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Given that in RGB we can represent 256^3 combinations = 16,777,216 colors, and since the human eye can only distinguish roughly 10,000,000, there is obviously a surplus of 6,777,216 RGB combinations that chromatically are indistinguishable from counterpart colors.

Compression algorithms work on this basis when approximating out spacial difference in color ranges across a frame I believe. With that in mind, how can one reliably compute whether a given color is within a range of 'similarity' to another?

Of course, 'similarity' will be some kind of arbitrary/tunable parameter that can be tweaked, but this is an approximation anyway. So any pointers, pseudocode, intuitive code samples, resources out there to help me model such a function?

Many thanks for your help

Darius
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  • You say "a surplus of 6,777,216" as if almost half the information was wasted. It's not the case. These 6,777,216 colours account for `1-log2(1000000)/24` ie. 3.11% of the information. Don't count on that for compressing! – sam hocevar Jan 03 '13 at 15:24
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    Years later, this question still seems relevant. In case it helps anyone, I found a different solution using HSL that I wrote about recently [here](https://medium.com/@dariushodaei/colour-coding-part-1-aa0d9910592) – Darius May 16 '17 at 15:47

3 Answers3

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There are many ways of computing distances between colors, the simplest ones being defined on color components in any color space. These are common "distances" or metrics between RGB colors (r1,g1,b1) and (r2,g2,b2):

  • L1: abs(r1-r2) + abs(g1-g2) + abs(b1-b2)
  • L2: sqrt((r1-r2)² + (g1-g2)² + (b1-b2)²)
  • L∞: max(abs(r1-r2), abs(g1-g2), abs(b1-b2))

These however don't take into account the fact that human vision is less sensitive to color than to brightness. For optimal results you should convert from RGB to a color space that encodes brightness and color separately. Then use one of the above metrics in the new color space, possibly giving more weight to the brightness component and less to the color components.

Areas of color that are indistinguishable form each other are called MacAdam ellipses. The ellipses become nearly circular in the CIELUV and CIELAB color spaces, which is great for computation, but unfortunately going from RGB into these color spaces is not so simple.

JPEG converts colors into YCbCr, where Y is brightness and the two C's encode color, and then halves the resolution of the C components. You could do the same and then use a weighed version of one of the above metrics, for example:

diff = sqrt(1.4*sqr(y1-y2) + .8*sqr(cb1-cb2) + .8*sqr(cr1-cr2))

The article on color difference in wikipedia has more examples for different color spaces.

Joni
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  • This is really great, and thank you for the suggestions. Tricky business approximating color! – Darius Aug 22 '12 at 11:41
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Perceptual color difference can be calculated using the The CIEDE2000 Color-Difference Formula. The CIEDE2000 formula is based on the LCH color space (Luminosity, Chroma, and Hue). LCH color space is represented as a cylinder (see image here).

A less accurate (but more manageable) model, is the CIE76 Color-Difference formula, which is based on the Lab color space ( L*a*b*). There are no simple formulas for conversion between RGB or CMYK values and L*a*b*, because the RGB and CMYK color models are device dependent. The RGB or CMYK values first need to be transformed to a specific absolute color space, such as sRGB or Adobe RGB. This adjustment will be device dependent, but the resulting data from the transform will be device independent, allowing data to be transformed to the CIE 1931 color space and then transformed into L*a*b*. This article explains the procedure and the formulas.

Lior Kogan
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  • Excellent resources! Brings back memories of a undergrad Graphics module I did on color perception. Thank you for the pointers – Darius Aug 22 '12 at 10:14
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RGB color system is designed such that if 2 colors have values that are close to each other then the colors are also perceptually close.

Example:

color defined by RGB = (100, 100, 100) is perceptually almost the same as colors RGB = (101, 101, 100), RGB = (98, 100, 99) etc...

Krešimir Lukin
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  • So a variance degree of perhaps n<5 in any column shouldn't yield a perceivable chromatic difference then? That's a good place to start for testing, thanks – Darius Aug 22 '12 at 10:03
  • Yes. Try this online tool for testing: [Colors scheme](http://www.colorschemer.com/online.html) – Krešimir Lukin Aug 22 '12 at 10:11
  • Note you have to check the closeness of values *component-wise*, you can't just go (color1 - color2) < threshold because of the data representation. This is obvious but can be a pitfall. – Thomas Aug 22 '12 at 10:25