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RGB Color Space

RED

GREEN

WHITE

BLACK

BLUE

MAGENTA

CYAN

YELLOW

Chapter 3

Color Spaces

RGB Color Space

The red, green, and blue (RGB) color space is

widely used throughout computer graphics.

Red, green, and blue are three primary addi-

tive colors (individual components are added

together to form a desired color) and are rep-

resented by a three-dimensional, Cartesian

coordinate system (Figure 3.1). The indicated

diagonal of the cube, with equal amounts of

each primary component, represents various

gray levels. Table 3.1 contains the RGB values

for 100% amplitude, 100% saturated color bars,

a common video test signal.

A color space is a mathematical representation

of a set of colors. The three most popular color

models are RGB (used in computer graphics);

YIQ, YUV, or YCbCr (used in video systems);

and CMYK (used in color printing). However,

none of these color spaces are directly related

to the intuitive notions of hue, saturation, and

brightness. This resulted in the temporary pur-

suit of other models, such as HSI and HSV, to

simplify programming, processing, and end-

user manipulation.

All of the color spaces can be derived from

the RGB information supplied by devices such

as cameras and scanners.

Figure 3.1. The RGB Color Cube.

Chapter 3: Color Spaces

The RGB color space is the most prevalent

choice for computer graphics because color

displays use red, green, and blue to create the

desired color. Therefore, the choice of the

RGB color space simplifies the architecture

and design of the system. Also, a system that is

designed using the RGB color space can take

advantage of a large number of existing soft-

ware routines, since this color space has been

around for a number of years.

However, RGB is not very efficient when

dealing with “real-world” images. All three

RGB components need to be of equal band-

width to generate any color within the RGB

color cube. The result of this is a frame buffer

that has the same pixel depth and display reso-

lution for each RGB component. Also, process-

ing an image in the RGB color space is usually

not the most efficient method. For example, to

modify the intensity or color of a given pixel,

the three RGB values must be read from the

frame buffer, the intensity or color calculated,

the desired modifications performed, and the

new RGB values calculated and written back to

the frame buffer. If the system had access to an

image stored directly in the intensity and color

format, some processing steps would be faster.

For these and other reasons, many video

standards use luma and two color difference

signals. The most common are the YUV, YIQ,

and YCbCr color spaces. Although all are

related, there are some differences.

YUV Color Space

The YUV color space is used by the PAL

(Phase Alternation Line), NTSC (National

Television System Committee), and SECAM

(Sequentiel Couleur Avec Mémoire or Sequen-

tial Color with Memory) composite color video

standards. The black-and-white system used

only luma (Y) information; color information

(U and V) was added in such a way that a

black-and-white receiver would still display a

normal black-and-white picture. Color receiv-

ers decoded the additional color information to

display a color picture.

The basic equations to convert between

gamma-corrected RGB (notated as R´G´B´ and

discussed later in this chapter) and YUV are:

Y = 0.299R´ + 0.587G´ + 0.114B´

U= – 0.147R´ – 0.289G´ + 0.436B´

= 0.492 (B´ – Y)

V = 0.615R´ – 0.515G´ – 0.100B´

= 0.877(R´ – Y)

Table 3.1. 100% RGB Color Bars.

Nominal

Range

White

Yellow

Cyan

Green

Magenta

Red

Blue

Black

R 0 to 255 255 255 0 0 255 255 0 0

G 0 to 255 255 255 255 255 0 0 0 0

B 0 to 255 255 0 255 0 255 0 255 0

YIQ Color Space

R´ = Y + 1.140V

G´ = Y – 0.395U – 0.581V

B´ = Y + 2.032U

For digital R´G´B´ values with a range of 0–

255, Y has a range of 0–255, U a range of 0 to

112, and V a range of 0 to

157. These equa-

tions are usually scaled to simplify the imple-

mentation in an actual NTSC or PAL digital

encoder or decoder.

Note that for digital data, 8-bit YUV and

R´G´B´ data should be saturated at the 0 and

255 levels to avoid underflow and overflow

wrap-around problems.

If the full range of (B´ – Y) and (R´ – Y) had

been used, the composite NTSC and PAL lev-

els would have exceeded what the (then cur-

rent) black-and-white television transmitters

and receivers were capable of supporting.

Experimentation determined that modulated

subcarrier excursions of 20% of the luma (Y)

signal excursion could be permitted above

white and below black. The scaling factors

were then selected so that the maximum level

of 75% amplitude, 100% saturation yellow and

cyan color bars would be at the white level

(100 IRE).

YIQ Color Space

The YIQ color space, further discussed in

Chapter 8, is derived from the YUV color space

and is optionally used by the NTSC composite

color video standard. (The “I” stands for “in-

phase” and the “Q” for “quadrature,” which is

the modulation method used to transmit the

color information.) The basic equations to con-

vert between R´G´B´ and YIQ are:

Y = 0.299R´ + 0.587G´ + 0.114B´

I = 0.596R´ – 0.275G´ – 0.321B´

= Vcos 33

– Usin 33

= 0.736(R´ – Y) – 0.268(B´ – Y)

Q= 0.212R´ – 0.523G´ + 0.311B´

= Vsin 33

+ Ucos 33

= 0.478(R´ – Y) + 0.413(B´ – Y)

or, using matrix notation:

R´ = Y + 0.956I + 0.621Q

G´ = Y – 0.272I – 0.647Q

B´ = Y – 1.107I + 1.704Q

For digital R´G´B´ values with a range of 0–

255, Y has a range of 0–255, I has a range of 0

152, and Q has a range of 0 to

134. I and Q

are obtained by rotating the U and V axes 33

These equations are usually scaled to simplify

the implementation in an actual NTSC digital

encoder or decoder.

Note that for digital data, 8-bit YIQ and

R´G´B´ data should be saturated at the 0 and

255 levels to avoid underflow and overflow

wrap-around problems.

YCbCr Color Space

The YCbCr color space was developed as part

of ITU-R BT.601 during the development of a

world-wide digital component video standard

(discussed in Chapter 4). YCbCr is a scaled

and offset version of the YUV color space. Y is

()

cos 33

()

sin

()

sin–33

()

cos

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