A little bit about gamuts

[Doug Kerr]

But what of its saturation? Could you plot that 3D "horseshoe"Asher

The contents of the horseshoe comprise all visible hues and all saturations. The saturation is defined as zero at the "white point" and as 100% at the boundary of the figure (the spectral locus or the locus of non-spectral purples).

For the "hypothetical" color space I mention ("all visible colors up to some maximum luminance), all hues, at all possible saturations, exist at any luminance up to that maximum.

Best regards,

Doug

 

[Jack_Flesher]

delete delete

 

[Jack_Flesher]

Hi, Jack,



No, "all humanly visible colors" doesn't imply any color space coding and thus some arbitrary maximum luminance. Colors exist without benefit of any color space definition.

I never said that visible color needed a colorspace definition -- I said colors expressed as RGB values need a colorspace designation to have any meaning. Big difference.

My last comment on this topic, but luminance is NOT arbitrary in human vision. I can only see COLOR between the 0 and 100% luminance limits of human vision; at the 0% luminance for human vision all I see is black and at 100% luminance limit of human vision all I see is white; there is no further color information available to me than what I can see. Therefore all colors I can see are between those specific limits and therefore, definitely are LIMITED.

I think the point you are missing Doug is that in this context the luminance range for human vision is not the same as the luminance channel value in the HSL or Lab models, but the actual limits of human vision. In color model terms, at 100% luminance and 0% saturation or the upper limit of human vision, all different hue values will generate the same pure white; hue becomes irrelevant to the final color.

Cheers,

 

[Jack_Flesher]

Hi Jack,

I nearly overlooked your helpful reply! Doug came back with a very impressive in depth representation of the influence of the white point which now I see in a way as the point by which one suspends the 3D tent of chromaticities in 3D space.




Yes Jack, this would work. But is it possible to generate a color "picker" palette that would have colors with luminance and saturation fixed?

Asher

Sure it would be possible. You would create the palette in the HSL dialog with saturation and luminance values fixed at your desired points, then work your way around the 360 degrees of the Hue wheel, using whatever spacing you wanted to create x number of patches. For example if you went every 3.6 degrees of hue, you'd end up with 100 distinct hue patches, all at the same luminance and saturation level.

However -- and you can do this in Photoshop and prove it to yourself -- if you set luminance at 100% and saturation at 0%, every different hue value you choose will all generate the same pure white (and all will be equal to Lab 100, 0, 0)

Cheers,

 

[Doug Kerr]

Hi, Asher and Jack,

Further to our earlier discussion, here is an illustration (in the CIE xyY coordinate system) of the gamut we could describe as "all visible colors" (with the understanding that we mean "with luminance up to a fixed value we would identify in our color coordinate system as 1.00"):

Note that this is not the gamut of any of the color spaces we commonly reference; they can all be thought of as subsets of this.

My apologies for the primitive illustration. (The oblique projection may not be exactly precise, either!)

Best regards,

Doug

 

[Jack_Flesher]

And here is a simple HSL cone model of human vision to illustrate what I mean about the 0% and 100% luminance endpoints being limits. Note that as you move away from the central Luminance values, saturation gets progressively reduced until it hits 0 at the Luminance endpoints:

 

[Jack_Flesher]

Here is a similar spherical Lab model of human vision, also showing saturation diminishing as you approach the Luminance endpoints. Another note about Lab and one of the many reasons imaging "gurus" prefer to work in it -- Note how the chromatic component channels a* and b* relate similarly to color temperature (b) and tint (a) sliders, making it relatively easy to adjust overall color and tint in an image independent of luminance:

Cheers,

 

[Doug Kerr]

Hi, Jack,

And here is a simple HSL cone model of human vision

I think perhaps this is an HSL transform of (some) RGB gamut, based on one of the accepted RGB to HSL transformation algorithms.

Like RGB color models, HSL is a device-dependent model, and an HSL space is predicated on the primaries of the "parent" RGB space.

Best regards,

Doug

 

[Jack_Flesher]

deleted***

 

[Jack_Flesher]

So Doug...

1) If the transform space for HSL is human vision, does it become device independant?

2) Is Lab truly device independant if it cannot render colors beyond human vision?

3) Are colors truly colors if they are outside human vision?

Cheers,

 

[Doug Kerr]

So Doug...

1) If the transform space for HSL is human vision, does it become device independant?

I don't know what "for human vision" means in this case. HSL is defined as a transform of RGB (actually, various HSLs are defined as various transforms of RGB). So no HSL color space can have a gamut that is "all human vision" (not even a chromaticity projection on the x-y plane that "fills the horseshoe"). Any HSL color space has the same gamut as the "parent" RGB space (although the mapping is very peculiar).

For example, these three colors (expressed in RGB terms) have the same L and S (for what is I think is perhaps the most widely-accepted RGB-HSL transform):

200,200,50
200,150,50
200,100,50
200,50,50

They of course do not have the same luminance (CIE luminance, that is) nor the same saturation (based on the normal colorimetric definition of saturation).

2) Is Lab truly device independant if it cannot render colors beyond human vision?

I'm not sure of the exact definition of "device independent" in this context. I generally take it to mean that the definition of color in a device-independent model does not make any assumption about the rendering device (such as its primaries, if it is a tricolor display). But I'm not sure. It has never really been a "clean" definition, in my opinion.

I can't imagine that the definition of "device independent color space" would require accommodation of of "colors outside human vision", since there are no such things (see below).

3) Are colors truly colors if they are outside human vision?

No. Color is a property of human vision. Light whose spectrum does not allow it to be seen does not have a color.

There is also no "invisible" light. The term "infrared light" is a misnomer - "infra-red radiation" is what we are speaking of.

