Sorry for a sort-of long question: I’m curious about using some 3-band measurements (as with a particular RGB camera) to estimate the response in a different band (call it X, assumed to be contained within the 400-700u limits). I think I understand that linear regression-type models often give good results – that for reasonable (i.e. mostly smooth) illumination and reflectance spectra, the response in some new band X is often well-represented with a combination of the available RGB responses as a regression calculation.

Your documentation also mentions the many-to-one mapping between incident spectral irradiance shapes, and RGB triplets. This essentially recognizes that the variety or space of “natural” spectral shapes is larger than can be represented with 3 values (RGB or any other 3 values).

My question is if you have some sense of “how bad” the cone-catch (regression) calculation could be for some unknown incident spectrum. I’m not thinking of a pathological, unnatural incident spectral shape – but maybe one that is not from the types of materials used to train the regression models for cone-catch. That is, if I measure some RGB, and perform the cone-catch calculation for the X-band, how bad could the result be (even if it is good for most spectral shapes)?

It seems that there may be some (small) fraction of the natural spectral shapes not well-represented by the regression equation.

Since the incident spectrum is unknown (we have just RGB values) do you know of a simple way to estimate or enumerate the distribution of X-band responses over the different incident spectral shapes that all produce the same RGB response? I guess this would depend on the band X, and also on the RGB values?

Is there some way to enumerate the possible spectral shapes (sampled, as in your database, say) that all produce the same RGB values (for some particular RGB)?

Sorry if you have explained this somewhere and I overlooked it.

Hi Breck,

In short, there will in theory be an infinite number of possible combinations of incident spectra and reflectance spectra which can combine to make metameric identical RGB measurement values. However, in practice, natural (which includes crazy structural colour) reflectance spectra and fairly smooth natural light sources will make these pretty rare.

The cone-catch models tend to report very high agreement (R^2 > 0.995). The greatest source of error seems to be when the receptor being modelled is towards the edge of the 400-700 range (tends not to be an issue with 300-700 because there’s so little sensitivity and sunlight at 300nm). The remaining error will presumably be metamerism type effects (due to really complex illuminant/reflectance peaks/troughs).

It also seems that the modelling can deal quite happily with spikey irradiance spectra (again, reflectance doesn’t tend to have such complex shapes that this becomes an issue).

It would be fairly straightforward to model all this though. You’d simply make a model with a subset of reflectance spectra, then test that model with whatever spectra you’re interested in (whether illuminant or reflectance or both). This would be a really neat way to demonstrate the robustness of the whole system, and model the parameter space. An even easier way is to simply measure various things (ideally diffuse reflectance charts) under different light sources, then see how the “wrong” lighting model affects measurements. Once normalised (von Kries), there won’t be much difference between e.g. sunlight and arc lamps designed to mimic sunlight. Things will probably get a bit weird with white LEDs though.

One thing to bear in mind is fluorescence though… we rarely consider it, but given many substances fluoresce to some degree this makes many real-world measurements taken with spectrometers/cameras under artificial light sources inaccurate (at least inaccurate to a degree where comparing values e.g. between camera and spec and different light sources will be measurably different).

Cheers,

Jolyon