35 Replies Latest reply on Mar 31, 2014 3:01 PM by Alp Er Tunga

# CIE tristimulus values

I'm searching for the unit of CIE XYZ tristimulus values (y-axis on the graph), but I could not success so far. Anyone knowing the unit of these values. Thanks a lot.

• ###### 1. Re: CIE tristimulus values

These are the color-matching functions x-bar, y-bar and z-bar.

y-bar shows the sensitivity of the eye with respect to luminance,

sometimes called V(lambda). The peak value is exactly '1' because

of normalization. The other curves are found by measurements in

the color-matching experiment for CIE-primaries R,G,B, resulting

in r-bar, g-bar and b-bar, followed by a mathematical transform into

an artificial System X,Y,Z instead of R,G,B.

All this is explained e.g. here:

http://docs-hoffmann.de/ciexyz29082000.pdf

This stuff is rather difficult, especially the reference to physical units,

as explained in Appendix B.

Hope this helps a little, so far.

Best regards --Gernot Hoffmann

• ###### 2. Re: CIE tristimulus values

Thank you. If y-bar is in luminance, then we can say that the values of x-bar, y-bar, z-bar color matching functions are all in luminance? I think that, because when calculating x-bar, y-bar, z-bar values form r-bar, g-bar, z-bar, they are multiplied by 5.6508, and so we again convert to the luminances from the custom units used for r-bar, g-bar, z-bar.

• ###### 3. Re: CIE tristimulus values

We may discuss the question for what are these Color Matching Functions good?

(I'm apologizing for not discussing single numbers).

P.7 (center)  shows how the values X,Y,Z for a given spectral distribution can be

calculated by integrals.

And then one can convert X,Y,Z by simple matrix multiplications into any RGB space,

like sRGB, CIE-RGB, AdobeRGB, ProPhotoRGB. Some examples are shown in

chapter 12.

Furtheron one can convert in a straightforward manner into CIELab, without using

an RGB space.

Concerning your question: all RGB spaces and XYZ are linear combinations of each

other. Y is the luminance. Coming from any RGB space, the correct calculation of

the luminance requires the application of the inverse matrix. The curve y-bar itself

is not the luminance. It says how different parts of the spectrum contribute to the

luminance. Unfortunately such an explication is not available for x-bar and z-bar

because X and Z are merely mathematical constructs.

Best regards --Gernot Hoffmann

• ###### 4. Re: CIE tristimulus values

Maybe, I asked in the wrong way. I think that I should not have asked with the word "luminance".

On the graph I posted in my first message, y-axis has some numbers. I would like to ask the units of them. So, for example, at 450 nm, z-bar has nearly the value of 1.8. I think that it may mean 1.8 cd/m2 or it can be unitless?

I'm sorry, I'm new on the subject and I'm now reading "Measuring Color" by Hunt. Maybe, I can read your documents later, because I think that they are not for a beginner, your documents are a little bit compact for me to understand the subject.

• ###### 5. Re: CIE tristimulus values

Yes, it's very reasonable to read this book:

R.W.G.Hunt: Measuring colour, 3.Edition, 1998

Ch. 2.6 Colour-matching functions .

Instead of three integrals we have here three sums, with la=lambda:

X = . . .
Y = K * ( P1(la) * y-bar1(la) + P2(la) * y-bar2(la) + . . . )
Z = . . .

K is a constant. Values of P are amounts of power per small constant-width wavelength interval.
That is a power spectrum density (or spectral power density).
x-bar, y-bar, z-bar are the mentioned functions, normalized for  y-bar = 1.0  at 555nm (peak).
If P is in Watts per steradian and per square meter and if K is put equal to 683, then Y is the luminance
in candelas per square meter.

My conclusion:
Now we can see immediately, that a new scale factor for the curves x-bar, y-bar, z-bar (simultaneously)
would require a new constant K for the same physical relations between radiometric and photometric data.
Therefore we can leave these functions as they are, normalized and without a unit for the vertical axis.

This factor 683 is mentioned as well by Monsieur C. in Appendix B of my doc.

This doc is in fact based very much on Hunt and Wyszecki&Stiles. I didn't explain the physical relations
between radiometric and photometric variables because this doesn't contribute much to applications
of color in computer science. But I'm grateful for your questions.

Best regards --Gernot Hoffmann

How can I write here greek letters (e.g. lambda) ?

