Three-Channel False Colour

"The world isn't rendered in black and white"

- Assemblage 23, "Binary"

Most humans' eyes are capable of sensing three different primary colours (red, green, and blue), so when building colour imagery upon the foundation of greyscale imagery it is useful to take advantage of our eyes' abilities by conveying three versions of an image simultaneously.

While this is a powerful technique, it's important to remember that our eyes are not equally sensitive to all three primary colours. They are most sensitive to green, followed by red, and least-sensitive to blue (with the ratio between them being roughly 6:3:1 or 7:2:1 depending on if you go by the values measured for use in determining the YUV or YCrCb broadcast standards). Subtle differences in a greyscale image will be much more visible if that image is used as the green channel than if it's used as the blue channel (where those differences may not be visible at all - see Your Eyes Are Terrible At Seeing Blue for a fairly dramatic example of this)).

A Detailed Introduction covered the most straightforward application of this concept in considerable detail: assigning one source spectral band each to the red, green, and blue primary colour channels in an image. Here are some "refresher" images to illustrate:

Basic Variations

NIR (Grey)

R (Grey)

G (Grey)

B (Grey)

UVA (Grey)

NIR-R-G

NIR-G-B

NIR-G-UVA

R-G-UVA

R-B-UVA

G-B-UVA

Date Shot: 2010-10-16
Camera Body: Nikon D70 (Modified)
Lens: Nikon Micro-Nikkor 105mm f/4
Filters: Standard Set
Date Processed: 2010-12-19
Version: 1.0

With so many additional greyscale images in hand thanks to the methods discussed in Calculated Greyscale Images, and Statistical Greyscale Images, even more three-channel combinations become possible along each of those branches.

Calculated Channel Variations

(Difference: NIR-B)-(Difference: R-B)-(Difference: G-B) [3C]

(Difference: NIR-G)-(Difference: NIR-B)-(Difference: NIR-UVA) [3C]

(Difference: NIR-G)-(Difference: R-B)-(Difference: B-UVA) [3C]

(Difference: NIR-R)-(Difference: G-B)-(Difference: B-UVA) [3C]

(Difference: NIR-R)-(Difference: NIR-B)-(Difference: NIR-UVA) [3C]

(Difference: NIR-R)-(Difference: NIR-G)-(Difference: NIR-B) [3C]

(Difference: NIR-R)-(Difference: NIR-G)-(Difference: NIR-UVA) [3C]

(Difference: NIR-R)-(Difference: R-G)-(Difference: G-UVA) [3C]

(Difference: R-G)-(Difference: R-B)-(Difference: R-UVA) [3C]

(Difference: R-UVA)-(Difference: G-UVA)-(Difference: B-UVA) [3C]

(ND (Pos): NIR-G)-ND (Pos): -G-B)ND (Pos): )-B-UVA) [3C]

(ND (Pos): NIR-G)-ND (Pos): -NIR-B)ND (Pos): )-NIR-UVA) [3C]

(ND (Pos): NIR-G)-ND (Pos): -R-B)ND (Pos): )-B-UVA) [3C]

(ND (Pos): NIR-R)-ND (Pos): -NIR-G)ND (Pos): )-NIR-UVA) [3C]

(ND (Pos): NIR-R)-ND (Pos): -R-G)ND (Pos): )-G-B) [3C]

(Ratio: NIR To B)-(Ratio: R To B)-(Ratio: G To B) [3C]

(Ratio: NIR To G)-(Ratio: NIR To B)-(Ratio: NIR To UVA) [3C]

(Ratio: NIR To G)-(Ratio: R To B)-(Ratio: G To UVA) [3C]

(Ratio: NIR To R)-(Ratio: NIR To B)-(Ratio: NIR To UVA) [3C]

(Ratio: NIR To R)-(Ratio: R To B)-(Ratio: G To UVA) [3C]

(Ratio: R To G)-(Ratio: R To B)-(Ratio: R To UVA) [3C]

Date Shot: 2010-10-16
Camera Body: Nikon D70 (Modified)
Lens: Nikon Micro-Nikkor 105mm f/4
Filters: Standard Set
Date Processed: 2010-12-19
Version: 1.0

Statistical Channel Variations

All Bands (Max)-All Bands (Med)-All Bands (Min) [3C]

All Bands (ADev)-All Bands (Var)-All Bands (Range) [3C]

All Bands (Max)-All Bands (ADev)-All Bands (Var) [3C]

All Bands (Max)-All Bands (Kurt)-All Bands (Min) [3C]

All Bands (Max)-All Bands (Skew)-All Bands (Kurt) [3C]

All Bands (Skew)-All Bands (Kurt)-All Bands (ADev) [3C]

All Bands (Skew)-All Bands (Med)-All Bands (Range) [3C]

All Bands (Skew)-All Bands (Var)-All Bands (Min) [3C]

Date Shot: 2010-10-16
Camera Body: Nikon D70 (Modified)
Lens: Nikon Micro-Nikkor 105mm f/4
Filters: Standard Set
Date Processed: 2011-01-02
Version: 1.0

It is possible to generate an extremely large number of permutations of these types of image, so when I wrote The Mirror's Surface Breaks, I used several techniques to cull them down to a manageable (and hopefully useful) level.

In the case of the "calculated" channels (which as previously discussed are generated through relatively simple calculations such as the ratio of one spectral band's data to another's), I borrowed the concepts of "similar motion" and "oblique motion" from the world of music theory.

Similar motion in music is a counterpoint in which the notes all move up, or all move down together along the scale (but they all move, and they do not move in different directions)^[1]. I translated this into the software by classifying a three-channel combination as similar motion if, for example, the first channel was some combination of infrared and red, the second was a combination of red and green, and the third was a combination of green and ultraviolet. That is, each successive channel's components are moving up in frequency (or down in wavelength).

Oblique motion in music is a counterpoint in which one note stays the same, while the other note moves up or down along the scale^[2]. So, when handling images, TMSB classifies the motion as oblique if, for instance, the first channel is some combination of infrared and red, the second is a combination of infrared and green, and the third is a combination of infrared and ultraviolet.

Those who have studied musical theory will have noticed that I've conspicuously left out "contrary motion", which a counterpoint in which the notes move in opposite directions on the scale. This is because TMSB uses the standard convention of ordering spectral bands from low- to high-frequency. In order to have a case of contrary motion, a sequence of channels such as green-blue/red-ultraviolet/infrared-gamma would be necessary, and that type of sequence doesn't make sense in the context of the conventional ordering, because green should come after red, and red should come after infrared. This ordering further contrains the number of permutations, reducing them to a manageable number.

Because the statistically-generated channels lack an inherent "low to high" ranking (there is no equivalent of frequency/wavelength to order them by), I designed TMSB to order them in whichever single way the user configured, and then set up the standard configuration so that the variations which seemed most useful to me were ranked first (meaning they would appear in more combinations than the other channels).

Both of these limiting factors can be overridden in the software configuration, but the result is an extremely large number of output images.

Footnotes

1.	For those familiar with musical theory, I used a loose definition of "similar" which also includes what would sometimes be considered a separate classification - parallel motion - rather than treating it as its own type.
2.	For an extremely prominent example of oblique motion, listen to the introduction of "Entropy" by Informätik (available on their Syntax album). The same technique recurs in other parts of the song, but is easiest to hear at the beginning.