Talk:LMS color space

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Which Illuminant is the given matrix for?
I have for Illuminant E:

{+ 0.243 , + 0.856   , - 0.044   } {- 0.391   , + 1.165   , + 0.087   } {+ 0.010   , - 0.008   , + 0.563   }

--User:GENtLe (talk)


 * I added quite a few matrices, and sourced them. Does it answer your question? --Adoniscik (talk) 05:37, 17 February 2008 (UTC)

LMS color space or LMS color spaces?
If there is no objective canonical transformation from XYZ color space to "LMS color space", then it would follow that there also isn't "the LMS color space", but rather LMS color spaces. In fact, at least as many LMS color spaces as there are transformations XYZ->LMS. --93.209.95.156 (talk) 14:32, 27 October 2017 (UTC)
 * Nope, there is one LMS color space and several mathematical XYZ → LMS transformations which are all approximations as no exact mathematical transformation exists, at least not one that can be executed many million times per second, which is required in digital imaging. See also my answer below. --Uli Zappe (talk) 20:36, 1 November 2017 (UTC)

Not objectively defined?
It's said that LMS is "represented by the response of the three types of cones", which as far as I understand are objectively defined, even though subject to experimental error and human to human variance. XYZ is also objectively defined by its color-matching functions, defined as spectral response curves. How comes that this article claims that "no single, objective transformation matrix between XYZ and LMS exists" and gives a bunch of such different matrices? It looks like there is a logical step missing in the exposition. bungalo (talk) 16:59, 26 July 2017 (UTC)
 * I agree. I'm inclined to remove those. This article does list several potential XYZ -> LMS matrices. I haven't looked into the details of all of them, but I suspect they were chosen for various engineering reasons. Either way, their results are similar. It appears that the first listed one maps the CIE XYZ curves very close to the cone-cell responses. The only thing it doesn't reproduce is the concave notch on the top-right of the S curve and the roughness atop the R curve. I'd be interested in understanding the details more. For example, were the precise LMS curves known in the 1920s through 1931 when the XYZ curves were defined? Would it be within experimental error of the XYZ curves to have different XYZ curves that are a linear combination of the precise LMS curves? —Ben FrantzDale (talk) 00:41, 28 October 2017 (UTC)
 * The trouble is that XYZ is defined by psychophysical experiments, and LMS by physiological. Both are objective, yet subject to some error.  So different estimates of each lead to different matrices relating them.  There may be some modern accepted standards and matrices; I'm not sure.  The XYZ curves have been standardized, so you don't need to worry about variation there, since 1931, but the LMS curves are not standardized, as far as I know, so may be a source of variation in otherwise objective measurements. Dicklyon (talk) 03:55, 28 October 2017 (UTC)
 * "Would it be within experimental error of the XYZ curves to have different XYZ curves that are a linear combination of the precise LMS curves?" Maybe, sort of.  If we had precise LMS curves, it might turn out that the standardized XYZ curves of 1931 are not quite equal to linear combinations of those, due to errors in the psychophysical measurements that led to the XYZ standard observer curves.  So depends on what you mean by "within experimental error" I guess. Dicklyon (talk) 03:59, 28 October 2017 (UTC)
 * Actually, I think the premise of that section is pretty messed up. The difference between chromatic adaptation transforms is precisely because they mostly do NOT use LMS as the space in which to do the adaptation. Dicklyon (talk) 04:03, 28 October 2017 (UTC)
 * According to Fairchild, Mark D. (2013). Color Appearance Models (3rd ed.), page 178, chromatic adaptation transforms universally do use the LMS color space. The problem with the LMS is that it ideally represents one objectively existing physiological color space, but there is no simple mathematical transform from XYZ to it. So the existing XYZ → LMS transforms are all approximations which are optimized for one task or another. --Uli Zappe (talk) 20:27, 1 November 2017 (UTC)
 * He more or less says that on p. 182. However, in my experience, I'd say that's not quite true, as there are "adequate" chromatic adaptation transforms using spaces other than LMS as the adaptation space. Perhaps not quite as accurate, to the extent that the von Kries hypothesis is accurate, but nevertheless probably not "worse" in any sense that matters to viewers. But Fairchild also notes that "Fortunately, cone responsivities can be accurately represented using a linear transformation of CIE tristimulus values."  I think the point is that whatever approximations we have for LMS are plenty accurate enough for such applications. Dicklyon (talk) 01:57, 4 January 2019 (UTC)

Here is my go at explaining how XYZ and LMS are linked. This is not good enough for putting in the article but I hope it may be the basis for a future edit...

The XYZ values can be calculated from the spectrum and the CIE 1931 XYZ weights. The LMS values can be calculated from the spectrum and the CIE 2006 LMS weights. Both sets of weights ought to be the same as they both describe the response of the human eye. However, they are not the same, so there is no way to transform directly from one to to the other using a 3x3 matrix. The various matrices are approximations. The differences between the matrices can be visible. There are other possible matrices - I have an experimental one that is better at preserving perceptual hue (research in progress).

The 2006 LMS weights are based on direct experimental techniques that were not available in 1931, so LMS is probably more accurate of the two. There is a large corpus of research data in 1931 XYZ which cannot be converted to LMS if the original experimental spectra were not recorded.

Richard A Kirk (talk) 15:58, 3 January 2019 (UTC)


 * They're not "the same", but ideally the XYZ and LMS functions span pretty nearly the same 3D subspace of the spectrum space. I haven't seen sources that characterize to what extent they miss.  Do modern LMS measurements really not fit well with the 1931 XYZ standard?  I'd like to see what you have on this.  Dicklyon (talk) 01:57, 4 January 2019 (UTC)

Thanks for your work on this. Expert help is needed to improve the article. North8000 (talk) 13:32, 4 January 2019 (UTC)

So, the answer to my original question above seems to be that LMS and original XYZ functions do not span the same 3D subspace of the spectrum space. Accordingly one can define different different matrices to convert from LMS to XYZ based on different optimality metrics. I edited the article accordingly to remove the vague phrasing.

Also, according to http://cvrl.ucl.ac.uk/database/text/cienewxyz/cie2012xyz2.htm there's a proposal to redefine XYZ based on LMS. That would give a unique "objective" transformation for the new XYZ.

bungalo (talk) 03:19, 31 May 2019 (UTC)


 * I don't think that source says that at all;
 * What part it doesn't say?
 * The source doesn't say, as far as I can see, that the new proposal would end up significantly different from the current XYZ definition. Dicklyon (talk) 10:37, 3 June 2019 (UTC)


 * LMS and original XYZ functions do span the same 3D subspace, very nearly; I don't see sources indicating that the difference is important; certainly not important to color appearance models. And that paragraph you edited is a mess of confusion between linear colorspaces and color appearance models; your edit did not address its main problem.  I removed the offending paragraph, as it totally conflates the linear subspace question with the appearance modeling question. Dicklyon (talk) 06:05, 31 May 2019 (UTC)


 * If it is so nearly the same subspace, can you explain then why there are multiple different matrices? Shouldn't the transform be unique? I'm genuinely trying to understand that. bungalo (talk) 19:25, 31 May 2019 (UTC)
 * Yes, if it was exactly the same subspace there would be a unique matrix. What matrices are you looking at?  How different are they?  Dicklyon (talk) 10:37, 3 June 2019 (UTC)
 * Though I suppose if they make Y from the "corrected" luminosity curve, it will be different by that much. Do you have matrices for both versions?  Dicklyon (talk) 17:04, 3 June 2019 (UTC)
 * I think the real confusion is that the article is using LMS for the various chromatic adaptation spaces; and it says "the LMS response spectra cannot be exactly expressed as linear combinations of the original XYZ color matching functions"; but as I mentioned above, Fairchild notes that "Fortunately, cone responsivities can be accurately represented using a linear transformation of CIE tristimulus values." Are there sources that contradict Fairchild on this? If not, let's back off on that, and if yes let's see what they say. Dicklyon (talk) 17:12, 3 June 2019 (UTC)

First of all, sorry that I did not participate in this discussion for so long; Wikipedia simply did not notify me of any changes in the article or the discussion, for whatever reason (thanks to Dicklyon for pointing out the ongoing discussion to me!). Second, it might well be that the paragraph discussed here was not clearly phrased, as I'm not an English native speaker. However, it was correct in its content:


