## The big picture (Colorspaces VIII)

29/05/2018

A few posts ago, I said that while the colorspaces looked random, they really weren’t, and that there was underlying order. The structure cannot be easily seen just by looking at the numbers themselves, but at how the numbers are obtained.

The story begins sometimes in the 1950s, were transmitting color TV images started to be the next logical step. Someone (not sure who was first, but it may have been Valensi, in the 1930s) proposed that TV color should be encoded in a perceptually friendly way [1]. It was known for a while that the retina had four types of sensors, rods for brightness with no color information, and three other types corresponding to red, green, and blue, but also that in, and beyond the retina, information travels as brightness, yellow-blue and red-green differences [2,3].

## Channel Mixing and Pseudo-Inverses

29/12/2009

Let’s say we want to mix three channels onto two because the communication device has only two available channels but we still want to emulate a three channel link. If we can afford coding, then it’s not a problem because we can build our own protocol so add any number of channels using a structured data stream. But what if we cannot control the channel coding at all? In CDs, for example, there’s no coding: there are two channels encoded in PCM and a standard CD player wouldn’t understand the sound if it was encoded otherwise.

The solution is to mix the three channels in a quasi-reversible way, and in a way that the two channels can be listened to without much interference. One possible way is to mix the third channel is to use a phase-dependant encoding. Early “quadraphonic” audio systems did something quite similar. You can also use a plain time-domain “mixing matrix” to mix the three channels onto two. Quite expygeously, let us choose the matrix:

$M=\left[~\begin{array}{ccc} \frac{2}{3} &0&\frac{1}{3}\\ 0 &\frac{2}{3}&\frac{1}{3}\end{array}~\right]$