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Old 01-10-2013, 09:24 PM   #11
ajdelange
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How did you determine that your PCA improved the specification of beer color? What test did you perform?
We could start a whole new thread on this.

Basically the SRM is a measure of the spectral absorbtion of 5" of beer at 430 nm. Doesn't tell you much about the actual visible color of the beer, does it? Well, actually it does tell you a great deal but clearly a 10 SRM Kriek doesn't look the same as a 10 SRM mild. This is because the absorption spectra are different shapes.

What I did was collect a whole bunch of spectra, normalize them by the absorption at 780, convert to transmission, find the average spectrum over the ensemble and then do PCA on the deviations from the average. It usually only takes a couple of principal components to come up with a correction to the average which models the original spectrum quite well. Thus the 81 point absorption spectrum required for visible color determination using ASTM E-308 can be regenerated from the SRM and 2 or 3 spectral deviation coefficients.

SRM: One number. General idea as to how dark or light a beer appears

ASBC Tristimulus: 3 numbers. Visible color under one limited (and ridiculous) set of viewing conditions.

Augmented SRM: 3-5 numbers. Visible color under any viewing conditions.

The beauty of the augmented system is that it requires the same data as the ASBC tristimulus method and processes it in much the same way.

Same offer here: if you want a copy of the paper PM me and it's yours.
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Old 01-10-2013, 09:35 PM   #12
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^^^^Smart

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Old 01-11-2013, 03:03 AM   #13
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We could start a whole new thread on this.

Basically the SRM is a measure of the spectral absorbtion of 5" of beer at 430 nm. Doesn't tell you much about the actual visible color of the beer, does it? Well, actually it does tell you a great deal but clearly a 10 SRM Kriek doesn't look the same as a 10 SRM mild. This is because the absorption spectra are different shapes.

What I did was collect a whole bunch of spectra, normalize them by the absorption at 780, convert to transmission, find the average spectrum over the ensemble and then do PCA on the deviations from the average. It usually only takes a couple of principal components to come up with a correction to the average which models the original spectrum quite well. Thus the 81 point absorption spectrum required for visible color determination using ASTM E-308 can be regenerated from the SRM and 2 or 3 spectral deviation coefficients.

SRM: One number. General idea as to how dark or light a beer appears

ASBC Tristimulus: 3 numbers. Visible color under one limited (and ridiculous) set of viewing conditions.

Augmented SRM: 3-5 numbers. Visible color under any viewing conditions.

The beauty of the augmented system is that it requires the same data as the ASBC tristimulus method and processes it in much the same way.

Same offer here: if you want a copy of the paper PM me and it's yours.
True. These equations, when integrated over the wavelength range, provide the tristimulus values which can then be converted to LAB or an RGB color space. 5" of beer... Hrmm... I believe it's 1 cm^3 of beer? Why would you normalize to 780nm? Most normalize to yellow about 530nm... My question is, How did you prove your findings? What are you comparing? How did you "collect a whole bunch of spectra"? Where did these spectra come from? Also, the equipment to do this sort of thing isn't exactly cheap.

Sorry shouldn't be hijacking this thread with so many questions.
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Old 01-11-2013, 05:50 AM   #14
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True. These equations, when integrated over the wavelength range, provide the tristimulus values which can then be converted to LAB...
...with respect to any white point...
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... or an RGB color space.
or Luv or any colorspace connected to XYZ.

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5" of beer... Hrmm... I believe it's 1 cm^3 of beer?
The measurement is, with modern instruments, made in 1 cm and multiplied by 12.7. It was originally specified that the measurement be made in 1/2" and multiplied by 10. Either of those, by Lambert's law, gives the absorption in 5".


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Why would you normalize to 780nm? Most normalize to yellow about 530nm...
You wouldn't. That was a typo and you responded before I noticed it. The normalization is done to the absorption at 430 nm, the wavelength at which the SRM is measured. This allows us to calculate an average transmission spectrum for an ensemble of beers from their individual transmission spectra in 1 cm after normalization to the 430 nm reading which means each normalized spectrum and thus the average has SRM 12.7. Given the specs for a beer one takes that average spectrum and adds a couple of eigenspectra to it each weighted by a spectral deviation coefficient. The result is an approximation to the normalized spectrum of the actual beer (all the eigenspectra are 0 at 430 nm) and you obtain the actual spectrum by converting back to absorption and multiplying by SRM/12.7. This can be scaled by Lambert's law to any path of interest and modified by any illumination function to yield, when inserted into E-308, Lab or any other color description. Thus 430 is chosen because it is the wavelength at which SRM is measured and Stone and Miller chose that wavelength because spectra normalized by that wavelength are very similar in shape which means that few PC's are needed to model them (Stone and Miller didn't know what they were on to). SRM by itself conveys 92% of the variation between beer transmission spectra.