• ###### 6. Re: CIE tristimulus values

G.Hoffmann wrote:

…How can I write here greek letters (e.g. lambda) ?

This will be a test:

λ  Λ     α β γ δ σ ω     Α Β Γ Δ  Σ Ω

I typed those characters the same way I would type them in any Adobe software, or MS Word, etc.

I use a Mac, so I simply change my keyboard layout in the Input menu, and then I type away:

• ###### 7. Re: CIE tristimulus values

Thanks, station_two.

As far as I know the mentioned option is not available under Windows, and it's normally not

necessary (for me), because in InDesign and in MathType all glyphs of a font are available

directly in boxes.

Copying from Charmap.exe doesn't help here either.

Best regards --Gernot Hoffmann

• ###### 8. Re: CIE tristimulus values

G.Hoffmann wrote:

Copying from Charmap.exe doesn't help here either.

It does here...? But straight copy from the table won't do it, you need to click Select then Copy. A bit cumbersome.

Σ Ω λ δ π

• ###### 9. Re: CIE tristimulus values

Thanks. Yes, I did select&copy, but using the OT-font Symbol.

A new attempt with Arial:

αελ

Seems to work.

By the way: MathType-EPS with TIFF preview cannot be shown here directly.

I had converted the EPS into PNG by Photoshop.

Best regards --Gernot Hoffmann

• ###### 10. Re: CIE tristimulus values

G.Hoffmann wrote:

…As far as I know the mentioned option is not available under Windows,…in InDesign and in MathType all glyphs of a font are available directly in boxes.

Hehehehe…   That's one of the many reasons I use Macs and not Windows boxes since 1984.

Just with the five keyboard layouts shown in post #6, I can type in German, Spanish, English, Italian, French, Portuguese, Greek and Russian directly on my Mac keyboard, without using any »modifier keys+code_numbers combinations«, without copying and pasting, and without having to summon any chart, table, keyboard viewer or »boxes«.

The only reason I added the screen shot of the Greek keyboard layout was to show where the individual glyphs are located on the keyboard, by virtue of software magic.  For instance if you press the »D« key +shift on the physical keyboard while the Greek software keyboard layout is selected in the Input Menu, the Greek Delta Δ is automatically inserted in the text you're typing, and so forth.

There is a huge number of additional software keyboard layouts that can be added to the input menu with a couple of clicks, from three variants of the languages spoken in Afghanistan:

to Welsh:

Für Deutsch kann man sogar zwischen einer deutschen, einer österreichischen oder einer schweizerischen Tastatur beliebig wählen, so daß man gegebenenfalls nicht eine neue Tastatur lernen muß.

With the one »Cantabria« keyboard software layout shown, which I created in the MacKeymeleon and Ukulele programs myself and which I use routinely  by default, one can type in German, Spanish, English, Italian, French, and Portuguese, as described above.  No awkward »modifier keys+code_numbers combinations«, no copying and pasting, and without having to summon any chart, table, boxes or keyboard viewer.

.

Message was edited by: station_two

• ###### 11. Re: CIE tristimulus values

I think that CIE XYZ color matching functions (x-bar, y-bar, z-bar) can be thought as efficiency curves, they in fact give us weighting values in photometric terms -like V(λ)- when identifying colors. They specify relative amounts of matching stimuli, so they are unitless.

Thanks a lot.

Measuring Color is the most understandable book I've found so far on the subject, it answers so many questions for me, I could not find any where before. But I still have some questions that I want to ask to a colorist (I hope this is the correct word for persons interested in color theory). So, I would like to use this topic for all kinds of question about color theory. Thanks to all who help me for better understanding the subject.

For equi-energy stimulus, we have X=Y=Z. It is ok. On the other hand, the reference white point, as we know, is different from this point and the value of Y is 100 at the reference white. As we know again, the white references are expressed with the name of illuminants standardized by the CIE, for example D65, D50 etc. But, I can not imagine how we can use these illuminants in the real setups of color matching experiments. Are color stimuli used in these experiments not self-luminous? I think that in these experiments, three monochromatic color stimuli used for matching the reference color. If these color stimuli are self-luminous, why we need an external illuminant in the setup of color matching experiments? Do we have a video on the internet showing the real setup of these experiments and the experiment itself?

By the way, I added Greek to my language bar on Windows 7 and I can type Greek letters with the keyboard without copying, pasting etc.

