why different colour? - some math

Started Sep 10, 2007 | Discussions
Iliah Borg Forum Pro • Posts: 22,139
why different colour? - some math

To start with, please look at the spectral sensitivity characteristics of a sensor. For numeric example we will use here curves of SONY ICX285AQ, see p.7 of SONY publication
http://products.sel.sony.com/semi/PDF/ICX285AQ.pdf

Digitizing the curves on page 7, we will have a table similar to:
400nm 450nm 500nm 550nm 600nm 650nm 700nm
R 0.03 0.02 0.04 0.07 0.96 0.94 0.82
G 0.03 0.13 0.56 0.9 0.31 0.04 0.15
B 0.22 0.66 0.55 0.04 0 0.01 0.01

Now let's take 4 wavelengths, 450, 500, 550, and 600nm; and play with them a little. Can we find a source that emits 450 and 550 nm that will provide a response equivalent to another source of light, emitting 500 and 600nm? Solving a simultaneous linear equation, we see that sensor will respond to first power source, emitting 65.4mW at 450nm and 41.6mW at 550 nm exactly the same way as to the second power source, emitting 81.5mW at 500nm and 1mW at 600nm.

Further, it is easy to see that we can find an infinite number of mixtures of those 4 wavelengts that will produce exactly the same sensor response. That means that for ICX285AQ a lot of colours between cyanish blue and cyanish green will trigger the same sensor response.

Reproduction of many shades of reds i9s even more challenging then that. If the series of wavelengths is 400, 500, 600, and 700nm with this sensor orange, brown, and even some shades of green trigger same response.

The above problem is'emphasized when shooting conditions are far from native sensor colour temperature, and with wrong exposure.

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Ron Parr Forum Pro • Posts: 13,784
Don't forget...

Don't forget that color is also additive and also a 3-space for the human eye. You can find an infinite number of possible power spectra that will produce the same perception of color for humans too. That you can do this for a camera doesn't, by itself, imply that you will have color reproduction issues. The color reproduction challenges occur in trying to reconcile our cone absorption spectra with the absorption spectra of the color filters, and the properties of our viewing media.

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OP Iliah Borg Forum Pro • Posts: 22,139
It is a little different

Dear Ron,

You can find an infinite number of possible power spectra
that will produce the same perception of color for humans too. That
you can do this for a camera doesn't, by itself, imply that you will
have color reproduction issues.

If you compute tristimulus values to those light sources and then convert results to RGB you will see a huge mismatch to human perception. For this particular case it does not matter that our eyes tend to err too; what matters is that sensors err differently from our eyes.

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Ron Parr Forum Pro • Posts: 13,784
Re: It is a little different

Iliah Borg wrote:
Dear Ron,

You can find an infinite number of possible power spectra
that will produce the same perception of color for humans too. That
you can do this for a camera doesn't, by itself, imply that you will
have color reproduction issues.

If you compute tristimulus values to those light sources and then
convert results to RGB you will see a huge mismatch to human
perception. For this particular case it does not matter that our eyes
tend to err too; what matters is that sensors err differently from
our eyes.

Well, I wouldn't call what our eyes do as erring, unless you think our eyes are supposed to be spectrometers and not eyes.

I hadn't realized that you picked spectra that were metameric for the sensor but not our eyes. Of course, I agree that such combinations will exist for typical color filter designs.

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MOD TOF guy Forum Pro • Posts: 13,456
Re: why different colour? - some math

That's why we need filters with more than colors than R G B. Sony was going in the right direction with Cyan. Too bad it did not catch up.

From the curves we can calculate the optimum filter for a range of color for various illuminants.
--
Thierry

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OP Iliah Borg Forum Pro • Posts: 22,139
Re: why different colour? - some math

Dear Thierry,

That's why we need filters with more than colors than R G B. Sony was
going in the right direction with Cyan. Too bad it did not catch up.

Adding filtered colours will negatively affect pixel size or resolution. With current tendency of consumers to demand larger pixels to improve noise characteristics such solutions may be hard to market.

The point of this little exercise was to attempt to answer why colour from different sensors is different; and why it depends on the exposure. White balance is one of the components of exposure, that is, if you compare two shots of the same scene lit with light of two different colour temperatures and neutralise both shots using a grey reference, some colours will differ between the shots.

I think it should be mentioned once more that for most of the situations the accuracy of colour is not very important. What we expect is that "memory" colours present in the image are "expected" and "believable". Only when two shots from two different cameras (or from one camera, but using two different light sources) are compared the colour differences on the images raise the question of "faithful colour reproduction". Humans are usually not good in evaluating "absolute colour", but very good in comparing two colours.

The other side of this sensor metamerism is that when recording a colour scene sensor behaves in a non-linear fashion. For example, two colours having different "L" values may be recorded as having the same "L" value. In the example above, particular range of blue/cyan/green tints having L from 65 to 67 will be recorded to the same L value; particular red tints having L from 45 to 58 will also be recorded as having the same L value. The opposite is also possible - two colours having same L value will be recorded to different L values.

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MOD TOF guy Forum Pro • Posts: 13,456
Re: why different colour? - some math

Dear Iliah,

Thank you for the detailed explanation.

So cameras don't have a gamut, but instead they cannot discern colors in specific regions of the color space.

The fact that certain colors give the same sensor signal does not surprise me: I've suspected that this effect exists and may be at play when some type of subjects give an impression of a feature-less "plasticky" appearance because of lack of subtle color details.

Glad to see you back and active in these fora.
--
Thierry

 TOF guy's gear list:TOF guy's gear list
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