 * 1) All relevant chromatic adaption models in colorimetry assume the LMS color space. (Fairchild, p. 182 [all emphases here and below are mine]: Any physiologically plausible model of chromatic adaptation must act on signals representing the cone responses (or at least relative cone responses) or simple combinations thereof.)
 * 2) XYZ and LMS are not identical, although they are similar. Therefore, a conversion is required.
 * 3) The context of color appearance models is practical applications in image and video technology. This means that millions of pixels must be converted without noticeable delay; therefore, the conversion must be simple (i.e. a linear matrix transform).
 * 4) The relation between LMS and XYZ is not linear; therefore, all linear transformations are approximations. Dicklyon quoted Fairchild, but omitted the context. The complete quote is: Fairchild, p. 182: Thus, in applications for which the use of CIE colorimetry is important, it is necessary to first transform from CIE tristimulus values (XYZ) to cone responses (denoted LMS, RGB, or rgb depending on the model). Fortunately, cone responsivities can be accurately represented using a [not: “the”] linear transformation of CIE tristimulus values. An example of such a transformation is graphically illustrated in Figure 9.1. This transformation, or a similar one, is common to all chromatic adaptation and color appearance models that are compatible with CIE colorimetry. This complete quote should make it clear that there is not “one” (i.e. a 100% precise) transformation, but several competing ones. Which one, depends on the color appearance model. Clearly, “accurately” is used in a “wider” meaning by Fairchild.
 * 5) It is true that the differences between LMS and XYZ are not huge. So one might think they don’t matter. In fact, that was the line of thinking of the International Color Consortium when they introduced ICC color management: For chromatic adaptation, they originally intended to use the van Kries chromatic adaptation transform method directly in XYZ, to reduce the required calculations. However, this turned out to lead to unsatisfactory results in many cases, so nowadays, the Hunt-Pointer-Estevez transformation matrix or the Bradford transformation matrix are used to convert XYZ to LMS before applying the van Kries chromatic adaptation transform method. (Most profiling software still offers “XYZ” as a chromatic adaptation setting, meaning van Kries in XYZ.) The takeaway from all this is that the difference between LMS and XYZ might seem small, and between the various transformation matrices even smaller, but the differences do matter to the eye. Which transformation matrix you prefer is, in the end, an artistic decision in each singular case. This is what I meant by not objectively defined.
 * 1) The relation between LMS and XYZ is not linear; therefore, all linear transformations are approximations. Dicklyon quoted Fairchild, but omitted the context. The complete quote is: Fairchild, p. 182: Thus, in applications for which the use of CIE colorimetry is important, it is necessary to first transform from CIE tristimulus values (XYZ) to cone responses (denoted LMS, RGB, or rgb depending on the model). Fortunately, cone responsivities can be accurately represented using a [not: “the”] linear transformation of CIE tristimulus values. An example of such a transformation is graphically illustrated in Figure 9.1. This transformation, or a similar one, is common to all chromatic adaptation and color appearance models that are compatible with CIE colorimetry. This complete quote should make it clear that there is not “one” (i.e. a 100% precise) transformation, but several competing ones. Which one, depends on the color appearance model. Clearly, “accurately” is used in a “wider” meaning by Fairchild.
 * 2) It is true that the differences between LMS and XYZ are not huge. So one might think they don’t matter. In fact, that was the line of thinking of the International Color Consortium when they introduced ICC color management: For chromatic adaptation, they originally intended to use the van Kries chromatic adaptation transform method directly in XYZ, to reduce the required calculations. However, this turned out to lead to unsatisfactory results in many cases, so nowadays, the Hunt-Pointer-Estevez transformation matrix or the Bradford transformation matrix are used to convert XYZ to LMS before applying the van Kries chromatic adaptation transform method. (Most profiling software still offers “XYZ” as a chromatic adaptation setting, meaning van Kries in XYZ.) The takeaway from all this is that the difference between LMS and XYZ might seem small, and between the various transformation matrices even smaller, but the differences do matter to the eye. Which transformation matrix you prefer is, in the end, an artistic decision in each singular case. This is what I meant by not objectively defined.
 * 1) It is true that the differences between LMS and XYZ are not huge. So one might think they don’t matter. In fact, that was the line of thinking of the International Color Consortium when they introduced ICC color management: For chromatic adaptation, they originally intended to use the van Kries chromatic adaptation transform method directly in XYZ, to reduce the required calculations. However, this turned out to lead to unsatisfactory results in many cases, so nowadays, the Hunt-Pointer-Estevez transformation matrix or the Bradford transformation matrix are used to convert XYZ to LMS before applying the van Kries chromatic adaptation transform method. (Most profiling software still offers “XYZ” as a chromatic adaptation setting, meaning van Kries in XYZ.) The takeaway from all this is that the difference between LMS and XYZ might seem small, and between the various transformation matrices even smaller, but the differences do matter to the eye. Which transformation matrix you prefer is, in the end, an artistic decision in each singular case. This is what I meant by not objectively defined.
 * 1) It is true that the differences between LMS and XYZ are not huge. So one might think they don’t matter. In fact, that was the line of thinking of the International Color Consortium when they introduced ICC color management: For chromatic adaptation, they originally intended to use the van Kries chromatic adaptation transform method directly in XYZ, to reduce the required calculations. However, this turned out to lead to unsatisfactory results in many cases, so nowadays, the Hunt-Pointer-Estevez transformation matrix or the Bradford transformation matrix are used to convert XYZ to LMS before applying the van Kries chromatic adaptation transform method. (Most profiling software still offers “XYZ” as a chromatic adaptation setting, meaning van Kries in XYZ.) The takeaway from all this is that the difference between LMS and XYZ might seem small, and between the various transformation matrices even smaller, but the differences do matter to the eye. Which transformation matrix you prefer is, in the end, an artistic decision in each singular case. This is what I meant by not objectively defined.

So I still think my last version from yesterday which Dicklyon just changed is the correct one; it certainly might be better phrased.

In any case, his change from Since colors in any color space (such as sRGB) can, by definition, be transformed to the XYZ color space to Since colors in most colorspaces can be transformed to the XYZ color space is incorrect twice: First, all color spaces are defined in XYZ coordinates, and second, if only “most” color spaces were defined in XYZ coordinates, then it would be a non sequitur that for the chromatic adaption of any color space you would need only one additional transformation, the one from XYZ to LMS. So if, against the best of my knowledge, there was a color space that is not defined in XYZ coordinates (which one?), then the whole argument would have to be changed.

Finally, with regard to XYZ vs. LMS: XYZ resulted from psychophysical experiments in the late 1920ies, where probands tried to adjust red, green and blue lights to match a target light visually. LMS stems from physiological, spectroscopic measurements of the cone cells in the 1990ies. It is remarkable how close the results are, but they are not identical, and there is no formula to translate one into the other precisely. CIE XYZ is deeply ingrained in all color technology we have today; I see no way in the foreseeable future to replace it by LMS.

For now, I will revert the paragraph to my last version from yesterday. Feel free to improve it phraseologically, but please discuss here before changing the content of the paragraph again. I will try and watch this page in case Wikipedia notifications still won’t work; if I seem to miss something, you can also reach me through my user talk page (where Wikipedia notifications do work). Uli Zappe (talk) 01:51, 4 June 2019 (UTC)

I think that one can learn more from the talk page than the article! :-)  Please stick around. North8000 (talk) 11:28, 4 June 2019 (UTC)


 * Indeed, discussion is useful. I'll get back to this eventually, but I'm busy vacationing in Portugal for a few weeks. Dicklyon (talk) 21:57, 4 June 2019 (UTC)
 * I'll work on comments starting with the 5 numbered points above.
 * 1. "All relevant chromatic adaption models in colorimetry assume the LMS color space." I very much disagree. Fairchild sort of says this, but doesn't really support it.  The Bradform transform, for example, uses what's been called a "sharpened LMS", which not very close to LMS color space.
 * 2. "XYZ and LMS are not identical, although they are similar. Therefore, a conversion is required."  So stipulated.  We're talking about whether they span the same 3D subspace of spectrum space; nobody has ever suggested they're identical.
 * 3. "the conversion must be simple (i.e. a linear matrix transform)". Not sure we agree on why, but yes we're talking about linear matrix transforms.
 * 4 "The relation between LMS and XYZ is not linear". I do not agree.  As usually understand, both LMS and XYZ are linear transformations from spectrum space. The fact that some color appearance models include a small nonlinearity is a red herring.  Fairchild's discussion of different transforms used in chromatic adaptation methods is not a statement about what the LMS space is.
 * 5 These comments are about chromatic adaptation methods, and I do not disagree that it's complicated and that preferences come into it. But as I said several times above, that's different from the question of whether the LMS and XYZ spaces can be linearly related.   And if these two spaces do not quite span the same 3D subspace of spectral space, then no nonlinearity or choice of different linear transform is going to fix that problem.  It is conceivable that the reason some other transforms are preferred over von Kries has to do with such a mismatch, but I have never seen any evidence in support of such a claim.
 * More as I have time. ... Dicklyon (talk) 21:52, 10 June 2019 (UTC)


 * A short reply; I won’t have much time for the next 1-2 weeks.


 * The Bradform transform, for example, uses what's been called a "sharpened LMS", which not very close to LMS color space. Well, it’s based upon it, as the name suggests. And Fairchild writes signals representing the cone responses (or at least relative cone responses) or simple combinations thereof, so he doesn’t talk about the one and only LMS. We could argue about what exactly distinguishes a signal to “represent cone responses”, but luckily, in the end we need not do this, since we agree that
 * some conversion must be performed, anyway.
 * We agree.
 * As usually understand, both LMS and XYZ are linear transformations from spectrum space. I never heard that this is a usual understanding, and I disagree strongly. LMS is based on objective, physiological/physical measurements (the spectral absorption of the cone cells), XYZ is based on the subjective sensation of “color”, something that doesn’t even exist in the physical realm. They cannot possibly be mere “transformations” from the same entity, because they are located on completely different epistemological levels. If anything, it’s truly remarkable how similar they are.
 * But as I said several times above, that's different from the question of whether the LMS and XYZ spaces can be linearly related. No, of course they can’t. Apart from the epistemological background, this can easily be checked empirically. Data for XYZ and LMS is available on the net. AFAIK, no-one has ever managed to transform one set of data to the other precisely; only approximations are possible. In your reply to bungalo above, you pointed out yourself that the proposal in http://cvrl.ucl.ac.uk/database/text/cienewxyz/cie2012xyz2.htm would end up significantly different from the current XYZ definition. If a transformation to XYZ proper was possible, this proposal would have certainly preferred it to the one they actually suggested.
 * What exactly in the article do we argue about? What is incorrect from your POV? Uli Zappe (talk) 23:06, 10 June 2019 (UTC)


 * Maybe we should insert a paragraph before XYZ to LMS which points out that
 * LMS stems from physiological data whereas the whole CIEXYZ colorimetry is based upon psychophysical data
 * that therefore, XYZ and LMS are very different animals and a precise transformation between these two “color spaces” is impossible but
 * that the CIEXYZ colorimetry needs LMS for chromatic adaption and that therefore, approximate transforms were created in the context of color appearance models which, among other tasks, all model chromatic adaption.
 * Because it isn’t self-explanatory why you would want to transform a physiological model into a psychophysical model at all. What do you think? Uli Zappe (talk) 01:58, 11 June 2019 (UTC)

I can't vouch for it's accuracy but it sounds like a good addition. North8000 (talk) 11:06, 11 June 2019 (UTC)


