YIQ

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The YIQ color space at Y=0.5 in IQ steps of 0.25 . Note that the I and Q chroma coordinates are scaled up to 1.0 . See the formulae below in the article to get the right bounds.

An image along with its Y, I, and Q components.

YIQ is the color space used by the NTSC color TV system, employed mainly in North and Central America, and Japan. In the USA, currently federally mandated for analog over-the-air TV broadcasting as shown in this excerpt of the current FCC rules and regulations part 73 "TV transmission standard":

(Quote) "The equivalent bandwidth assigned prior to modulation to the color difference signals EQ′ and EI′ are as follows:

Q-channel bandwidth: At 400 kHz less than 2 dB down. At 500 kHz less than 6 dB down. At 600 kHz at least 6 dB down.

I-channel bandwidth: At 1.3 MHz less than 2 dB down. At 3.6 MHz at least 20 dB down."

(End quote.)

I stands for in-phase, while Q stands for quadrature, referring to the components used in quadrature amplitude modulation. Some forms of NTSC now use the YUV color space, which is also used by other systems such as PAL.

The Y component represents the luma information, and is the only component used by black-and-white television receivers. I and Q represent the chrominance information. In YUV, the U and V components can be thought of as X and Y coordinates within the color space. I and Q can be thought of as a second pair of axes on the same graph, rotated 33°; therefore IQ and UV represent different coordinate systems on the same plane.

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. Broadcast NTSC limits I to 1.3 MHz and Q to 0.4 MHz. I and Q are frequency interleaved into the 4 MHz Y signal, which keeps the bandwidth of the overall signal down to 4.2 MHz. In YUV systems, since U and V both contain information in the orange-blue range, both components must be given the same amount of bandwidth as I to achieve similar color fidelity.

Very few television sets perform true I and Q decoding, due to the high costs of such an implementation^{[citation needed]}. Compared to the cheaper R-Y and B-Y decoding which requires only one filter, I and Q each requires a different filter to satisfy the bandwith differences between I and Q. These bandwidth differences also requires that the 'I' filter include a time delay to match the longer delay of the 'Q' filter. The Rockwell Modular Digital Radio (MDR) was one I and Q decoding set, which in 1997 could operate in frame-at-a-time mode with a PC or in realtime with the Fast IQ Processor (FIQP). Some RCA "ColorTrak" home TV receivers made circa 1985 not only used I/Q decoding, but also advertised its benefits along with its comb filtering benefits as full "100 percent processing" to deliver more of the original color picture content. Earlier, more than one brand of color TV (RCA, Arvin) used I/Q decoding in the 1954 or 1955 model year on models utilizing screens about 13 inches (measured diagonaly). Around 1990, at least one manufacturer (Ikegami) of professional studio picture monitors advertised I/Q decoding.

[edit] Image Processing

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 colors in relation to one another, resulting in an image with colors that no longer make sense. Instead, the histogram equalization is applied to the Y channel of the YIQ representation of the image, which only normalizes the brightness levels of the image.

[edit] Formulas

These formulae approximate the conversion between the RGB color space and YIQ for a very popular non-FCC version of NTSC.

$R, G, B, Y \in \left[ 0, 1 \right]$

$I \in \left[-0.5957, 0.5957\right]$

$Q \in \left[-0.5226, 0.5226\right]$

From RGB to YIQ:

$Y =$	$0.299$	$R +$	$0.587$	$G +$	$0.114$	$B$
$I =$	$0.5957$	$R -$	$0.2744$	$G -$	$0.3212$	$B$
$Q =$	$0.2114$	$R -$	$0.5226$	$G +$	$0.3111$	$B$

From YIQ to RGB:

$R =$	$Y +$	$0.9563$	$I +$	$0.6210$	$Q$
$G =$	$Y -$	$0.2721$	$I -$	$0.6473$	$Q$
$B =$	$Y -$	$1.1070$	$I +$	$1.7046$	$Q$

Or, using a matrix representation:

$\begin{bmatrix} Y \\ I \\ Q \end{bmatrix} = \begin{bmatrix} 0.299 & 0.587 & 0.114 \\ 0.595716 & -0.274453 & -0.321263 \\ 0.211456 & -0.522591 & 0.311135 \end{bmatrix} \begin{bmatrix} R \\ G \\ B \end{bmatrix}$

$\begin{bmatrix} R \\ G \\ B \end{bmatrix} = \begin{bmatrix} 1 & 0.9563 & 0.6210 \\ 1 & -0.2721 & -0.6474 \\ 1 & -1.1070 & +1.7046 \end{bmatrix} \begin{bmatrix} Y \\ I \\ Q \end{bmatrix}$

Two things to note regarding the RGB transformation matrix:

The top row is identical to that of the YUV color space
If $\begin{bmatrix} R & G & B \end{bmatrix}^{T} = \begin{bmatrix} 1 & 1 & 1 \end{bmatrix}$ then $\begin{bmatrix} Y & I & Q \end{bmatrix}^{T} = \begin{bmatrix} 1 & 0 & 0 \end{bmatrix}$ . In other words, the top row coefficients sum to unity and the last two rows sum to zero.

NOTE: The FCC version of NTSC, which is currently on the books for over-the-air analog color TV broadcasting, uses a slightly different matrix, which is:

"EQ′=0.41(EB′-EY′)+0.48(ER′-EY′). EI′=-0.27(EB′-EY′)+0.74(ER′-EY′). EY′=0.30ER′+0.59EG′+0.-1EB′." (Quoted from Code of Federal Regulations §73.682.)

[edit] References

Buchsbaum, Walter H. Color TV Servicing, third edition. Englewood Cliffs, NJ: Prentice Hall, 1975. ISBN 0-13-152397-X

Color space ■ Color models
RGB color spaces ■ RGB color model ■ CMYK color model ■ HSV color space ■ HSL color space ■ RYB color model ■ CIELAB (Lab) ■ YUV for PAL television ■ YDbDr for SECAM television ■ YIQ* for NTSC television