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CM Theory and Practice Profiles, color spaces, perception, science.

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Old September 19th, 2010, 10:01 AM
Doug Kerr Doug Kerr is offline
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Default Color - spectral and chromaticity outlooks

Color is a wholly perceptual property - it does not correspond to any physical property of light, although it is determined by a physical property. It is defined solely in terms of its perception by a living organism (we mostly speak of in the context of observation by homo sapiens).

That physical property that controls color is the spectral power density (SPD) of the light. This is a "function of wavelength" (meaning that its numerical value is potentially different for each wavelength) that tells us how the power in the light is distributed over different wavelengths. The SPD is of "infinite dimensionality" (in the mathematical sense); that is, it would take an infinite number of values to precisely describe a certain SPD. Even if we wanted to use an approximation - say, state the value for each band of wavelength 1 nm in width, it would take 300 values.
We often call the SPD the "spectrum" of the light, perfectly reasonable. Still, to avoid problems later, when another kind of "spectrum" emerges, I'll keep speaking of it as the SPD.
But fortunately for color photography, the property of color - determined by the SPD of the light being observed - is (for humans) only three-dimensional: only three values are needed to describe a certain color.

Thus there is an infinity of different SPDs that all have the same color - they all look identical to the viewer. This situation is called metamerism.
Unfortunately, we often encounter that word used to describe something different, and almost opposite - as if we used "reciprocity" to mean "reciprocity failure".
Note that, owing to the definition of color, it is not just that "these appear to be the same color" - they are the same color.

As a result, we are able to "capture" the color of an instance of light with a camera that delivers only three values for each point in the image, and from that reproduce light of the same color (but not necessarily, or even likely, the same SPD) on a display for the benefit of a viewer.

The SPD of the light emerging from an illuminated reflective surface is the product of the SPD of the incident illumination and the reflective spectrum of the surface (a function of wavelength that tells us the reflectance of the surface at each wavelength - again, infinitely-dimensional).

Now, we can "synopsize" the SPD of the reflected light in terms of its color. We can do the same for the SPD of the incident illumination. And in fact we can do a similar thing with regard to the reflective spectrum of the subject surface - we can describe its "reflective color". (The L*a*b* color space was originally developed to let us do just that.)

Does that mean that, if we know the color of the incident illumination and the reflective color of the surface, we could "calculate" the color of the reflected light?

Sadly, no. To actually determine the color of the reflected light we would need to multiply the SPD of the incident light by the reflective spectrum of the surface, giving us the SPD of the reflected light. From that, we could determine the color of the reflected light.

When we do white balance color correction, we transform the color captured by the camera (the color of the reflected light from the object surfaces) to take into account the difference between the actual incident illumination used for the shot and that contemplated by the color space in which the image will be carried forward. We normally do this by determining (in some way) the chromaticity of the incident light (the chromaticity aspect of its color, which depends on its SPD, but which we normality measure "directly").

Can we really rely on this to give the "best" result? No, for the reason I mentioned above: we cannot predict the color of the light reflected by a surface from (a) the color of the incident light and (b) the reflective color of the surface.

But, as a practical reality, if the SPD of the incident light is what I will call "well-behaved" (and I don't propose to give a technical definition of that), and the reflective spectrum of the surface is "well-behaved", then the calculation I mentioned (based on color, not spectrums) will give a good approximation of the color of the reflected light.

And it's a good thing, for (until recently), almost all white balance color correction has been based on that predicate.

What if those presumptions are not well-founded? In particular, suppose the spectrum of the incident light is not "well-behaved" (whatever that means). Then white balance color correction, done in the familiar way, may produce a result that is not "reasonable" aesthetically (nor even "theoretically correct").
"Theoretically-correct" color balance means that the color recorded in the image file for each spot on the subject corresponds to the reflective color of that spot.
Let me tell of a related situation in another field. A man in a haberdashery picks out a pastel shirt and a tie that seem to complement each other, as he views them in front of the mirror. He is on his way to an important speaking engagement, so he puts them on in the store. He steps outside, where his assistant has been waiting. "My God, Chris, what have you done - that shirt and tie don't go together at all."

The reason is that reflective surfaces in the tie and the shirt from which the reflected light, under the ambient light in the store, have SPDs that, although probably different, have the same color (not just, "appear to be the same color"), will, under daylight (with a different SPD than the shop lights) exhibit two new SPDs that do not have the same color.
It is this problem that is sometimes, inappropriately, called "metamerism".
Fighting this problem is the central theme of an important aspect of applied color and illuminating science, the making of light sources whose SPD's are "well behaved" and will thus not contribute to this problem. Today, if we shop for compact fluorescent lamps, we will generally find among their specified properties a color rendering index (CRI), which quantifies what I have called the "well-behavedness" of the SPD of the light from that lamp.

How can we fight this problem as it applies to white balance color correction. Until recently, we had no practical tools. We had no choice but to transform the chromaticity of the colors of light recorded by the camera in a uniform way for all parts of the color space (and usually, for all parts of the frame as well).

Now, it seems as if (with the new work being done for the ColorChecker product and the like) we have the prospect of a "remapping" of chromaticities that varies with the location of the "captured" color in the color space. I have to learn more about this. (Maybe this afternoon.)

Note, incidentally, that we already have the ability to separably map colors depending on their location in the color space, but mainly only in accommodating the properties of an output device, such as a display or a printer, in the interest of "accurate" rendition of the image as described in the digital file.

The new development (I think) is our ability to do this to the image as it will be delivered in digital form, in the context of correction for the SPD (not just the chromaticity) of the incident light.

Now, I'm off to study "Barbie's eye shadow compact by X-Rite", or, "The Scottish play goes to war".

Best regards,

Doug
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Old September 19th, 2010, 11:59 AM
Andrew Rodney Andrew Rodney is offline
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Well said!

In terms of the misunderstanding of metamerism (as you point out, its actually a good phenomena) when we get the mismatch you describe above, it appears the term metameric failure is becoming a more accepted term to describe this unfortunate experience.
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