 * Maybe we can come up with something. But first, we should realize that the physiological and psychophysical approaches are both trying to get at the same thing, except that the physiological approach is more specific.  That is, both are trying to measure the 3D subspace of spectra that color is perceived in.  Both recognize that the three cone types are the relevant sensors.  In the physiological experiments the properties of the three cone types are measured directly and used as color matching functions.  In the psychophysical, we only measure color matching, and then produce a sort of arbitrary set of color matching functions that span the relevant space.  If both experiments are accurate, both sets of color matching functions will span the same 3D subspace of spectra.  If they don't, it's due to experimental error, not to the two approaches measuring different things.  Some books about such things:, , .  I'm afraid that Uli is far from understanding this when he says "it isn’t self-explanatory why you would want to transform a physiological model into a psychophysical model".  I mean, I agree it isn't self-explanatory, but we need to understand that these are not different models, just different experimental approaches to quantifying the model. Dicklyon (talk) 21:31, 11 June 2019 (UTC)
 * Plus, as I said before a few times, all this stuff about chromatic adaption methods is a red herring. The differences between the various transforms used in chromatic adaptation methods, in terms of their supposed LMS color matching functions, is large compared to the experimental errors between the various generations of CIE standard observer color matching functions and the proposed new ones based on the Stockman & Sharpe cone fundamentals.  That is, though there are minor discrepancies, the agreement between the psychophysical and physiological method is pretty good, and there is a narrow range of matrix transforms that will relate them, compared to the wider range of matrix transforms used in chromatic adaptation methods.  And when something like the Bradford method is specified by a matrix from XYZ to its "sharpened LMS" or other adaptation space, that matrix necessarily presumes operating within the 3D subspace defined by the 1931 CIE standard observer color matching functions; direct physiological measurements of LMS are not involved.  However, when such methods are applied to actual camera data, the real big discrepancy is from the fact that the RGB camera sensors do not even nearly satisfy the Luther–Ives condition; that is, the camera is measuring the wrong subspace, so chromatic adaptation methods based on human color vision are just a crude starting point for trying to get good-looking color out of them.  That's why there are so many such methods.  Dicklyon (talk) 21:33, 11 June 2019 (UTC)
 * But first, we should realize that the physiological and psychophysical approaches are both trying to get at the same thing – I'm afraid that Uli is far from understanding this when he says "it isn’t self-explanatory why you would want to transform a physiological model into a psychophysical model". I mean, I agree it isn't self-explanatory, but we need to understand that these are not different models, just different experimental approaches to quantifying the model. – We have a basic disagreement here. These are very different models, for there is no such thing as “colors” in physics and no such things as “spectra” in human perception. And the only way to find out if and how electro-magnetic spectra and human color perception correlate, is to perform both kinds of experiments and then compare them. And yes, it turns out they correlate amazingly close. But that does not make them the same thing. If they wouldn’t correlate that much for whatever reason, clearly the psychophysical experiments would be authoritative for color related calculations, not the physiological ones. Your equation makes sense only under the premise of psychophysical reductionism which you cannot presume to be universally accepted in the theory of science.


 * LMS describes the spectral subspace that human cone cells respond to. XYZ describes the color space humans can perceive. If we take terminology seriously, I wouldn’t even call LMS a “color space”, it’s a “spectrum space”, and as such, completely different from all the “color spaces” we deal with within CIEXYZ colorimetry. The whole CIE colorimetry is based on XYZ, so you really need an explanation why someone working in colorimetry would want to correlate XYZ with LMS (apart from scientific interest). That being said, I’m open to other explanations of why there is XYZ and LMS, what is their difference, why the correlation between the two is relevant, and why there are different, competing transforms. But I do think some kind of substantial, easy-to-understand explanation should be given. Uli Zappe (talk) 01:58, 12 June 2019 (UTC)
 * The alternative to what you call "psychophysical reductionism" here is that human color comparisons are based on some other kind of physical sensor signals than just what the three types of cone cells measure. At low light levels, where rod cells are relevant, that's true, but I don't think that's the domain we're talking about here.  The single (reductionist) model that I'm talking about is that color perception is mediated by the three types of cone signals.  My impression is that that model is universally accepted in color science.  Dicklyon (talk) 09:48, 12 June 2019 (UTC)
 * The alternative to what you call "psychophysical reductionism" here is that human color comparisons are based on some other kind of physical sensor signals than just what the three types of cone cells measure. Uhm, no. That would again be psychophysical reductionism. The non-reductionist alternative is that color comparisons are not exclusively based on physical sensor signals of whatever kind. In the sense that (from the non-reductionist POV) there is no way to understand what a person is thinking or feeling by measuring her/his brain wave activity, or to transform one into the other. But I agree that this is a discussion beyond the scope of this article. My plea for this article would be to remain neutral with regard to the reductionism problem, which means you cannot state that the physiological and psychophysical approaches are both trying to get at the same thing, which is 100% the reductionist POV. Even from a simple “didactic” perspective I think it makes sense to point out that the difference between XYZ and LMS is of a different kind than the differences between XYZ, Lab, sRGB etc. (Which is true for both the reductionist and the non-reductionist POV: In the reductionist POV, XYZ and LMS describe the same thing, and the difference is only due to imprecise measurements, historical contingencies etc., whereas Lab, sRGB etc. are different in that they are transformations. In the non-reductionist POV, XYZ and LMS are located on different epistemological levels which can, by principle, never be 100% transformed into each other, whereas Lab, sRGB etc. are mere transformations on the same epistemological level.)
 * Yes, certain aspects of color science are pretty reductionist. In particular, the models and experiments that went into defining the XYZ system via color matching experiments presumes that there is a 3D subspace of spectra that needs to be identified, because we have three spectral sensitivities of light detectors.  No part of the brain is involved here except for saying when the stimuli are equivalent, which is completely determined by the quantum efficiencies (vs. wavelength) of the opsins involved.  Color scientists knew this when they did the experiments and defined the XYZ system (or knew something like this; I don't know how much was known about opsins at the time).  They had no model that depended on what a person is thinking or feeling; they only needed to say to turn this knob until the two sides match.  They predumed that the match would depend on the signals from three sensor types.  In these respects, XYZ space is no different from LMS space, except that in the measurement of the opsins themselves a free linear transformation is pinned down (it's just a "rotation" within the 3D subspace of colors).  XYZ is a "spectrum space" in the same way that you say LMS is.  And they call the coordinates "tristimulus" values because they are the effective stimuli to the visual system, not the response or percept, which are very nonlinearly related to the stimulus, via many layers of nonlinear neurons starting in the retina.  Dicklyon (talk) 22:30, 12 June 2019 (UTC)
 * Once again, one can learn more from the talk page than the article. Thanks to you two. North8000 (talk) 01:23, 13 June 2019 (UTC)
 * Well, yes, but our goal should be to make the article just as informative.
 * They had no model that depended on what a person is thinking or feeling; they only needed to say to turn this knob until the two sides match. But they could only say this because of their perception of color, which is something that does not exist in the physical world, only in our mind (just as thoughts and feelings). We see color (not spectra), and we measure spectra (not color). No part of the brain is involved here except for saying when the stimuli are equivalent, which is completely determined by the quantum efficiencies That’s again only true for the reductionist POV. The non-reductionist POV would point out that no human can say whether stimuli are equivalent, she/he can only say whether colors are equivalent – simply because humans have no way to perceive “stimuli”. Whether equal stimuli means equal color perception is impossible to know a priori. It might turn out to be true as a result of two experiments, one to measure color perception (psychophysical) and one to measure stimuli (physiological), but this still does not mean that stimuli and colors are the same thing. The result of these two experiments is not (the rather trivial) A ≙ A, but rather (the more meaningful) A ≙ B. Martians without eyes but with highly developed measurement technology would have no difficulty at all to measure the stimuli of human cone cells, but they’ll have not the slightest idea what “color” is.


 * But back to the article. I would assume the average reader of this article has at least some basic knowledge of colorimetry and knows about XYZ and comes here because she/he is confused why there is this additional thing called LMS, that somehow seems to be almost the same as XYZ, and then again, not (because there are not only one, but several competing transformations between the two). We must answer this question in a profound but epistemologically neutral way. One explanation is the one I tried to articulate – XYZ and LMS located on different epistemological levels, not precisely transformable, therefore only several competing approximations. Dicklyon, what would be your alternative suggestion? XYZ and LMS differ for only historical reasons and should ideally be consolidated, color appearance models and their transformations are a different subject? But then why are there several competing transformations? If XYZ and LMS differed for only historical reasons, then there should be one optimal and therefore canonical approximation – but which one is it?


