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I Color Theory Equations

  1. Jun 1, 2017 #1
    Hey guys I figured out something new about color theory in additive color mixing.

    So, the primary colors in additive color mixing are R, G, and B (Red, Green, and Blue).

    The secondary colors are C, M, Y (Cyan, Magenta, Yellow).

    Using basic knowledge we know that

    R + G = Y
    R + B = M
    G + B = C

    The secondary colors can also be added to make up primary colors:

    M + Y = R
    C + Y = G
    M + C = B

    We know that from looking at Adobe Photoshop's color wheel that these are the opposite colors:

    B = -Y
    G = -M
    R = -C

    In further detail:

    B = -(R + G) = - Y
    G = -(R + B) = - M
    R = -(G + B) = - C

    So essentially Blue is the inversion of Red and Green. Green is the inversion of Red and Blue. And Red is the inversion of Green and Blue combined.

    This can be further proved in the following:

    R + G = Y
    R + B = M
    M + Y = R
    M + Y + B = M
    B = - Y

    This is all I have in terms of simple equations on color.

    The rest is analytical.

    This is the graph of luminosity of different colors. We notice G is the brightest of primary colors, R is the second brightest, and B is the least bright primary color. We notice there is a bump in brightness at C, M, and Y, which are formed by combining two primary colors. This probably is because combining two colors triggers two cones in the human eye that causes the luminosity to shoot up and make the bump on the graph.

    I believe there is a way to define color as the change in luminosity (slope) and the overall luminosity.

    I know I am missing a lot of things in this, so can anyone who's knowledgeable about light and physics help me make equations that can define color scientifically and mathematically?

    Many thanks in advance.
    Last edited by a moderator: Jun 2, 2017
  2. jcsd
  3. Jun 2, 2017 #2
    I should mention that colour mixing does not produce the colour, only the perception of the colour. It is a psycho-perceptual effect. So that for the case of your luminosity diagram, a true Cyan, for instance, does not consist of two colours.
  4. Jun 2, 2017 #3


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    There have been many YouTube videos about how colors are perceived by our eyes, as well as generated by computer monitors (and 4-color printing). Vsauce and PhysicsGirl are 2 channels which come to mind for that.

    So I was wondering about your luminosity measurements. Did this come from an actual device which measures it? You talk about the cones being activated in a person's eye, which leads me to think about a person perceiving one color to be more luminous than another.
  5. Jun 2, 2017 #4
    The measurements come from Adobe Photoshop.

    Perhaps Cyan consists of two colors (blue and green) and one color (cyan) at the same time?
  6. Jun 2, 2017 #5


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    That makes no sense. Cyan can't consist of two primary colors and itself. You'd get a recursive definition.
  7. Jun 2, 2017 #6
    The thing that concerns me the most is how the colors have different luminosity and when mixed the luminosity dont add up. Is there an equation that explains this?
  8. Jun 2, 2017 #7


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    Staff: Mentor

    Are you referring to the "brightness" of each of the RGB color channels? There are several different ways of defining luminosity. For example, in video there is the luma, and there are a half-dozen or more different ways when talking about the "lightness" of a color. Here's another page on lightness.

    That depends on the exact color theory, model, or format that you're talking about. There are equations in some of the links I just posted. Have a look at those.
  9. Jun 3, 2017 #8


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    The eye is not a spectrometer (how many times have I mentioned that fact?) It does the best it can with just three analysis curves. It works with Perceived Colours and not wavelengths.
    You can produce Cyan 'colour' with Blue and Green Phosphors and it is also possible to manufacture a Cyan phosphor which would be centred around 490nm. Neither is more correct than the other.
    I don't know of an additive system that used the secondaries for phosphors. Three phosphors are sufficient to do a good job of synthesising matching colours by addition. Subtractive mixing is another matter and it's only with (by now ancient) film technology and low quality colour printing that only three primaries are used CMY dyes and pigments give a reasonable result but even humble home printers use six or more inks. High quality printing uses spot colours which are aimed at a particular critical colour - as in advertising logos.
  10. Jun 3, 2017 #9
    As a matter of interest, Professor Land demonstrated that a perception of any colour can be be obtained using just two primaries, these being colours located at opposite sides of the colour triangle.
  11. Jun 3, 2017 #10


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    It would depend on which colour triangle your talking of.
    That's not surprising if you are referring to the appropriate triangle. Two appropriate primaries can produce any colour match that lies on a line between them on the CIE chart. But that's not a very useful fact. More usefully, three primaries can produce any colour in the triangle with the primaries at the vertices. Colour TV relies on that.
  12. Jun 4, 2017 #11
    I agree with what you are saying, but Edwin Land observed accidentally that certain pairs of colours would stimulate full colour perception, including those colours not lying on their axis.
  13. Jun 4, 2017 #12


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    I had heard of that already and Land did extensive tests, involving the 'Mondrian' patterns to justify the theory. His 'Retinex' theory was developed in depth. It's true that the blue/violet part of the spectrum contributes very little energy to our vision and that there are many clues about colour in most scenes that allow some 'colour blind' people to identify colours (though perhaps not so good at actual colour matching). It's a set of three ill conditioned equations that the brain has to solve if one channel is missing.
    There is strong evidence of a tristimulus colour vision system in humans. A standard (additive) colour reproduction system is based on three sets of curves - the camera analysis with three filters, the display with three phosphors and the eye with three more analysis filters. The camera analysis will give RG and B channel signals, which give the Chrominance values and the Luminance. Bearing in mind how good the brain is at 'filling in' for missing information, I guess it's not too surprising that other clues can make up for lack of a B component in certain scenes. I guess you could say that TV Engineers are lucky that the brain makes such a good job of making sense of an RGB generated image. The Maths that is involved in a three colour reproduction system works very well and the two colour system clearly doesn't work as well - or that could have been what we use today.
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