• ###### 12. Re: CIE tristimulus values

Hello, hopefully I can give some information:

The first color-matching experiments, as performed by Wright (1928 – 1929), used
primaries (primary stimuli) with wavelengths at 460 / 530 / 650nm.
There was no reference white involved. Color-matching requires only the matching of
three primaries, using variable intensities, and a sample. The human adaptation is
'floating'. There are no statements about color appearance ("melongreen", "pinkish grey")
or about the luminance of samples relative to each other. The question is only:
How can the sample be matched by primaries directly or indirectly (using 'negative' colors)?

Guild was the founder of the CIE (1931) system, of course together with others.
He used new primaries 435.8 / 546.1 / 700nm which were chosen so, that Equal Energy Light
had chromaticity coordinates r = g = b = 1/3 (so far not x, y, z).
He used Wright's data (transformed) and his own.
The next step was the invention of the XYZ system. The human gamut should be entirely in the

first octant, that means, X, Y, Z are not negative. Y is the luminance and the system uses artificial

invisible primaries for X and Z (all this is merely linear algebra).

Additionally the feature for Equal Energy was taken into account again: x = y = 1/3. One could

this consider as well as an additional demand for the definition of the XYZ space, in order to

remove ambiguities. Still no white reference was necessary for matching experiments.

The Equal Energy feature was just a method how to center this special light in the chromaticity

diagram.
Furtheron some corrections were made, especially for using y-bar(lambda) like V(lambda),
because there was (and is still) a tiny difference.

The situation about the reference illuminant is very different for CIELab: here we need such a
white like D50 or D65.

Which shape has the human gamut in XYZ? For self-luminuous sources one doesn't have a
reference white. The gamut is an open cone, irregularly shaped, as shown on p.9 in my doc.

But then we have to consider reflected light from objects, surface colors. The illuminating
light can be of any type, for instance A, D50, D65 or what else. This is the reference light.
The reflected light cannot be brighter. It cannot be a spectral color, because a single line
spectrum of a reflected color doesn't have energy. Here we have so called Optimal colors,
which deliver the most saturated color for any level of reflected luminance. The surface of
an object has a reflection spectrum which is either one compact range, or which consists of
two compact ranges, one part at the violet end, the other at the red end (Roesch, in German

Again, spectral colors are impossible. The area of Optimal colors is smaller than the area
of the horseshoe. And even more important: The gamut is in XYZ a closed volume like a

"wet sack". At Ymax we find the white point of the illumination. This is usually normalized:

Ymax=1 or Ymax=100.

Sources:

Hugh S.Fairman, Michael H.Brill, Henry Hemmendinger
How the CIE 1931 Color-Matching Functions Were Derived from Wright–Guild Data

1996
Use Google search by title „How … Data“.

The text is not optimized because of limited time. Feel free to ask again.

Best regards --Gernot Hoffmann

• ###### 13. Re: CIE tristimulus values

I'm sorry for the late reply. Thanks a lot, I have some questions, but before I think that I need to read until sixth chapter of the book at least in order to understand completely what you mean in the last paragraph. Thanks again.

• ###### 14. Re: CIE tristimulus values

Hi Alper, I ve recently used color measurement techniques in my graduate thesis. I explained all about the colorimetry in a chapter of my thesis. I can send you the link when it will be available on internet. These are other books about color science that I found helpful:

Bouma, P. J., Physical Aspects of Colour: An Introduction to the Scienti c Study of

Colour Stimuli and Colour Sensations

Wyszecki, G., and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data

and Formulae

Evans, R. M., An Introduction to Color

• ###### 15. Re: CIE tristimulus values

Thanks a lot Omcan. I would be very happied to read your thesis when it is available online.

I have some questions about the details, but I think that I've understood the general framework of the CIE colorimetry (until appearance models, I've not studied those subjects yet).

• ###### 16. Re: CIE tristimulus values

Some internet sources define photometric measures using the term "perceived brightness".

For example, lightness is defined as "the perceived brightness of an object compared to that of a perfect white object". As we know from the formula of lightness, the first part in the definition, "the perceived brightness of an object" refers to the CIE luminance value, Y.

But, as we know again, photometric measurements are not directly proportional with perceived brightness and it largely depends on environmental conditions.

