prime }}_{sRGB}+0.055)$}\!\left/ \!\raisebox{-1ex}{$1.055$}\right.\right]}^{2.4}\\ G_{sRGB}={\left[\raisebox{1ex}{$({G^{\prime }}_{sRGB}+0.055)$}\!\left/ \!\raisebox{-1ex}{$1.055$}\right.\right]}^{2.4}\\ B_{sRGB}={\left[\raisebox{1ex}{$({B^{\prime }}_{sRGB}+0.055)$}\!\left/ \!\raisebox{-1ex}{$1.055$}\right.\right]}^{2.4}\end{array}$$

Then the block converts the sRGB values to XYZ values using the following equation:

$$\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]=\left[\begin{array}{ccc}0.41239079926596& 0.35758433938388& 0.18048078840183\\ 0.21263900587151& 0.71516867876776& 0.07219231536073\\ 0.01933081871559& 0.11919477979463& 0.95053215224966\end{array}\right]\times \left[\begin{array}{c}{R}_{sRGB}\\ G_{sRGB}\\ B_{sRGB}\end{array}\right]$$

The XYZ to sR'G'B' conversion is also a two-step process. First, the block converts the XYZ values to linear sRGB values using the following equation:

$$\left[\begin{array}{c}{R}_{sRGB}\\ G_{sRGB}\\ B_{sRGB}\end{array}\right]={\left[\begin{array}{ccc}0.41239079926596& 0.35758433938388& 0.18048078840183\\ 0.21263900587151& 0.71516867876776& 0.07219231536073\\ 0.01933081871559& 0.11919477979463& 0.95053215224966\end{array}\right]}^{-1}\times \left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]$$

Then the block applies gamma correction to obtain the sR'G'B' values. This process is described by the following equations:

$$\begin{array}{l}\text{If}\begin{array}{cc}& R_{sRGB},G_{sRGB},B_{sRGB}\le 0.00304\end{array}\\ {R^{\prime }}_{sRGB}=12.92R_{sRGB}\\ {G^{\prime }}_{sRGB}=12.92G_{sRGB}\\ {B^{\prime }}_{sRGB}=12.92B_{sRGB}\\ \text{otherwise,}\begin{array}{cc}& \begin{array}{cc}\text{if}& R_{sRGB},G_{sRGB},B_{sRGB}>0.00304\end{array}\end{array}\\ {R^{\prime }}_{sRGB}=1.055R_{sRGB}{}^{(1.0/2.4)}-0.055\\ {G^{\prime }}_{sRGB}=1.055G_{sRGB}{}^{(1.0/2.4)}-0.055\\ {B^{\prime }}_{sRGB}=1.055B_{sRGB}{}^{(1.0/2.4)}-0.055\end{array}$$

Note

Computer Vision Toolbox™ software uses a D65 white point, which is specified in Recommendation ITU-R BT.709, for this conversion. In contrast, the Image Processing Toolbox™ conversion is based on ICC profiles, and it uses a D65 to D50 Bradford adaptation transformation to the D50 white point. If you are using these two products and comparing results, you must account for this difference.

Conversion Between sR'G'B' and L*a*b* Color Spaces

The Color Space Conversion block converts sR'G'B' values to L*a*b* values in two steps. First it converts sR'G'B' to XYZ values using the equations described in Conversion Between sR'G'B' and XYZ Color Spaces. Then it uses the following equations to transform the XYZ values to L*a*b* values. Here, $$X_n$$, $$Y_n$$, and $$Z_n$$ are the tristimulus values of the reference white point you specify using the White point parameter:

$$\begin{array}{l}L*=116{(}^Y-16,\begin{array}{cc}for& Y/Y_n\end{array}>0.008856\\ L*=903.3Y/Y_n,\begin{array}{cc}& \text{otherwise}\end{array}\\ \\ a*=500(f(X/X_n)-f(Y/Y_n))\\ b*=200(f(Y/Y_n)-f(Z/Z_n)),\\ \begin{array}{cc}\text{where}& f(t)=t^{1/3}\end{array},\begin{array}{cc}for& t>0.008856\end{array}\\ f(t)=7.787t+16/166,\begin{array}{cc}& \text{otherwise}\end{array}\end{array}$$

The block converts L*a*b* values to sR'G'B' values in two steps as well. The block transforms the L*a*b* values to XYZ values using these equations:

$$\begin{array}{l}\begin{array}{cc}\text{For}& Y/Y_n\end{array}>0.008856\\ \\ X=X_n(P+a*/500{)}^3\\ Y=Y_n{P}^3\\ Z=Z_n(P-b*/200{)}^3,\\ \\ \begin{array}{cc}\text{where}& P=(L*+16)/116\end{array}\end{array}$$

References

[1] Poynton, Charles A. A Technical Introduction to Digital Video. New York: John Wiley & Sons, 1996.

[2] Recommendation ITU-R BT.601-5, Studio Encoding Parameters of Digital Television for Standard 4:3 and Wide Screen 16:9 Aspect Ratios.

[3] Recommendation ITU-R BT.709-5. Parameter values for the HDTV standards for production and international programme exchange.

[4] Stokes, Michael, Matthew Anderson, Srinivasan Chandrasekar, and Ricardo Motta, “A Standard Default Color Space for the Internet - sRGB.” November 5, 1996.

[5] Berns, Roy S. Principles of Color Technology, 3rd ed. New York: John Wiley & Sons, 2000.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.