 * How do we proceed from here to come up with an improvement for the article? Uli Zappe (talk) 02:52, 13 June 2019 (UTC)

I know a lot of people who are considered experts in color measurement (including myself) who could probably recite half the stuff in the Wikipedia color articles, but who have no fundamental understanding of the things being discussed on this talk page. May I suggest starting with fundamental explanations of the underlying concepts without assuming an unde4rstanding.....especially transformations and how the various color spaces/standards do and don't connect with human perception? North8000 (talk) 03:05, 13 June 2019 (UTC)
 * The problem is that to do this, we’d first have to agree what these underlying concepts are. I tried to back up my explanation with quotes from Fairchild, which, admittedly, could be clearer than they are. Dicklyon, are there sources for your POV?
 * What can we already agree upon? Hopefully at least that LMS is physiological, XYZ (and the whole CIE colorimetry that is based on it) is psychophysical, and that this is a difference which should be pointed out. As to the consequences of this difference, so far we have no common understanding.
 * North8000, when you write fundamental explanations of the underlying concepts […] especially transformations, do you mean it should (also) be explained what linear transformations are, or do you only mean it should be explained which role they play in the context of LMS? Uli Zappe (talk) 11:48, 13 June 2019 (UTC)
 * I don't think we can do a good job of a color science tutorial here. But I must say I find Uli's approach to be idiosyncratic. In my experience, colorimetry wrt to CIE spaces is physical, not so much psychophysical. It's about quantifying what is the space of effective stimuli for human color perception, not about the rest of the perceptual mechanism. XYZ and LMS are not on "different epistemological levels" in any treatment I've ever seen, and the small discrepancies in transformations between them are just due to small experimental error. The different transformations that he speaks of (if I may repeat for the Nth time) are about different strategies for chromatic adaptation of camera data, not much to do with LMS or XYZ per se. And why are there different spaces? Because they evolved for different purposes, like uv space and Lab and others. The XYZ space specifically was chosen to have one of the color matching functions represent luminance. The LMS was chosen to have the color matching functions describe the cones. But they both describe (very nearly) the same subspace, because they are both from experiments aiming to quantify the same model. Dicklyon (talk) 11:55, 13 June 2019 (UTC)
 * Color science tutorial or not, obviously we must do something to improve this article.
 * In my experience, colorimetry wrt to CIE spaces is physical, not so much psychophysical. – How so? Color does not even exist in the physical world, how can colorimetry possibly be only physical? If it was purely physical, the experiments used to create XYZ would have only involved measurement equipment. But that was not the case. People were involved as test objects who were asked what they see. If that is not a prime example of a psychophysical test setting, I don’t know what is. This is not a question of experience, but of understanding theory of science. If you mean by “experience” that you haven’t met many people practicing colorimetry who are aware of this theoretical background, that might be the case, but is no argument.
 * And why are there different spaces? Because they evolved for different purposes, like uv space and Lab and others. – But each of the transformations between XYZ and uv space and Lab and others is unambiguous and precisely defined, without any approximations. The transformation between LMS and XYZ is not. Why? Uli Zappe (talk) 12:26, 13 June 2019 (UTC)
 * I thought we agreed that the XYZ and LMS spaces are based on different experimental data, and that LMS is not part of what the CIE standardized. So there a minor differences due to different experimental error.  But do we also agree that these differences are small compared to say the difference between the LMS and Bradford spaces used in chromatic adaptation? Dicklyon (talk) 16:06, 17 June 2019 (UTC)

A good book on standard colorimetry
Standard Colorimetry: Definitions, Algorithms and Software by Claudio Oleari is a book that goes into great detail on the various standards and definitions. It treats LMS as "psychophysical", but see its definition of that at the start of chapter 1, which is based on color matching. It treats LMS as a linear transformation of XYZ and such. Anyway, give it a look. Dicklyon (talk) 16:37, 13 June 2019 (UTC)
 * Thank you so much!  Selection by an expert means an immense amount.   I bought it and am reading it. Sincerely,. North8000 (talk) 01:19, 18 June 2019 (UTC)
 * Other than what I just found by looking at it online, I don't know the book. But it looks good.  I hope it will help you help us here. Dicklyon (talk) 17:54, 18 June 2019 (UTC)
 * Well, it depends on the exact usage of terminology. Wikipedia says (and rightly so): Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they produce. Ideally speaking, LMS is the only purely physiological entity in colorimetry (no sensations and perceptions involved, only spectral absorption of cones). Only when you want to point out that the interest in the physiological data of LMS is to correlate it to psychological data in a psychophysical procedure, you might call LMS itself already “psychophysical”.


 * But as I wrote, that’s the idealized situation. Turns out that in reality, Stockman & Sharpe, who probably are the canonical authors here, combined their physiological measurements with psychophysical ones; Spectral sensitivities of human cone visual pigments determined in vivo and in vitro has both in vivo and in vitro already in its title.


 * And there’s more. The CIE proposal for a definition of LMS, which makes use of the work of Stockman & Sharpe, is described as follows in the Info window [emphasis is mine]: The cone spectral sensitivities are defined as linear combinations of the Stiles and Burch (1959) 10-deg CMFs […] Their derivation requires a knowledge of the five unknowns […]in the following equations: […] Stockman, Sharpe & Fach (1999) and Stockman and Sharpe (2000) estimated the five unknowns from L- and M-cone spectral sensitivity measurements in single-gene red-green dichromats, S-cone spectral sensitivity measurements in blue cone monochromats and normals, and from existing color matching data. So not only did Stockman & Sharpe indeed use psychophysical data for their definition of LMS, they also started out from the existing CIE CMFs, i.e. their work resulted in a linear transform by approach, and it’s only an(other) estimation.


 * So in the end, this formula (already proposed as a CIE standard in 2006 and still not finalized …) is just one more approximation for the transform between XYZ and LMS, in addition to Hunt-Pointer-Estevez and Bradford. It would be interesting to compare these three transformations; I might find time to create graphs with this data, but only in a few weeks at the earliest, as I’m extremely busy now. I won’t be able to reply again before next week. Uli Zappe (talk) 22:24, 13 June 2019 (UTC)
 * The Bradford transform is not, and never was, an attempt to approximate LMS. Not sure about the Hunt-Pointer-Estevez; I'll look. Dicklyon (talk) 22:28, 13 June 2019 (UTC)
 * According to Fairchild, it is … Uli Zappe (talk) 22:36, 13 June 2019 (UTC)
 * Bradford's color matching functions are not even nonnegative, so can't be spectral sensitivity curves. What does Fairchild say? Dicklyon (talk) 22:39, 13 June 2019 (UTC)
 * The CIECAM02 paper says sharpening is OK (like in Bradford) in chromatic adaptation, but "The nature and degree of this sharpening is still subject to debate but it should be noted that CAT02 does incorporate some degree of sharpening. In comparison the use of a space closer to the cone fundamentals, such as the Hunt-Pointer-Estevez or Stockman-Sharpe fundamentals, provides better predictions of perceptual attribute correlates."  So Hunt-Pointer-Estevez is "closer" to LMS, but I haven't found exactly what it is or where it comes from.  Do you know? Dicklyon (talk) 22:45, 13 June 2019 (UTC)

Sorry it took me so long to reply. As I wrote, I was (and probably still will be) short on time.

First, concerning the recent change on the article page by Dicklyon: Again, you wrote that Since colors in most colorspaces can be transformed to the XYZ color space. Why most? Which color spaces are exceptions? As I already tried to explain, the conclusion in the remaining sentence (that you only need one additional conversion from XYZ to LMS) becomes wrong in this case, because for the color spaces that cannot be converted to XYZ a conversion from XYZ to LMS won’t help. Also, the following paragraph assumes that this paragraph explains what a CAT is, which it currently does not. So independently from our discussion about LMS, this paragraph can’t stay the way it is now.

To proceed with our discussion about what LMS is and is not, I created a graph depicting XYZ and several approaches to LMS:



Data sources:

Mark D. Fairchild: Color Appearance Models, Wiley Interscience, 2013 (3rd edition)

Jan Henrik Wold: XYZ representations of the Stockman-Sharpe-Fach cone fundamentals with alychnae referring to the Sharpe-Stockman-Jagla-Jägle luminous efficiency functions for daylight adaptation, Oslo, 2008, PDF

CVRL Database

It’s a bit hard to cram that much information into one graphic. I tried it as follows and hope it’s readable:

The well-known CIE 1931 XYZ color matching functions (CMFs) are displayed in uniform light gray as a reference in the background.

The CMFs of the “classical” LMS color spaces, which were created for color appearance models, are displayed in thin lines with saturated colors: Hunt–Pointer–Estevez (solid lines), Bradford (dashed lines), CAT02 (dotted lines). These were calculated from the CIE 1931 XYZ CMFs and the respective conversion matrices in Fairchild.

The CMFs of the Stockman-Sharpe-Fach LMS color space, which aims at being a “physiologically relevant” LMS color space, are displayed in thick solid lines with pastel colors. These were calculated from the “2-deg XYZ CMFs transformed from the CIE (2006) 2-deg LMS cone fundamentals” in the CVRL database and the inverse LMS to XYZ conversion matrix in Wold, p. 17.


 * All LMS spaces move Green and Red to the left to a certain extent (≙ smaller wavelength). So it is probably this common feature that makes the von Kries chromatic adaptation transform method work fine in all these color spaces.
 * Blue is almost unchanged except for Stockman-Sharpe-Fach which only differs in amplitude though, not wavelength (this might be based on the new measurements of the S cone that Stockman performed).
 * Hunt–Pointer–Estevez and Stockman-Sharpe-Fach on one hand and Bradford and CAT02 on the other are closer related pairs. The latter seem to exaggerate the Green curve, presumably for better chromatic adaptation results.

The question remains whether the Stockman-Sharpe-Fach LMS is somehow “special” compared to the others.Uli Zappe (talk) 10:41, 7 July 2019 (UTC)

