Notes by Dr. Optoglass: The Human Eye – Part III

Topics Covered:

  • How the Cones produce color
  • The visible spectrum
  • Defining Color Space
  • The CIE XYZ 1931 color space

It is the eye of other people that ruin us. If I were blind I would want, neither fine clothes, fine houses or fine furniture – Benjamin Franklin

Humans normally have three kinds of cones. They are called L, M and S – for long, medium and short (I knew you were expecting RGB) – based on their sensitivity to the wavelengths of light.

L responds to red light (564–580 nm). M responds to green light (534–545 nm). S responds to blue light (420–440 nm).

If you remember, Rod cells have a peak sensitivity at 498 nm, roughly halfway between S and M. Here’s how they stack up:

The lower limit for visible light in humans is 380 nm. Anything beyond this is ultraviolet light. The upper limit is 750 nm. Anything beyond this is infrared light. At normal light levels, the eye is most sensitive to yellow-green light (555 nm) – this is because this wavelength stimulates the two most common cone types, M and L, equally. S cones are randomly placed and appear much less frequently than the M and L cones. The reason for this might be due to the availability of rods. The ratio of L and M cones to S cones is about 100:1.

One of the theories of color (Yes, there are many) about the eye is that the rods and S cones contribute to luminance, and that the L and M cones contribute to color, very similar to the YCbCr color model adopted for broadcast. This should tell you that engineers who came up with the model were nothing short of brilliant geniuses.

All in all, it is estimated that the human eye can perceive about 10 million colors. The average human can only distinguish and name about a maximum of 100 colors during a lifetime (Some can’t get past VIBGYOR). An artist or expert could possibly distinguish and name thousands of colors. But all of us can see millions of colors. Evolution has been democratic that way. So let’s not complain about the lack of color in our lives. That’s just not true!

White light is seen by the eye as a combination of all the colors. It is very tough to sometimes predict the actual color in a scene as perceived by the eyes. E.g., our memory of the color of objects, like white paper or black hair, etc, cause our eyes to compensate when viewing these same objects under different lighting conditions. Our brain is constantly white balancing, but not in the way cameras do.

The quality of the cones outside the fovea as far as color is concerned cannot be faulted. If it were below par, we would only see color in the central portion of our vision. As it stands, we don’t see the ‘joins’, and even if our eyes are only focused on a small area, the rest of the visual scene does not lose its color.

One additional fact of having three cone types is that our eyes are essentially ‘mosaiced’, similar to (but much more advanced than) a Bayer sensor array. It has to perform real-time color operations without breaking the flow of vision.

With so much going on ‘underneath the hood’ it is a miracle that the eye has managed to keep its workings secret for thousands of years, and still elude us today. Bravo!

So how do engineers get a handle on color? They use what is called a Chromacity diagram:

The triangle in the middle represents the sRGB color space, what most monitors are built to display. The bigger cone is the CIE 1931 XYZ color space – in short, what the eye can see. Quite a bit of difference, right?

The chromacity diagram is actually a 3D image, of which the above diagram is only a 2D cross section.

First, let’s talk about the black region. In the visible color spectrum, there are an infinite wavelengths. I’m sure Professor Sampler told you about the nature of continuous systems, so it shouldn’t come to you as a big surprise. Mathematically, this infinite space is crushed to 3D Euclidean space so we can draw graphs and talk about it.

Colors are just sensations that our brain produces based on certain wavelengths of light. Since our cones follow an LMS or RGB pattern, it is quite all right for us to base our diagram on it. Using the cone values to understand colors is the job of a Color Space.

A Color Space is simply all the colors a given system can reproduce. It’s fine for everyone to talk about RGB or CMYK color models – they are abstract concepts not corresponding to reality. It is the job of a color space to take those concepts and ‘map’ them into actual values that can be understood and compared. It’s quite a bit of mathematical work combined with actual measurements, none of which are simple things one does in one’s free time.

So please remember, there is no such thing as an RGB color space or CMYK color space. These are color models. The same color can be reproduced by a combination of entirely different wavelengths.

The nature of analog systems show us that no two devices have the same color space. Even if we do our best to reproduce two monitors to exacting standards under the sRGB color space (or any other color space), these monitors will still have slightly different 3D color diagrams when measured. Want to know a funny thing? You are probably trying to view a CIE color space on an sRGB monitor right now – you can’t really see the space on any media – paper or monitor. The only way you can really see the CIE XYZ color space is with your eyes!

The problem with basing our color space model on RGB is that using mathematics, sometimes one gets negative values! Mathematicians normalize these values and come up with three new values called X, Y and Z – hence the name CIE XYZ color space. X, Y and Z do not strictly correspond to R, G or B, even though you might be tempted to refer to them as such.

What do X, Y and Z mean then?

If you have to know, in this model, Y means luminance, Z is somewhat equal to blue, and X is a mix of cone response curves chosen to be orthogonal to luminance and non-negative. Say goodbye to any notion that XYZ means RGB.

The easy way to think of a color space is as if it were a bag filled with coins of different colors. The more the colors the bigger the bag. The drawings you see of color spaces are always 2D cross sections – don’t base your judgments on just this. A proper assessment of any color space takes a whole lot of mathematics and actual measurements – don’t worry about it too much.

Takeaways:

  • There are three types of cones – L, M and S – that are the basis for color vision.
  • Colors are just sensations that our brain produces based on certain wavelengths of light.
  • A Color Space is simply all the colors a given system can reproduce.
  • The CIE XYZ 1931 color space represents the colors as seen by the eye, and is the basis from which all other spaces are measured and compared to.
  • The eye can see 10 million colors, but the brain can’t think about all of them in one go.

Links for further study:

Next: Eye Geometry
Previous: The Human Eye – Part II