Summary of Color
Let’s recap some of the main concepts we have covered in this particular lecture. We want to explain where the idea of color comes from and it’s a multi-step process.
The first step in the process is the illuminant; that is the object that emits light which falls onto the scene. That incoming light we refer to as illuminance and it’s kind of a spectrum; it is a function of the wavelength and we refer to it by the letter E. That light falls onto an object, and the object has got a reflectance which is also a functional wavelength, so a red object reflects more red light and other sorts of light. A blue object would reflect more blue light then other kinds of light. The light that leaves the object we refer to as the luminance, the luminance of the object, and the spectrum of the luminance is a function of the spectrum of the illuminance, the incoming light and the reflectance of the object.
That light enters the eye of an observer, and within the observer at the back of the observer’s eye are a number of different light sensitive cells—they have different responses and they respond to different parts of the spectrum. The response of theses cone cells is denoted by N and it is a function of lambda. The different cone cells have got different Ns. The overall response of the cone cell is the integral over the wavelength of the spectrum of the incoming light, the reflectance of the object, and the response of the individual cone cell. Within the cone cell the photons are converted via a chemical reaction to electrical impulses which travel through to visual cortex of the observer, and they result in a sensation that we have learned to associate with the word red.
There are many sources of light and we have touched on some of these. Incandescence is the light admitted by hot objects that could be the white hot filament of a tungsten light bulb or it could be the sun. Other sources of light are electron stimulation as occurs in old fashion cathode ray tubes, light admitting diodes, compact fluorescent tubes and other gas discharged tubes and lasers. Each of these has a different luminance spectrum. Light is a form of electromagnetic radiation and this radiation varies in terms of its wavelength.
With our eyes we are only able to see that part of the electromagnetic spectrum, but with wavelengths between 400 and 700 nanometers a lot of light emitted by common light sources—particularly the sun and incandescent light bulbs—is in the infra-red part of the spectrum, and although we can’t see infra-red we can feel it. We can sense it as heat.
In the retina of our eyes we have a large number of light sensitive cells: there are rod cells and cone cells. Now it is the cone cells that give us our sense of color vision. There are three different types of cone cells: those that are sensitive to red, those that are sensitive to green and those that are sensitive to blue. Often times they are referred to as the short, medium and long wavelength cones. The cones have somewhat overlapping response functions; in particular, the red and green cones are significantly overlapped. The fact that we have three types of cones means that we are called trichromats—we have three-color vision. Not all animals have three-color vision; most mammals only have two-color vision. We call them dichromats. Many other animals have four-color vision. We call them tetrachromats and birds are a typical example of that.
When we create cameras, we borrow a lot of these principles; we have an underlying array of silicone photo sensors and each of those are sensitive to a wide range of colors.
To make them color sensitive we print color filters on top of them and generally in a 2 by 2 array which we refer to as the Bayer pattern, so each 2 by 2 array contains two green filters and a red filter and a blue filter. So we create in silicone an analogue of the color sensing mechanism in the human eye.
If I look at an object with a particular color and I change the intensity of the illumination the appearance of the object will change, and here we see examples of the object at 100%, 75%, 50% and 0% brightness. The RGB values are changing, but the color of the object itself does not change, so we want to find a way to disentangle color from intensity.
To map the three what we call tristimulus values—that is, the red, green and blue value into a brightness value and two color values—now we can do this very simply by converting the RGB values to what we call chromaticity coordinates, indicated by the lower case r, g and b. Now these three numbers are actually redundant. I can compute any one of them given the other two, so we only need to use two of them and typically we keep only R and G, these numbers vary between zero and one.
So if we make a graph where on the horizontal axis we have the r coordinate, on the vertical axis we have the g coordinate, then every possible color appears within this triangle … pure red appears here, pure green appears here, pure blue appears here, and it is not possible for any colors to exist above the blue line.
Let’s recap the important points from the topics we have covered about light, wavelength, spectrums, light sources, reflection, reflectance functions, cone cells, tristimulus and chromaticity space.
This content assumes an understanding of high school level mathematics; for example, trigonometry, algebra, calculus, physics (optics) and experience with MATLAB command line and programming, for example workspace, variables, arrays, types, functions and classes.