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What
Happened to My Colors!?! Illegal Colors RGB is the color space of our retina, of picture tubes, of still cameras and of motion cameras. RGB is the color space of ray tracing and other simulations of the interactions between light and objects. Why? Because our eyes have red, green and blue detectors. Therefore, RGB color space accurately models the way that our retina detects light. In addition, if you work in RGB space you can take the contributions of two lights, add them together, and get a meaningful result. However, RGB is not the color space of our visual cortex. Somewhere between our retina and where we perceive color, another color space becomes a better representation of how our mind sees color. Although artists find it convenient to work with hue and saturation, our mind seems to perceive color roughly as a combination of brightness and two axes of color information. YUV and YIQ color space attempt to capture this color space. Y stands for luminance (brightness) and it is calculated as: Y = .299R'+.587G'+.114B'
The weightings are based on our eye's sensitivity to the different primaries. The prime signals after R, G and B indicate that these are gamma corrected RGB values, which I'll discuss later. U and V represent no numerical value per se. They're just two adjacent letters of the alphabet and are calculated as:
U =0.492(B'-Y) This gives
us two numbers that are zero when we have gray and can hold all of the
color information of an RGB color. You can think of the Y coordinate of
YUV as measuring how far along the gray diagonal of the RGB color cube
to go. The U and V coordinates then specify how far from gray to go, and
in which direction.
I =V cos(33)-U sin(33)=0.736(R'-Y)-0.258(B'-Y) U and V don't stand for anything, but what about I and Q? You probably shouldn't ask. Since YIQ was first used by NTSC television, its name reflects the method used to squeeze the I and Q signals together into one signal. The method used is called "quadrature modulation" (a method also used in modems). Thus, I stands for "in-phase" and Q stands for "quadrature." After I and Q are squeezed together into one signal, they are added to the Y component to produce a composite signal resulting in Y, I and Q all being mixed together on a single wire. It's very complicated to explain how and why this signal can usually be pulled apart into its components again by a TV, and Jim Blinn's article on NTSC spends a lot of time explaining why this works (Blinn 98). However all this high powered math to explain how to extract YIQ from a composite signal hides the fact that going in the other direction, creating a composite signal from YIQ, is actually trivial. Since we are starting with an RGB image we first convert from RGB to YIQ. Then we need to filter Y, I, and Q to remove the high frequencies, which is discussed in more detail in the following section. Then, I + Q are combined using quadrature modulation to make chroma, the color information. The formula for this is simply (Jack 98): 
3.579545 MHz is the color carrier frequency, carefully chosen to go through precisely 227.5 cycles for each horizontal line, and t is time. The effect of this formula is to take two copies of the color carrier, one offset by ninety degrees, and multiply them by I and Q. When they are added together the result is another sine wave at the color carrier frequency. The amplitude of this resultant sine wave stores the saturation of the color, measuring how pure it is. The offset of the sine wave in t, known as the phase, stores the hue of the color. Finally, C is added to Y, and you've got your composite signal: Composite =Y+C When the signal gets to your TV, your TV has to convert it back to RGB, because televisions are fundamentally RGB devices. If you use enough precision and do careful rounding then converting from YIQ and back to RGB is lossless. So why do we care about this conversion? To understand why we care we need to look a little bit more at the quadrature encoding that adds I and Q together to make C. As I mentioned above, quadrature modulation gives us a sine wave. The amplitude of this sine wave is:
Remember that this sine wave is added to the Y signal so the Y + C signal will swing higher and lower than Y by itself. It will go as high as Y + |C| and as low as Y - |C|. A little experimentation will show that some combinations of red, green, and blue will create large swings. If R', G' and B' go from 0.0 to 1.0 then the maximum value for Y + |C| is 1.333 and the minimum value for Y - |C| is -0.333. Pure red and pure green will cause the signal to swing down to -0.333 and pure cyan (blue and green) and pure yellow (red and green) will cause it to swing as high as 1.333. Meanwhile, pure white only goes up to 1.0, and pure black sits at 0.0. In general, highly saturated colors, colors with very little white in them, will cause high voltage swings. It may seem odd that yellow and cyan cause higher signals than pure white, but this actually does make sense. The average signal for pure yellow is just 0.886, but the color carrier, C, swings up 0.447 and down 0.447 from 0.439 to 1.333. It is this wild swinging of the color carrier that tells the TV to display yellow. Meanwhile, pure white gives a steady 1.0 signal. NTSC Composite Waveform for Pure Yellow Notice how the composite signal for yellow goes up quite high. In this image the signal would have gone up to 1.333 but it was clamped at 1.20. The high amplitude of the signal indicates a highly saturated color.
NTSC Composite
Waveform for White The composite waveform for white is quite boring. It's just a straight line. That shows that it has zero saturation, or no color. Also note that while the yellow signal goes much higher than white does, the average height of the white signal is higher than the average height of the yellow signal. This indicates that white is a brighter color, and it has greater luminance.
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