So, in this respect, using the term "perceived brightness" in the definitions related with photometric measurements can be correct? In place of "perceived brightness", would "radiant power that can sensitize the eye" or any other phrase like this be more plausible?

• ###### 17. Re: CIE tristimulus values

R.W.G.Hunt (Measuring Colour) says:
---
1.7 Brightness: Attribute of a visual sensation according to which an area appears to exhibit more or less light.

3.2 If the Y tristimulus value is evaluated on an absolute basis, in candelas per square meter, for example,
it represents the luminance of a colour. This provides the basis for a correlation with the perceptual attribute
of brightness. As has already been explained, the correlation is complicated by the effect of the viewing conditions,

by the non-linear relationship between brightness and luminance, and the partial dependance of
brightness on colourfulness. These factors will be discussed in some detail in Chapter 12. For the moment,
however, we shall simply regard luminance as an approximate correlate of brightness.
---

Thus, it's tautological, talking about perceived brightness. Luminance is measurable, brightness is perceived.

One of the most striking effect in the field of color appearance is the Helmholtz-Kohlrausch effect:
Hunt: Increasing brightness by increasing purity for the same luminance.

Saturated colors appear brighter. This is demonstrated here on p.8 – p.10:

http://docs-hoffmann.de/gray10012001.pdf

256 colors in each indexed color image are sorted either by CIELab lightness L* or by luminance Y.

I don't remember which one, but both deliver the same order, because L*(Y) is a monotonic function.

In very colorful images (images with partly strong saturations) the sorting seems to be wrong.

But we can verify that the sorting is correct: Place any page into Photoshop, based on sRGB,

and measure L* by 'Info Palette'. The sorting is correct, besides tiny rounding effects. We may find

a sequence ... 60 59 60 61 65 70 ... with globally increasing values L*. The sorting was not done by

Photoshop but by my specific program.

In my opinion one should not use Y as a correlate for brightness. That's as well the reason, why formalistic
grayscale conversions for color images are normally not convincing.

Best regards --Gernot Hoffmann

Message was edited by G.Hoffmann

with respect to sorting by L* or Y, which results in the same order.

• ###### 18. Re: CIE tristimulus values

In my opinion one should not use Y as a correlate for brightness. That's as well the reason, why formalistic
grayscale conversions for color images are normally not convincing.

Can I ask a stupid question?

Luminance is not a uniform correlate for vision brightness, ok. But I think that non-uniform luminance values are what our eyes need for creating correct brightness sensation.

I think the luminance as the input and the brightness as the output for our eyes. That is, eyes are the functions taking luminance and converting it to the brightness. So, do grayscale conversions (with the 2.2 gamma for compensating the monitor gamma) not give us linear scene luminances for processing them later in our eyes for getting the correct brightness sensation?

• ###### 19. Re: CIE tristimulus values

First let us consider a case of accurate color reproduction:

A painting is illuminated by flash, approximately 5000K. An image is taken by a color-calibrated camera.
After the assignment of the camera profile the image is not further processed but printed by a calibrated
printer. The print is put aside the painting. Both look alike under D50 and under different  roomlight
(in limits). Both together can be shot again – they will look alike in the image.
The whole process – camera calibration, image handling, printer calibration – is fully controlled by CIE
colorimetry. Inherent nonlinearities, like inverse gamma encoding, are compensated somewhere else in
inverse order. The process is linear. The printing is not really linear, but there are definitely no corrections
for perceptual appearance, because the viewing conditions are the same for the original painting and the

reproduction. CIELab values are preserved or regenerated, e.g. by applying the camera profile.

In this example just a little more contrast had been added, not touching the automatic color correction:
http://docs-hoffmann.de/camcal17122006.pdf

See p.13.

If the viewing conditions are different, then the theories of Color Appearance Models (Mark Fairchild and
others) offer means how to modify an image for different types of illuminants, backgrounds, surrounds, etc.
http://www.amazon.de/APPEARANCE-IMAGING-SCIENCE-TECHNOLOGY-Fairchild/dp/B00IH7711O/ref=sr_ 1_1/277-9872972-1598965?s=books&ie=UTF8&qid=1392978327&sr=1-1&keywords=Fairchild+Color

Second, let us consider the 'Gamma Question', traditionally in the context of TV with cathode ray tubes:

Here I'm following mainly these books

R.W.G.Hunt, The Reproduction of Colour (this not the same as Measuring Colour)
http://www.amazon.de/Reproduction-Colour-Imaging-Science-Technology/dp/0470024259/ref=sr_1 _1/280-6435932-5887840?s=books-intl-de&ie=UTF8&qid=1392977381&sr=1-1&keywords=Hunt+Reprodu ction+of+Colour

and my own doc:
http://docs-hoffmann.de/gamquest18102001.pdf

A scene photo is taken by a video camera. A CRT monitor has an overall transfer function between
control voltage y and luminance z like z=y^G, with gamma G=2.8. The camera signal y can be created
from scene luminance x by y=x^(1/G)  which would result in an overall Gamma of 1.0.
Actually, TV monitors are not viewed in entirely dark rooms. There is always some flare (stray light).

This requires an increased artificial contrast (a kind of early Color Appearance Model correction, but

mainly for luminance, though useful for better saturation in color TV as well).
Finally we have y=x^(1/2.2)=x^0.4545 and z=y^2.8, which results in z=x^1.28 or so.

Now we can see, that different viewing conditions require (theoretically) modifications  of  the image in
order to create the same appearance.

Brightness depends in a nonlinear fashion from object luminance and the background, see Fig.1 here:
but these curves are not used for active correction. Just the same as the Helmholtz-Kohlrausch effect:
Vibrant red appears with 'exaggerated' brightness, but this happens in the scene and in the reproduction

as well. Thus, corrections are not required,  as long as the color is in-gamut for all devices.

I hope this explanation will shed some light on this rather complex scientific area. There is one (implicit)
question not yet answered: under which conditions is luminance Y a good correlate for brightness?
It would be necessary to read more about color appearance (e.g. Fairchild).

Best regards --Gernot Hoffmann

• ###### 20. Re: CIE tristimulus values

Thanks a lot for your time. I have a question about the books you mentioned in your posts, but first of all I would like to ask about the gamma.

After reading your gamma document and the Gamma FAQ by Charles Poynton, I need some confirmations for testing my understanding.

1. Gamma is not related with the human vision at all.

2. Human being needs just the linear scene luminances for extracting the brightness information. Our eyes have already a gamma embedded in it for extracting the brightness values from the linear secene luminances, so we don't need any other artificial gamma.

3. We don't need, but in the past, the CRT displays needed the gamma for linearizing the signal arriving to the CRT displays.

4. Today we need it for two reasons: one of them is backward compatibility and the other is our 8-bit image files. As far as I know, LCDs have approximately linear response, so if we start to use 32-bit floating point files as a new standard for image files in the future (Poynton says even 16-bit files would be enough), we will not need gamma anymore. At this point, we will have inherently linear systems for tone reproduction on our displays.

• ###### 21. Re: CIE tristimulus values

You're welcome, I have time enough and I like your questions – the same as I asked many years ago.

1. Gamma is not related with the human vision at all.

The nonlinear brightness-luminance function of vision is not the basic reason for gamma encoding.
There is just one objection remaining: the resolution in dark areas should be larger than in light areas.
This is true only if the eye is dark adapted, see test images p.17:
http://docs-hoffmann.de/gamquest18102001.pdf
Then one should have more levels per luminance unit in the dark than in the bright. If the source is in

8 bpc (bits per channel) then the application of y=x^(1/G) produces an overall loss of levels (184 instead

of 256) and large gaps in y in the dark region, is therefore entirely useless. Aha – one needs a source

with more bits, for instance 12, 14 or 16bpc.

2. Human being needs just the linear scene luminances for extracting the brightness information.

Our eyes have already a gamma embedded in it for extracting the brightness values from the linear

secene luminances, so we don't need any other artificial gamma.

That's my opinion too. If we didn't have the phenomenon of 'brightness', then image processing would be

just the same.

3. We don't need, but in the past, the CRT displays needed the gamma for linearizing the signal arriving

to the CRT displays.

Yes, the first step is establishing linearity from scene view to display view. The second step may be a
correction because of the viewing conditions.

4. Today we need it for two reasons: one of them is backward compatibility and the other is our

8-bit image files. As far as I know, LCDs have approximately linear response, so if we start to use

32-bit floating point files as a new standard for image files in the future (Poynton says even

16-bit files would be enough), we will not need gamma anymore. At this point, we will have

inherently linear systems for tone reproduction on our displays.