What the units of the vertical axis? I think that a precise answer would be very helpful. Thanks. North8000 (talk) 12:54, 7 July 2019 (UTC)
 * CMFs are always specified with Relative Intensity on the vertical axis, with 1 set to the maximum of the Y (green) curve by definition. Because in a wide range it does not matter how bright (in absolute terms) the light is that the eye reacts upon. (The horizontal axis is wavelength in nm, of course.) Uli Zappe (talk) 13:26, 7 July 2019 (UTC)
 * I guessed that. But what I meant, is that "relative intensity" in terms of physics (e.g. power density), perceived intensity etc. or some other standard? <b style="color: #0000cc;">North8000</b> (talk) 13:33, 7 July 2019 (UTC)
 * Hmm, whether it’s luminance or illuminance or luminous flux or … – all these are linearly related (all else unchanged), so it really does not matter, I think. It’s any one of these. Of course, the CMFs are functions of wavelength, so they operate on the spectral power distribution of a light source. Is this what you meant?
 * BTW: I realize that all three curves of the Stockman-Sharpe-Fach LMS (which I just calculated for this graphic) top almost exactly (0.02 maximum deviation) at 1 which is certainly no coincidence. Uli Zappe (talk) 13:57, 7 July 2019 (UTC)
 * I was trying to get unconfused but perhaps it's a bit early for that. All three of those that you mention contain a a unit (e.g. lumen, candela) which modifies the energy spectrum based on human visual response curves. <b style="color: #0000cc;">North8000</b> (talk) 02:33, 8 July 2019 (UTC)
 * OK, new trial: The vertical axis of the CMFs has no unit because it’s just a modification factor of a spectral power distribution (SPD). It modifies the values in the unit of the SPD, no matter what this is, and the unit itself remains (lumen, whatever …). Therefore, the CMFs have no unit of their own. You simply multiply the CMF value of a specific wavelength with the SPD value at this wavelength. If the CMF had a unit of its own, you would change the unit resulting from this operation, which you do not. Uli Zappe (talk) 08:11, 8 July 2019 (UTC)
 * Thanks! <b style="color: #0000cc;">North8000</b> (talk) 12:10, 8 July 2019 (UTC)
 * The graphic is certainly over-packed and confusing. It would be useful to omit the ones that are not trying to be LMS (XYZ and Bradford and I'm not sure what else), so that we can compare the others that do represent LMS.  The reason I said "most" is that colorspaces are most often defined in terms of transformations from XYZ; that is, it's a widely used standard, shortcomings notwithstanding, since nobody has shown anything better that's compelling enough to take over the industry and science and color.  When spaces are so related, there's no exact transformation between them, but there are still pretty good approximate transformations. Dicklyon (talk) 16:33, 7 July 2019 (UTC)
 * See for example the first paragraph on this page by Fairchild. That the spaces are based on CIE XYZ is assumed.  Several CAT methods use the Hunt LMS space, with different normalizations.  But none of this is all that relevant to the question about what LMS is, or how it's measured or defined, or to how different the different derivations are.  Comparing different normalizations and different not-quite-LMS spaces isn't going to get us closer to that. Dicklyon (talk) 16:41, 7 July 2019 (UTC)
 * It would be useful to omit the ones that are not trying to be LMS – If you omit XYZ you cannot see anymore that all other spaces have in common a shift against XYZ. And all other spaces claim to be representations of LMS, even if you dispute that. There are many more, I limited it to 4 because with even less there’s not much to compare anymore.
 * The reason I said "most" is that colorspaces are most often defined in terms of transformations from XYZ – I still do not understand. From my POV, color spaces are defined in terms of transformations from XYZ not most often, but always. Please name a single color space (apart from LMS) that is not defined in terms of XYZ. If there isn’t, delete the “most”.
 * But none of this is all that relevant to the question about what LMS is – But then what is? I quoted Fairchild to back up my claim that Hunt–Pointer–Estevez, Bradford, CAT02 and others are all LMS representations, which you reject. But you don’t come up with a different description and a quote to back it up. Uli Zappe (talk) 18:01, 7 July 2019 (UTC)
 * Stockman-Sharpe-Fach LMS is not based on CIE colorimetry; the others are; so I thought the question was about how different Stockman-Sharpe-Fach LMS is from the "standards based" (Hunt) one. Please show me again the Fairchild quote yuo're referring to (a diff link or direct quote would be good).  And I still don't get what you think you're going to see by plotting XYZ along with LMS.  It's just a distraction.  And I don't think Bradford was ever claimed as a representation of LMS; rather, it's a "sharpened LMS" as usually described (which means not LMS, but a sharpening transformation away from it).  The LMS curves are necessarily nonnegative; any set that goes negative is not an admissible estimate of LMS. Dicklyon (talk) 18:11, 7 July 2019 (UTC)
 * I thought the question was about how different Stockman-Sharpe-Fach LMS is from the "standards based" (Hunt) one – No, the context in the article is the claim that only one additional transformation (namely, XYZ → LMS) is required to transform any color space to LMS. This claim is true if and only if any color space can already be transformed to XYZ. Of course, in the context of this argument, LMS itself does not count as a non XYZ based color space.
 * Stockman-Sharpe-Fach LMS is not based on CIE colorimetry – Well, it’s connected to the “new” (proposed) XYZ 2006 color space, which is not that different.
 * And I still don't get what you think you're going to see by plotting XYZ along with LMS. – To explore if all other color spaces in this diagram (which all claim to be LMS related) share something in contrast to XYZ. And from my POV, the diagram suggests this might well be the case.
 * And I don't think Bradford was ever claimed as a representation of LMS; rather, it's a "sharpened LMS" – Depending on the definition of LMS, a “sharpened” LMS might still be an LMS.
 * The LMS curves are necessarily nonnegative – Why? By the same rationale, CIE RGB couldn’t be negative.
 * Please show me again the Fairchild quote you're referring to – Fairchild, p. 182: Any physiologically plausible model of chromatic adaptation must act on signals representing the cone responses (or at least relative cone responses) or simple combinations thereof. Thus, in applications for which the use of CIE colorimetry is important, it is necessary to first transform from CIE tristimulus values (XYZ) to cone responses (denoted LMS, RGB, or rgb depending on the model). This is in the introduction to chromatic adaption models, which are then discussed in detail and use (among others) Hunt–Pointer–Estevez, Bradford and CAT02 for the transform from CIE tristimulus values (XYZ) to cone responses (denoted LMS, which clearly says that in Fairchild’s understanding, Hunt–Pointer–Estevez, Bradford and CAT02 are all transforms to LMS. Uli Zappe (talk) 18:48, 7 July 2019 (UTC)
 * But that's not inconsistent with CAT methods that are NOT "physiologically plausible" due to using curves that imply a negative response to some wavelenghts. I think Fairchild work on CATs is continuing to distract you from the issues here.  Statements like Depending on the definition of LMS, a “sharpened” LMS might still be an LMS suggest that you don't know what the definition of an LMS system is; should we try to resolve that?  And yes, LMS spaces are close to each other and far from XYZ; we don't need to plot XYZ to understand that. Dicklyon (talk) 19:24, 7 July 2019 (UTC)
 * But that's not inconsistent with CAT methods that are NOT "physiologically plausible" due to using curves that imply a negative response to some wavelenghts. – You mean Fairchild says there’s also “physiologically implausible” models of chromatic adaptation that nevertheless work fine? That’s far fetched from my POV. And anyway, he says in no uncertain terms, if you want to use CIE colorimetry, a transformation to LMS is required, and all the matrices he lists afterwards (including Bradford etc.) are explicit examples of such transformations.
 * Statements like […] suggest that you don't know what the definition of an LMS system is; should we try to resolve that? – YES, please! And not specifically for me, but for the article. I mean, this is why we are talking here, right? I think I know very well what an LMS is, but you say I don’t. Then please come up with something better which you can back up with a quote.
 * And yes, LMS spaces are close to each other and far from XYZ; we don't need to plot XYZ to understand that. – But we might need it to see that in this respect, Bradford and CAT02 behave like other LMS color spaces. And please, don’t spend too much time on this graphic. It was never meant as an image for the article, but rather as a heuristic help for our discussion.Uli Zappe (talk) 20:09, 7 July 2019 (UTC)
 * Definition: an LMS color space is one in which the tristimulus coordinates attempt to capture the effective stimuli of the three types of human cone cells. Agree? Dicklyon (talk) 06:25, 9 July 2019 (UTC)

I could recite half of what is in all of the color space articles in Wikipedia without looking at them. And the physics side is easy for me. Yet I am unable gain some very basic fundamental understandings of color spaces from the articles. Maybe this dummy would be a good guinea pig for your quest in this article. :-) <b style="color: #0000cc;">North8000</b> (talk) 12:04, 9 July 2019 (UTC)


 * Starting with the lead sentence. "LMS is a color space represented by the response of the three types of cones of the human eye, named for their responsivity (sensitivity) peaks at long, medium, and short wavelengths. "  Why are we talking about the human eye "representing" a color space?    Should it really read "LMS is a color space intended to represent the response of the three types of cones of the human eye, named for their responsivity (sensitivity) peaks at long, medium, and short wavelengths.?  And, if so, since "response" is a perception in people's brains, exactly what does the vertical axis / individual numbers in the triplets of numbers mean?  Feel free to not get into this if you prefer. <b style="color: #0000cc;">North8000</b> (talk) 12:11, 9 July 2019 (UTC)
 * To start with, "response" is the wrong concept here; it's too nonlinear, complicated, perceptual, etc. What LMS is about is the "effective stimulus" that the cones react to, which is a physical/physiological concept (just an intensity with wavelength-dependent spectral weighting).  The weighting functions are what it's all about.  Physically, weights must be nonnegative, unlike RGB and Bradford and other spaces where negative weights are used at some wavelengths.  XYZ also uses nonnegative weighting functions, but not for any physical reason (these "fundamentals" or "color matching functions" were constructed to have various nice properties such as nonnegativity and Y being luminance weighting, but not attempting to represent L, M, and S; the resulting two-humped X curve does not represent anything physiological; LMS curves are one-humped (unimodal), due to how opsins work.  Of course, as Uli says, any set of LMS curves differs from XYZ curves (and RGB curves) in these ways; but should also be nonnegative.  I'm pretty sure the Bradford University folks never claimed their "sharpened LMS" curves were plausible LMS weighting curves. Dicklyon (talk) 14:55, 9 July 2019 (UTC)
 * Just looking at the beginning, doesn't "wavelength-dependent spectral weighting" mean to emulate human perception? Or cone responses (if such can be separated from perception)? — Preceding unsigned comment added by North8000  (talk • contribs)
 * It's a first step in emulating human color vision, which is to compute the effective stimulus that each cone type responds to. How they respond to that physical stimulus is a next step, outside the scope of the objective physical linear color space, but still physiological.  Dicklyon (talk) 17:46, 9 July 2019 (UTC)

The epistemological status of LMS
Just for the ease of editing, I’m starting a new subchapter.

The POV Dicklyon emphasizes is that LMS is a purely physical/physiological concept, measuring spectral absorption of cones or related brain waves or some other physiological entity. Of course, if this is the case, then there is only one LMS. Variance will only stem from measurement dispersion and variance among specimens, so an average of measurements will give us the LMS.