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My question is, How did you prove your findings? What are you comparing?
The thesis was that one could accurately describe visible beer color under any reasonable set of viewing conditions with the SRM and handful of spectral deviation coefficients (SDC's). The method was to compute actual beer color under several sets of viewing conditions (using the full 81 point spectrum required by E-308) and compare (Euclidian distance in Lab space) those colors to colors computed from the SRM and a few SDC's.


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How did you "collect a whole bunch of spectra"?
Well, it involved drinking a bunch of beer as only a few mL are required to fill a 1 cm cuvet and I couldn't just pour the rest of the bottles down the drain. The final paper was based on an ensemble of 99 beers.

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Where did these spectra come from?
Hach spectrophotometer hooked up to a Mac.

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Also, the equipment to do this sort of thing isn't exactly cheap.
True.
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Old 01-11-2013, 01:51 PM   #15
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The thesis was that one could accurately describe visible beer color under any reasonable set of viewing conditions with the SRM and handful of spectral deviation coefficients (SDC's). The method was to compute actual beer color under several sets of viewing conditions (using the full 81 point spectrum required by E-308) and compare (Euclidian distance in Lab space) those colors to colors computed from the SRM and a few SDC's.
So what was your min/max DeltaE? (Assuming you were using DE 1976)...
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Old 01-11-2013, 04:40 PM   #16
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So what was your min/max DeltaE? (Assuming you were using DE 1976)...
That depends on the path, the illuminant, the observer and the beer. The eigenspectra came from the ensemble of 99 beers. Looking at those beers 12% can be represented to DeltaE(1976) < 3 with just the SRM; 50% to < 3 with one SDC, 98% of them to < 3 with 2 SDC's and all with 3. For DeltaE < 1 8% can be represented by just the SRM, about 25% with 1 SDC, 57% with 2 95% with 3 and all with 4. When I measure a new beer I pick the amount of spectral deviation I want to tolerate, let the spreadsheet figure out how many SDC's I need, and compute the colors for that many SDC's for a chosen path, illuminant and observer. If I think the DeltaE is to big I just compute more SDC's. It is incredibly robust in this sense. It usually takes 2 SDC's for a 'normal' beer and 3 for a fruit beer to get better than 3 DeltaE. But the scheme could do orange soda or blue jello though it looses its appeal as the number of required SDCs increases beyond a few.

I can easily send you a pdf of the paper if you want. And the spreadsheet and a strawman Beer 10D MOA too.
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Old 01-11-2013, 06:37 PM   #17
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That depends on the path, the illuminant, the observer
Of course any can be used, but isn't this standardized to Illuminant C, 10 Degree?
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Old 01-11-2013, 07:02 PM   #18
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For MOA Beer 10C (the ASBC's Tristimulus method) the viewing conditions are 10 ° Observer, 1 cm path, Illuminant C. Remember that Illuminant C was developed by the women's magazine industry as supposedly representative of the mix of tungsten and daylight that would fall on the house wives' kitchen tables as they turned the glossy pages of Ladies Home Mycologist or whatever. It would seem to me that one of the D illuminants would be a more reasonable choice and I almost never hold my beer close enough to my face (except when actually drinking it) to subtend 10 ° and I never drink it in a 1 cm wide glass. That's why I said in an earlier post that the Beer 10C conditions were, IMO, ridiculous. So, again, IMO, one of the advantages of the augmented SRM is that you aren't restricted to someone else's choice of viewing conditions. You can, equipped with the SRM and SDC's compute visible color for any illuminant, glass width or either observer. The D illuminants are particularly nice to work with because they are put together exactly the way I do the beer absorption spectrum i.e. by adding together three eigenspectra with the weights being easily calculated from the correlated color temperature of interest.

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Old 01-11-2013, 07:24 PM   #19
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Agreed. I prefer D50 2Deg. I have a rather large list of labeled Illuminants as well as any CCT in my beer software. Kinda neat, but maybe not so practical IMO.

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Old 01-11-2013, 08:56 PM   #20
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Well since this thread now seems to be steering off topic....

Out of curiosity, how many of the 99 spectra in the data set came from highly available commercial beers? If there were enough examples from beers that one could go out and buy then you could construct the spectrum of a target beer by mixing calculated amounts of commercial beers. Of course you don't want to have to mix tiny amounts of 99 different beers together, so when you calculate the mixing components you'd want to regulate the reconstruction to promote solutions which use a small number of beers in the mix, which (to steer this back on topic ... ish) could be a possible in-class demonstration for L1-regularized/Lasso style techniques if the class covers that (of course mixing a dark beer with a few light beers to make an amber beer may not be all that impressive). Alternatively, you could try using spectra PCA weightings and/or L1-reconstruction weightings to predict recipe formulation for various beers.

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