Yes, my opinion as well. This issue with banding in dark areas for 8bpc images may arise in synthetical

images (gradients, computer graphics), but not in real-world photos.
Some tests are here:
http://docs-hoffmann.de/optigray06102001.pdf

An interesting discussion about brightness, lightness, gamma etc (year 2006):

Please note, my old URLs (as found in the internet) are no more valid, e.g.:
http://www.fho-emden.de/~hoffmann/howww41a.html

http://docs-hoffmann.de/howww41a.html

And it's still going on...

Best regards --Gernot Hoffmann

• ###### 22. Re: CIE tristimulus values

The gamma mystery is solved for me at the end ))

It is a little bit technical subject of course, but it should not be so mysterious. I think that its mystery is mainly coming from the incomplete information and/or misinformation abound on the net and even present in some published books.

Thank you so much.

• ###### 23. Re: CIE tristimulus values

I'm looking at the ICC specification for input profiles, but there are some points that I could not figure out completely.

Specification says that input profiles have three tone reproduction curves for each channel and these curves convert between nonlinear device data to linear RGB value and then, it uses 3 x 3 matrix for mapping the linear RGB values to the PCS.

I could not understand why the device data is nonlinear at this stage.

I would be very grateful if you advise me a source explaining all the imaging process with numerical examples from the point of view of color, from sensor-state to the output-referred file. There are some books giving workflows of this process, but none of them completely explain all the steps in the process.

• ###### 24. Re: CIE tristimulus values

Which chapter in the newest version of ICC profile specifications are you referring to?

http://www.color.org/icc_specs2.xalter

Then we can try, with the help of other contributors here, to decipher  the ICC specs

(which are in my opinion enigmatic).

One answer may be: nonlinearities are considered as possible, whether they exist or not.

Or: no device in the world is truly linear.

Best regards --Gernot Hoffmann

• ###### 25. Re: CIE tristimulus values

Hi Gernot, ICC specification v4.3 explains the calculations of matrix based input profiles in Annex F.3.

One answer may be: nonlinearities are considered as possible, whether they exist or not.

Or: no device in the world is truly linear.

I'm not sure but I think that sensor values are linearized by the linearization step in the workflow before the demosaicing step.

• ###### 26. Re: CIE tristimulus values

1. What is the CIE definition of "luminosity"? I could not find the definition of this term.

2. CIELAB does not have the definition of saturation. What is the reason for this?

• ###### 27. Re: CIE tristimulus values

Hello, let me begin with luminosity:

----

(1)
http://en.wikipedia.org/wiki/Luminosity
"In the field of computer graphics the concept of luminosity is different altogether, a synonym

in fact for the concept of lightness..."

Mr.C., member of the Photoshop staff, said:
"In this case it is the approximate grayscale value of the colors in the image. It is approximate

because the calculation is done in the image colorspace (instead of linear) and done using

"average" color weighting functions instead of using  the image profile. Basically, it's designed

for speed, not accuracy. But it gives a good approximation to the gray values for common

RGB colorspaces."

(3)

http://docs-hoffmann.de/gray10012001.pdf

----

Opposed to astronomy, the term luminosity was and is undefined in color science (1).

In (2) we find an extensive discussion about the meaning in Photoshop.

Here, this expression is used in the sense of 'easily calculated approximation for luminance'

or 'lightness'.

In my opinion it's something like 'luma', which means a weighted sum of inverse gamma-

encoded values R', G', B', like Luminosity = 0.4*R' + 0.5*R' + 0.1*B'.

The weighting factors depend on the color space (sRGB, aRGB, pRGB), mainly on the

chromaticity values of the primaries . This calculation is physically never correct, but mostly

sufficiently useful and (of course) fast, as Mr.C. said.

Best regards  --Gernot Hoffmann

• ###### 28. Re: CIE tristimulus values

Hi again ...

Mr.C., member of the Photoshop staff, said:
"In this case it is the approximate grayscale value of the colors in the image. It is approximate

because the calculation is done in the image colorspace (instead of linear) ..."

...

In my opinion it's something like 'luma', which means a weighted sum of inverse gamma-

encoded values R', G', B', like Luminosity = 0.4*R' + 0.5*R' + 0.1*B'.

I'm sorry if I misunderstand, but in your document, it is said that Ps applies conversion coefficients to the "linear" RGB values ... on page 4.