The problem is that whatever LMS is in this concept, it is not a color space, since color does not exist in the physical world. Of course, we could assume that the mental representations of these physical stimuli which create the colors in our brain are somehow linearly related to these physical stimuli. But that’s just an assumption. The only way to find out are psychophysical experiments. If we integrate the results of such experiments in our concept of LMS, then LMS can be a color space, but it is not purely physiological anymore and negative stimuli values are not necessarily a problem.

Since psychophysical experiments arguably offer less precise results, we get several LMS variants in this case. One of them is Bradford. Bradford is most often described as a “sharpened LMS”, and a sharpened LMS is still an LMS, just as a tuned car is still a car. In fact, since chromatic adaption is arguably one of the most basic features of the color processing in our brain, an LMS variant such as Bradley that excels at modelling chromatic adaptation might be considered an especially good model of a psychophysical-physiological LMS.

Looking at my graphic, I still think the least common denominator of purely physiological and psychophysical-physiological LMS is their green/red shift to the left (compared with XYZ). That’s what seems to make chromatic adaptation work reasonably well in all LMS color spaces.

To sum up: We have two approaches to LMS: the purely physiological one (that Dicklyon favors), which makes LMS unambiguous, but in which LMS isn’t a color space, and the psychophysical-physiological one, in which LMS is a color space, but ambiguous and subject to variants as Bradford’s sharpening.

How much of this should be part of the article? Uli Zappe (talk) 16:03, 9 July 2019 (UTC)


 * I'm pretty sure I didn't say anything about absorption or brain waves. But yes, there is essentially only one LMS color space, though formally there are variations based on how it's estimated from experimental data of different sorts.  I'm not sure why you say it's not a color space.  XYZ and RGB spaces are physical in exactly the same way, and I think we mostly agree that they are color spaces.  If you think the Bradford space is an LMS space, or is based on psychophysical experiments, please show evidence for that.  Your observation about "least common denominator" is not wrong, but I fail to see the relevance to anything here. Dicklyon (talk) 17:43, 9 July 2019 (UTC)
 * In "Sharp transformations for color appearance", Hubel and Finlayson 1998 compare "sharp" transforms to the von Kries (LMS) approach in chromatic adaptation. Read the first paragraphs of the introduction:


 * Here are the refs for that paragraph (ref 4 is the source for Bradford):


 * 1) K. M. Braun, M. D. Fairchild, and P. J. Alessi, "Viewing techniques for cross-media image comparisons", Color Res. Appi. 21 (1) pp. 6 - 17, 1996.
 * 2) G.D. Finlayson, M.S. Drew, & B.V. Funt, "Spectral Sharpening: Sensor Transformations for Improved Color Constancy," JOSA, 5:1,553-1,563 (1994).
 * 3) J. von Kries, "Chromatic adaption", Festschrfi der Albrecht-Ludwig-Universitat, 1902.
 * 4) K. M. Lam, "Metamerism and color constancy" Doctoral thesis, University of Bradford, Bradford, UK, 1985.  (this is the Bradford source)
 * I hope this makes it clear that a "sharp" or "sharpened LMS" stands in contrast to the von Kries approach of using LMS. I'm pretty sure I'm not misrepresenting Hubel and Finlayson here; partly on the strength of this work, I hired them shortly afterward to work with me on color at Foveon; I understand them well, and they would never call one of these sharp or sharpened spaces an LMS space, because that would defeat the point. Dicklyon (talk) 19:09, 9 July 2019 (UTC)


 * I'm pretty sure I didn't say anything about absorption or brain waves – You wrote What LMS is about is the "effective stimulus" that the cones react to, which is a physical/physiological concept. If LMS is purely physically/physiologically defined, then you need physical/physiological measurements to determine its characteristic. Spectral absorption (which Stockman used) and brain waves were just possible examples of such methods; which physical methods would you suggest?


 * I'm not sure why you say it's not a color space. – Because there is no such thing as color in the physical world, just electro-magnetic spectra. You could measure the physical response of the cones to spectral stimuli with the utmost precision and would still not have the slightest idea about what color they produce – until you ask a human what she/he sees, i.e. conduct a psychophysical experiment. XYZ and RGB spaces are physical in exactly the same way – No. They are based on psychophysical experiments. Therefore, they can represent color. But at the same time, they are ambiguous. If you consider how XYZ was constructed, it is quite clear that from the same data a different color space could have been constructed as well. This is the same with LMS: As soon as you include psychophysical data in its construction, you’ll get a color space, but not one, but many possible variants.


 * If you think the Bradford space is an LMS space, or is based on psychophysical experiments, please show evidence for that. – I do not deny that there is a school of thought that agrees with your POV; the works you quote support that. But at the same time, there’s as many people (or more) who would argue that any color space a von Kries chromatic adaptation works in is an LMS color space by definition. Fairchild says so in the chapter I already quoted repeatedly and which you persistently ignore or say he didn’t really mean it. Another source would be Henry R. Kang: Computational color technology, Published by SPIE—The International Society for Optical Engineering (PDF), where Kang explicitly lists all CATs as transformations into LMS. Bradford is on page 52, and the Bradford matrix is shown to transform XYZ into LMS in the published equation. Kang also describes the color space generated by the Bradford transform explicitly as representing “cone responsivity”.


 * As I wrote, there seem to be two schools of thought. Your POV represents one of them, but Wikipedia, being an encyclopedia, must reflect both. I freely admit that from my POV, your idea of a “physiologically defined color space” is epistemologically impossible, for the reasons mentioned above (no color in the physical world). Uli Zappe (talk) 23:54, 9 July 2019 (UTC)


 * You're making me crazy. Fairchild is not a supporter of your odd second school of thought, in spite of how you twist his words.  I don't know of any sources supporting the idea that a physical LMS is not a color space or anything else you're saying here.  Color spaces are physical; they define 3D subspaces of spectral space that represent the space spanned by the effective stimuli of cones, and they provide ways to quantify that.  Linear LMS, XYZ, and RGB spaces all do that the same way, with color matching functions that specify spectral weighting, with different aims and constraints; nonlinearities like gamma compression come next.  I can't fathom why you don't get this.  Dicklyon (talk) 03:04, 10 July 2019 (UTC)


 * I can't fathom why you don't get this. – Sorry, but personal insult doesn’t get us any further. I might as well say that I can't fathom why you don’t seem to get the most basic concepts of epistemology.


 * […] spaces […] define 3D subspaces of spectral space that represent the space spanned by the effective stimuli of cones, and they provide ways to quantify that. – Yes, we have no disagreement here. But this in itself has nothing to do with color. I can only repeat: A Martian who does not have eyes as we do, but is a brillant scientist, would not have any difficulty conducting experiments to define these 3D spectral subspaces just as we do. But he wouldn’t learn anything about color when he does that. The only way for him to learn about color would be to talk to a human and ask her/him what s/he sees.
 * Where exactly would you disagree here?
 * But as soon as the Martian asks a human, he leaves the “physical” level and adds a psychological level. So either you have a purely physical 3D spectral space that describes the space spanned by the effective stimuli of cones, or you have a psychophysical 3D color space that describes the space of colors humans can see. But there is no way to get a physical color space.


 * Linear LMS, XYZ, and RGB spaces all do that the same way. – XYZ and RGB are psychophysical color spaces. You maintain LMS is not. So how can they do it the same way? If you agree that LMS, too, is psychophysical, then of course this is true. But then, just as XYZ was just one out of many possible ways to construct a color space out of the raw measurement data, the same would be true for LMS, and there wouldn’t be just one possible LMS. Of course, the scientific community could agree on one specific space being the LMS space, just as it did with XYZ. But the diverse literature seems to make it painfully clear that this standardization of “LMS” does not exist as of today.


 * Fairchild is not a supporter of your odd second school of thought, in spite of how you twist his words. – If we cannot agree on Fairchild, what about Kang? And, BTW, an encyclopedia should maintain a neutral stance. It doesn’t help to characterize a POV that differs from one’s own as “odd”. Uli Zappe (talk) 10:01, 10 July 2019 (UTC)

Maybe this dummy can help sort a few small points out.


 * As I understand it, color space is any system that attempts to define color by 3 (or occasionally 4) numbers. So, to me it looks like LMS certainly is a color space?


 * Is there any widely accepted authority (e.g. CIE) that has defined what LMS is in respect to the disputed areas above? If not, is the alternative is that it's a lot more squishy, where there are various differing prominent views and uses by various experts/authors?

Sincerely, <b style="color: #0000cc;">North8000</b> (talk) 13:33, 10 July 2019 (UTC)


 * As I understand it, color space is any system that attempts to define color by 3 (or occasionally 4) numbers. – Yes, but a long as you stick to the physical world you cannot even attempt to define color, because color does not exist in the physical world and you cannot measure it. Color only exists inside our brain. The only thing that you can measure in the physical world are electro-magnetic waves and their spectra. To find out if and how these correlate with the human perception of „colors“, you must ask humans what they see, no spectrometer will ever tell you. But as soon as you ask humans about their perception, it’s not physical anymore, it’s psychophysical. Since we are all humans, it’s easy to forget that we, as humans, already know what color is from our everyday lives. But as a scientist, you must not use this everyday human knowledge if you want to explore the world on a purely physical basis. Therefore my example with Martians. Uli Zappe (talk) 13:52, 10 July 2019 (UTC)
 * Thanks. I understand that in general terms, and that once we leave the area of pure physics we leave the area where I have a pretty thorough understanding of the math details. I think that to those two universes that y'all are discussing (physics and human perception), I would add a third universe (the english language) which, as a starting point, "color" and "color space" and other terms are merely words in the English language. And it appears that by the widely used meaning of "color space" (any system that attempts to define color by 3 (or occasionally 4) numbers) LMS is (vaguely speaking) a color space or set of color spaces, which was one of the questions in the debates above.  Sincerely, <b style="color: #0000cc;">North8000</b> (talk) 15:17, 10 July 2019 (UTC)


 * You’re certainly correct that the bridging between physics and psychology is one issue that makes “color physics” so difficult. Basically, the same applies to sound waves and sounds, but here, the relations are beautifully simple. Double frequency = the same tone, but one octave higher – it doesn’t geht any simpler than that. With color, unfortunately, it’s the contrary. Therefore, it is said of many musicians that they are akin to mathematicians. You rarely hear that about painters.


 * As for the language, I see your point, and in most contexts, it’s certainly OK to use everyday language without giving much thought to it. But if things get complicated, I think being very precise with language, beyond its everyday usage, helps. And if you do this, you’ll find that you just cannot measure color (let alone define color spaces) in a purely physical universe. Calling a spectrum space a color space is common (because human scientists always already have their everyday knowledge about colors), but only adds to the confusion. Uli Zappe (talk) 15:40, 10 July 2019 (UTC)
 * I don't think anyone would call a spectrum space a color space. A color space is a human-relevant 3D subspace of spectrum space. Dicklyon (talk) 15:45, 10 July 2019 (UTC)


 * (ec) Well, LMS and RGB spaces are most often just linear coordinate transformations of XYZ; they all span the 3D subspace of spectral space that humans can distinguish (and no Martian would have been able to discover that without access to either human observers or their three types of cones cells to work with). When LMS is defined from different data from new experiments designed to specifically get at cone responses (psychophysically or physiologically), rather than modeled as a transformatin from XYZ, it's still very close to the same.  In all cases these physical wavelength-weighting-based spaces are physical, and in all cases they're tied to human color vision, so I don't get what Uli is criticizing as "not a color space" or what his second POV is.  Yes, about Bradford, Kang says "The source cone responsivity is converted to destination cone signals" and calls their values L, M, and S.  That's by analogy with other CATs and certainly not an "explicit" claim that a sharpened LMS space is actually an LMS space, which it's not.  There's not POV there, just some imprecise writing. Dicklyon (talk) 15:44, 10 July 2019 (UTC)

To hopefully close this: no Martian would have been able to discover that without access to either human observers or their three types of cones cells to work with – Well, of course not. You need access to your subject. The difference is simply whether the Martians have only access to cone cells of dead humans or to living humans they can communicate with. In the first case, they can only learn about the spectral space humans might possibly react to (= physiological/physical), in the second case they can also learn about the color space as they talk with their subjects (= psychophysical).

LMS and RGB spaces are most often just linear coordinate transformations of XYZ; they all span the 3D subspace of spectral space that humans can distinguish – In this case it’s trivial that the resulting LMS space is a color space (since XYZ itself is psychophysical and, of course, a color space). The question in this case: What is special about linear coordinate transformations that create an LMS color space, as opposed to other such transformations that do not?

When LMS is defined from different data from new experiments designed to specifically get at cone responses (psychophysically or physiologically), rather than modeled as a transformatin from XYZ, it's still very close to the same. – The question here is twofold, depending on whether the cone responses are reconstructed psychophysically or physiologically:
 * (physiologically, measuring spectral absorption of the cones or whatever) How do you jump from spectrum to color? Do you simply assume the spectral sensitivity curves that you measured are also CMFs? (Not a trivial assumption!)
 * (psychophysically) What makes the psychophysical test setup differ from the setup of Wright and Guild that led to the CIE RGB and then the CIE XYZ color spaces? What is special about the setup so that it measures “LMS”?

These questions imply that so far, there is no standard answer to the question what makes a color space an LMS space, let alone a standard that defines “the” LMS the same way XYZ is defined. And as long as this is the case, you cannot blame people with a different concept of LMS as just being imprecise, analogous etc. The majority of literature I read about this topic sticks with the definition that every color space in which a von Kries transform works well is an LMS color space, especially Bradford. You might find this non-sensical, but as long as there is no standardized definition of what LMS means and how it’s derived, you cannot claim that these people are wrong or imprecise. They just use an only vaguely defined concept differently than you do.

What does that all mean for the Wikipedia article? Could you agree to a version that first describes your “narrow” concept of LMS and then adds that (because a standardized definition is missing) there’s also a “wider” usage of the concept referring to all CATs? If so, we/you’d need to answer the applicable of the bold questions above, to make clear how to tell an LMS color space from other color spaces in the “narrow” concept you emphasize. Uli Zappe (talk) 23:14, 10 July 2019 (UTC)


 * Yes, I agree that's a good approach. First a space literally modeling the LMS cone sensitivities, and second a more general concept used in CATs.  Go for it. Dicklyon (talk) 00:42, 11 July 2019 (UTC)

OK, I think that two tiny things have been answered: #1  LMS is a color space, by the common meaning of "color space". #2 There is no single recognized authority that defines the answers to the aspects that you are debating. 2% nailed down, 98% to go! :-)

On to my next question, which may be building towards a resolution and also article content. Is there such a thing as measuring or positing the response of cone cells, prior to the interpretation of such by the brain? <b style="color: #0000cc;">North8000</b> (talk) 23:33, 10 July 2019 (UTC)


 * Yes, there's a lot known about the nonlinear and adaptive response properties of cones, and interrelated processing in the retina. Cone signals do not get sent to the brain, unless you consider the retina part of the brain (some do). Dicklyon (talk) 00:42, 11 July 2019 (UTC)
 * Thanks. Would the response graph at the beginning of this article be a graph of the response of the cones, the retina, or the main brain? <b style="color: #0000cc;">North8000</b> (talk) 14:20, 11 July 2019 (UTC)
 * No. Responsivity is not response; it's a poor term for sensitivity; it characterizes the effective stimulus, a linear physical thing, a weighted intensity.  It's about the opsins, not how the cone cells react to the opsins' sensitivities.  The only thing it says about response is that the responses (of the cones, the brain, the human observer, etc.) will be same (because the effective stimuli will be the same) if two different stimulus spectra produce the same three weighted intensities (see metamerism).  Yes, this approach is "reductionist", but it's also realistic. Dicklyon (talk) 14:35, 11 July 2019 (UTC)


 * Cone signals do not get sent to the brain – So what is sent to the brain? Some kind of already processed signals? Is it known exactly which kind? Uli Zappe (talk) 14:28, 11 July 2019 (UTC)
 * The optic nerve sends adaptive/nonlinear/mixed/enhanced "opponent" signals to the brain. See Retina for more of what it does (it doesn't talk about opponent there, but should). The details are not exact, but it's well studied. Dicklyon (talk) 14:35, 11 July 2019 (UTC)
 * Thanks! I wasn’t aware that it’s the opponent signals that are sent to the brain.
 * Yes, I agree that's a good approach. First a space literally modeling the LMS cone sensitivities, and second a more general concept used in CATs. Go for it. – Well, I cannot do this alone, because of constraints of time as well as knowledge. For easier editibility, I’ll start a new subchapter once again and will ask you some questions there. Uli Zappe (talk) 19:16, 12 July 2019 (UTC)

"Color does not exist in the physical world, color only exists in human brain" -- I'm tired of this mantra repeated by some, as I find it unscientific. A given observer induces a pseudometric on the space of physical spectra, measuring color similarity. Averaging over the entire population gives a pseudometric for a standard observer. Given such a pseudometric, colors aren't sole products of the human brain anymore, but are objectively defined equivalence classes that can be assigned to physical spectra induced by that pseudometric, and compared independently of a human observer. Colorimetry, in its core, tries to quantify that structure. bungalo (talk) 08:05, 1 December 2019 (UTC)
 * You might find it “unscientific”, but it’s the only scientifically sound way. Yes, there is a pseudometric you can objectively quantify once the equivalence classes were (subjectively, not objectively!) defined, but what you quantify is nothing but the averaged output of 17 human brains (far, BTW, from the entire population, but that’s not the point here), not something that would exist in the physical world even if there were no humans. Martians could never talk about “color” (the “color” we talk about) before the human brain created this pseudometric. Uli Zappe (talk) 12:46, 1 December 2019 (UTC)

Preparation of a new article version
I hope we can focus on the preparation of a new article version in this subchapter.

@Dicklyon To start with the “narrow” concept of LMS you favor: You wrote above that among other approaches, there are those that are […] just linear coordinate transformations of XYZ. Is there an especially prominent/wide-spread variant in this group, and if so, which one? If not, could you name any example for this kind of approach?

BTW: In studying some literature in connection with our discussion, I also read a few chapters in Colorimetry: understanding the CIE system, edited by János Schanda, John Wiley & Sons 2007. This is a publication of the CIE and is certainly as official as it gets. There, it reads on page 306 (in the context of image appearance modelling): Although it seems counter-intuitive to have negative LMS cone responses because of the chromatic adaptation on sharpened RGB values, as well as the linear transformation from CIE XYZ, it is possible to have negative LMS values. I just quote this as a backup to my claim that the “second school of thought” may feel odd to you but is not a strange minority. Therefore, Wikipedia will definitely have to factor it in. Uli Zappe (talk) 19:38, 12 July 2019 (UTC)
 * Why did you truncate your quote right there? Seems disingenuous when I look at the context. Dicklyon (talk) 00:41, 13 July 2019 (UTC)
 * Because we discussed whether negative LMS values can happen at all, not where they can happen. Uli Zappe (talk) 00:50, 13 July 2019 (UTC)
 * Well they can happen in spaces that are not LMS spaces. Dicklyon (talk) 02:17, 13 July 2019 (UTC)
 * ? If L, M or S can be < 0, of course this happens in the LMS space. The “LMS space” is nothing more than a combination of its three components. Anyway, I’d appreciate if you could reply to my question. Uli Zappe (talk) 18:59, 13 July 2019 (UTC)
 * You cut off "... in the IPT transform". Physically, there is no light spectrum or wavelength that causes a cone to respond negatively.  The spectral sensitivity curves are based on nonnegative quantum efficiencies of photo conversion to the excited opsin state.  There's no negative light spectram, no negative excitation.  Of course, mathematically you can put in an "imaginary color" with negative spectrum and get out negative L, M, or S values.  And you can define a transform that's not LMS and call it LMS if you use it sort of like LMS.  The more complete quote, in the context of appearance modeling, not cone response characterization, says:


 * I think I have the Ebner and Fairchild paper they cite in my library, since I was at that Color Imaging Conference with them. I don't see a free one online.  I'll see if I can find out what they mean by "a different cone-response space".  Not quite LMS, I'd say. Dicklyon (talk) 19:49, 13 July 2019 (UTC)

If rewriting the article perhaps we should include the main statements which seem to be missing. Things like: Sincerely, <b style="color: #0000cc;">North8000</b> (talk) 21:45, 12 July 2019 (UTC)
 * ....color space where the co-efficients represent____________________
 * The numerical range of the co-efficients is_______________________
 * The numerical range is not really specified usually, like if stimuli can be arbitrarily bright. But they are bounded below by zero for any reasonable LMS space. Dicklyon (talk) 00:41, 13 July 2019 (UTC)
 * That's the kind of basic statements that are missing in the article. I'll put that one in. <b style="color: #0000cc;">North8000</b> (talk) 18:36, 13 July 2019 (UTC)
 * Not sure about that. This is nothing specific to LMS, it’s valid of all Color Matching Functions. A link to that article might help, and if it’s not clearly enough explained there, it’s that article that should be improved. In any case, as much as Dicklyon dislikes it, LMS values in general can be negative. It depends on the concept of what LMS is. Uli Zappe (talk) 19:08, 13 July 2019 (UTC)
 * We can say something about it. Nonnegativity is true of a good LMS and of XYZ, for nonnegative spectra.  For "imaginary primaries" they can go negative, of course.  For RGB and "sharpened LMS" and some other spaces, no nonnegativity constraint. Dicklyon (talk) 19:21, 13 July 2019 (UTC)
 * I added a bit about nonnegativity at that CIE article you linked, and added the CIE RGB curves, which are not nonnegative. Dicklyon (talk) 19:50, 13 July 2019 (UTC)
 * Of course I’m aware that Physically, there is no light spectrum or wavelength that causes a cone to respond negatively. The question if LMS values can be negative is equivalent to the question if LMS tries to model physiology (concept 1, “good LMS” in your diction) or tries to be “human-like” in that it is suited for chromatic adaption (concept 2, “sharpened LMS” etc.). For concept 2, it would be interesting to know the criteria that make a color space “suited for chromatic adaption” (apart from empirical trial and error) and therefore “an LMS”. Uli Zappe (talk) 20:14, 13 July 2019 (UTC)
 * Being suitable for chromatic adaptation does not make a space an LMS. Bradford, for example, is not an LMS but rather a "sharp" colorspace as I showed you.  The von Kries method is to use an LMS space.  People found that other, sharper, spaces do a better job sometimes; there's no strong reason to think that the von Kries method was uniquely good, and it's not.  But when you use that idea with a different space, and use the same terminology, that doesn't make the different space an LMS space.  So let's write about how various spaces "stand in" for LMS in von Kries variants, instead of assuming any space used that way is an LMS space. Dicklyon (talk) 23:08, 13 July 2019 (UTC)
 * Oh, please! Bradford is an LMS space (a “sharpened LMS space”) in concept 2. I thought we already agreed on dealing with both concepts, the narrow and the broad one, in the article? It makes no sense at all to be stuck in this loop. I understand that you insist on concept 1 and find concept 2 odd, but it’s a concept that is used a lot. You say that when you use that idea with a different space, and use the same terminology, that doesn't make the different space an LMS space, but in concept 2, that is exactly what makes the different space an LMS space. And wouldn’t it be ridiculous to use the same terminology (L, M and S) but then say it’s not an LMS space? You might call this imprecise, analogous, bad thinking or whatever, but the fact is that “LMS” is used so often in this way that an encyclopedia cannot ignore this usage. Rather than insisting on concept 1, please help writing about it by replying to my question (“You wrote above that among other approaches, there are those that are […] just linear coordinate transformations of XYZ. Is there an especially prominent/wide-spread variant in this group, and if so, which one? If not, could you name any example for this kind of approach?”). Uli Zappe (talk) 23:36, 13 July 2019 (UTC)
 * I have not suggested ignoring the concept, but treating it as a variation. There are LMS variations that can take negative values.  They are not LMS spaces. Dicklyon (talk) 23:39, 13 July 2019 (UTC)
 * Your favorite "handprint" site on this page talks about "sharpened" color matching functions (which include negative values) in contrast with cone fundamentals. But it's otherwise pretty unclear about all that. Dicklyon (talk) 00:49, 14 July 2019 (UTC)

I think the bottom line is this - there are the LMS cone response functions $$L_\lambda(\lambda),M_\lambda(\lambda),S_\lambda(\lambda)$$ and the XYZ "response" functions, $$X_\lambda(\lambda),Y_\lambda(\lambda),Z_\lambda(\lambda)$$. Given a spectral power distribution $$J_\lambda(\lambda)$$, the LMS and XYZ coordinates are:


 * $$L = \int_0^\infty\,J(\lambda)L_\lambda(\lambda)\,d\lambda$$
 * $$M = \int_0^\infty\,J(\lambda)M_\lambda(\lambda)\,d\lambda$$
 * $$S = \int_0^\infty\,J(\lambda)S_\lambda(\lambda)\,d\lambda$$


 * $$X = \int_0^\infty\,J(\lambda)X_\lambda(\lambda)\,d\lambda$$
 * $$Y = \int_0^\infty\,J(\lambda)Y_\lambda(\lambda)\,d\lambda$$
 * $$Z = \int_0^\infty\,J(\lambda)Z_\lambda(\lambda)\,d\lambda$$

Clearly, the transformation at a particular color between LMS and XYZ space is objective, but not unique. It rather depends highly on the particular form of the spectral distribution $$J(\lambda)$$ producing the given color. There is no fixed 3x3 matrix which will transform XYZ to LMS, even for a particular color, much less the entire gamut of colors. Any such proposed transformation will be an approximation at best, generally requiring certain assumptions about the spectral distributions producing the color.

It follows that if the human eye were a mathematically perfect discriminator (e.g. the MacAdam ellipses were points in the LMS color space), and that a perceived color was only determined by the LMS cone response functions, then there will be a unique point in LMS space corresponding to that color, but there will be a whole range of points in XYZ space that correspond to that color. The XYZ coordinates do not specify a color. But we are not interested in a mathematically perfect discriminator. With the human eye, we are dealing with a "perceptually perfect discriminator" (sort of a tautology). In other words, there *may* exist a transformation which, for every conceivable spectral distribution which yields a mathematical point {L,M,S} in LMS space, the corresponding set of calculated XYZ points will all fall within the boundary of the just-noticeable-difference (JND) region about the {L,M,S} point. Then again, maybe not. If not, then the XYZ points which fall outside of the JND region about {L,M,S} will define a set of restrictions on the spectral distributions which are "allowed" at that point. These restrictions *may* be fairly benign. Then again, maybe not. The restrictions on the spectral distribution (if any) that are necessary in order to define a perceptually perfect transformation between the spaces at a particular point will almost assuredly vary significantly from point to point in LMS space. PAR (talk) 11:07, 18 October 2023 (UTC)


 * I'd recommend you try engaging with the color science research literature, where people have done concrete experiments to test this, instead of just speculating. The keyword to look up is "Grassman's laws". There's a relevant chapter in the 2007 book Colorimetry, . –jacobolus (t) 11:41, 18 October 2023 (UTC)
 * The six equations at the beginning of my comment are simply a statement of Grassman's laws applied to the LMS and the XYZ color spaces. What I wanted to say is that when you assume Grassman's laws and the assumption that perceived color/luminance is uniquely and completely determined by the three cone responses, you arrive at certain conclusions, one of which is that there is not a one-to-one relationship between a point in LMS space, and a point in XYZ space, which may or may not be ameliorated by the idea of a JND boundary about a particular LMS point. I don't think anything I said was speculative, I just did not clutter up that main point with a dissertation on experimental results to resolve the "maybe"s and "maybe not"s. I don't think I need a tutorial on Grassman's laws, but if you know of any references which resolve the "maybe"s and "maybe not"s, I would be interested. PAR (talk) 04:00, 23 October 2023 (UTC)

I fixed incorrect matrix
Also look here https://en.wikipedia.org/wiki/ICtCp, that is where I found the mistake. This matrix is mentioned in errata http://rit-mcsl.org/fairchild//PDFs/Errata2e.pdf and is correct in 3rd edition (but this matrix is for entirely another thing). That is a very important thing! Ready for comments. 2A00:1370:812C:5D73:4493:5501:BB24:D2E6 (talk) 03:31, 21 March 2020 (UTC)
 * Good find. Dicklyon (talk) 04:15, 21 March 2020 (UTC)
 * After disscusion here https://github.com/colour-science/colour/issues/121 we actually came to a conlusion the original was correct. So who knows how they get IPT matrix... Also maybe add this http://brucelindbloom.com/Eqn_ChromAdapt.html, though again who knows if everything there is correct)) 2A00:1FA0:4690:7E51:6DD2:9FBF:715F:2C3B (talk) 05:50, 21 March 2020 (UTC)


 * ICtCp color space was derived specifically in the context of displaying images on displays with a native color space near Rec.2020 and with the PQ transfer function. During its construction many of the parameters were optimized based on these factors and although the initial values of the model may have derived from the HPE code fundamentals, they may have changed during the optimization of ICtCp. (i.e. Initial vs. final value). [ref. personal communications, sorry I don't have anything better to cite! ] TDcolor (talk) 02:40, 18 October 2021 (UTC)
 * I was talking about IPT as used in Dolby Vision. Not ICtCp, which is btw can be used for any space, not only 2020 gamut and pq transfer, any. Just the change of first mttix is needed. Valery Zapolodov (talk) 21:40, 11 December 2021 (UTC)