• ###### 29. Re: CIE tristimulus values

You're right, this sounds wrong, but it can be explained:
My doc Luminance Models for Grayscale Conversions does not concern luminosity but luminance.
Luminance is calculated accurately in the linear space R,G,B ( R=R'^2.2 etc.) , using the transformation
for Y from R,G,B to X,Y,Z, followed by inverse gamma encoding for Y for grayscale data files (here the
actual value for grayscale gamma should be used, which is not necessarily 2.2).
Mr.C. said as well, the grayscale conversion is done accurately, opposed to the calculation of luminosity.

Sorry for the confusion and thanks for critical reading!
I should not have quoted my doc without further explanation.

About saturation in the CIE chromaticity diagram and in CIELab:

Definition according to Hunt:
saturation – colorfulness in proportion to brightness (of an object)

In chromaticity diagrams the luminance or lightness is left out, therefore the term saturation
(in a strict sense) would be meaningless (my opinion).

Nevertheless one may say: on a ray from a (previously defined) whitepoint to the periphery
(spectral locus or purple line) the saturation is increasing.

http://en.wikipedia.org/wiki/Saturation_%28color_theory%29

Two alternatives are mentioned:

with c = Sqrt(a² + b²)  (asterisks omitted):

S = c / L

or

S = c / Sqrt(L² + c²)

Best regards --Gernot Hoffmann

• ###### 30. Re: CIE tristimulus values

Thanks, I see ... luminosity (not a colorimetrically defined term) is just a specific term in Ps for histogram values, which are not exact luminance values used in grayscale conversions, but they are very good approximations for luminance of an image.

Saturation is defined in CIELUV, but not in CIELAB according to Hunt ... and according to the Wiki page, the reason is that there is no chromaticity diagram for CIELAB.

Why is there not a chromaticity diagram for CIELAB?

I think that ... because CIELAB axes are not defined by primaries (like X, Y, Z in XYZ) or by the relative values of primaries (such as x, y as in xyY) but its axes are defined as the ratios of primaries to reference white values. I'm not sure ... Am I thinking correctly?

• ###### 31. Re: CIE tristimulus values

I've just noticed that why there is no correlate for saturation in CIELAB is mentioned in Hunt. Thanks.

• ###### 32. Re: CIE tristimulus values

Perhaps we should use subjective expressions like Brightness or Saturation  merely

in a qualitative sense: Increasing brightness means increasing luminance, but not related

linearly to each other. Increasing saturation means increasing vibrance or color intensity,

in the sense 'more far away perpendicularly from the neutral axis (the gray axis)'.

In HLS or HSB the saturation is just one of the three coordinate axes. HSB is in my opinion

nonsensical, because at B=1 the saturation is anything between S=0 and S=1, which is a

singularity by concept.

Best regards --Gernot Hoffmann

• ###### 33. Re: CIE tristimulus values

I would like to ask an unimportant question.

Gernot ... when drawing chromaticity diagrams, do you know why x and y axes were chosen?

I'm not a Matlab user, but I think that, chosing z in place of y does not create any significant difference, because x + y + z = 1.

But, as we know, y is the relative value of the luminance dimension Y ... so, if we choose to draw chromaticity diagrams with the x and z axes, would it be more reasonable?

• ###### 34. Re: CIE tristimulus values

If you and the other readers don't mind, I would like to answer your question again using my own

illustration. The reason is simply, that I had asked many years ago the same questions.

http://docs-hoffmann.de/ciexyz29082000.pdf

Page 8

The top illustration shows the plane x+y+z=1, or simply the plane through the three points  (1,0,0),

(0,1,0), (0,0,1)  in xyz. The curve on this plane is already a chromaticity diagram (boundary points

from XYZ, projected by a perspective projection onto this plane, thus actually throwing away one

of the three dimensions).

It's a 2D curve in a 3D space, and this curve can be projected further onto xy or yz or zx. In my opinion

these three alternatives are equivalent. There is no special benefit, that Y is the luminance, which is,

as far as I can see, nowhere practically used in the horseshoe diagram.

By the way: In the bottom illustration on p.8 meanwhile I have corrected a graphical offset, which

was  introduced by the transition from PageMaker to InDesign one year ago.

Best regards  --Gernot Hoffmann

• ###### 35. Re: CIE tristimulus values

I would like to thank to you especially for such wonderful documents ...

They're helping me so much in my study and the good news is that I've started to understand them