So what do points on the x-y plane outside the horseshoe represent? They don't represent any physical phenomenon (not even some "invisible" radiation). The reason is that if we take some spectrum not having any visible spectral components and analyze it (using the standard observer functions), its X, Y, and Z would all be zero, and x and y would be undefined (or zero, depending on how you like to treat 0/0).

So they are just "places on the paper" with no physical nor perceptual significance.

I think.

This is all neat, and makes one's head hurt, no?

I enjoy these discussions with you. Of course, in many cases I am just trying to be "thought provoking" but may come off as just "provoking".

Best regards,

Doug

 

[Jack_Flesher]

Indeed, we hit many theoretical conundrums when debating color science

No. Color is a property of human vision. Light whose spectrum does not allow it to be seen does not have a color.

There is also no "invisible" light. The term "infrared light" is a misnomer - "infra-red radiation" is what we are speaking of.

Right. So if light outside human vision is radiation and not color, it seems that any color gamut can only be as large as the limits of human vision, and therefore has no unlimited components, either in HSL or Lab models.

 

[Doug Kerr]

So if light outside human vision is radiation and not color, it seems that any color gamut can only be as large as the limits of human vision, and therefore has no unlimited components, either in HSL or Lab models.

The gamut is limited in HSL, since HSL is defined as a transform of RGB (at least all the flavors of HSL I have encountered).

Now one could perhaps craft an extension to the transform to visible colors outside some particular RGB gamut (by allowing R, G, or B values that were negative, or greater than 255), this giving a "wide-gamut" HSL. But the transform is very peculiar (it doesn't faithfully follow any colorimetric concepts, as I illustrated in my last message). So I think an extended version of it would be pretty silly (the regular form is pretty silly).

Now, if we speak of a true luminance-hue-saturation model (HSL is not a luminance-hue-saturation model - the L of HSL does not follow CIE luminance, or even a transform of it, and the S of HSL doesn't follow colorimetric saturation), then indeed that would span "all human vision".

Incidentally, the often seen "bi-conic" presentation of the HSL space is very baffling to me. If we consider its coordinates to be L (vertical), S (radius), and H (angle), then the full HSL gamut is a cylinder, not a bicone (of course, there are singularities at the very top and bottom, where H and S are undefined).

That is, for any value of L (except for exactly 0.0 and 1.0, where there are singularities), the range of S is 0-1 on a 0-1 scale.

For example, this RGB color:

255, 245, 245

has this perfectly valid HSL representation:

0, 1.00, 0.98 (the scale of S and L here is 0-1).

And this one:

RGB 5, 5, 0

is this in HSL:

60, 1.00, 0.01 (again, S and L on a scale of 0-1).

So I'm not sure what coordinate system the bicone is plotted in, and what it is supposed to be a "homey" way of showing.

Maybe you can help me out there.

I'm afraid that is was perhaps crafted as a misguided way to illustrate some concept, and has just survived through inertia.

Best regards,

Doug

 

[Asher Kelman]

Doug and Jack,

So how does the b-conal HSL model compare with the classic Munsell system used in a lot of older biological studies where color is described and is today marketed by XRite?

Diagram by xRite™

It also appears to use the ranges of the "color temp" and "tint" seen in Adobe Camera RAW.

Munsell Color Tree

"The Color Tree is an attractive, three-dimensional model that makes it easy to comprehend the Munsell three-dimensional color space.

It features 309 colors from 10 constant hues mounted on clear acrylic panels assembled on an acrylic base. Height 12-1/2”, Width 16”, Base diameter 12”. MSRP: $269.00"


It's a very expensive thing! I wonder who uses it!

How is it different from the HSL model (besides having merely 309 loci depicted in this particular desktop version)?

Asher

 

[Doug Kerr]

No cone of my own

I have just done a few calculations using what I find (today) to be the consistently-cited equations for the HSL color space (in particular, for taking a color description in RGB terms and converting it to HSL terms). Presumably, any HSL triple we get from these equations by putting in bona fide RGB values must be a part of the "HSL color space."

The calculations I have done seem to prove that, for any value of L, we can attain an S value (note that this is not colorimetric saturation) of 1.0 (I will use the 0-1 scale for L and S here). In fact, we can get S=1.0 for any hue we want, at any value of L that we want (note that L is not photometric luminance).

In every case, to get an S of 1.0, one of R, G, and B must be either 255 (on the 0-255 scale) or 0.

Now (even forgetting about the cones) this may seem weird. How could it come out that way? How could this relate to familiar colorimetric concepts?

Well, this is because the HSL transform equations are very peculiar. Keep in mind that this color space was defined in the early days of computer graphics. There was a desire for a color space that would make sense to the user. Ideally, it would work in terms of the familiar "qualitative" color attributes: luminance, hue, and saturation.

But it was too complicated to define such a color space, and the computations to convert an input in those terms to RGB (and vice-versa) were burdensome. So the wonks invented a "bogus luminance/hue/saturation" color space and defined it in such a way that the conversion between it and RGB would be very simple.

As a result, it has some really peculiar properties.

One of its properties is that, going from RGB to HSL, to determine L and S we only need to know the values of the highest and lowest of R, G, and B. That is why these RGB colors have the same values of S and L in their HSL representation (they have different values of H.:

200, 200, 50
200, 150, 50
200, 100, 50
200, 60, 50
200, 50, 50

even though they actually have quite different (photometric) luminance and (colorimetric) luminance.

The determination of the H value is not quite so peculiar, and in fact involves R, G, and B.

In any case, if the coordinate system in which the infamous bicone (or bi-hexcone) is drawn is, as it seems to be, L (vertically), S (radially), and H (azimuth angle), then there is no way that the gamut of the HSL space is a bicone (or bi-hexcone) or anything even close to it.

I found a reference to the Canon Picture Styyles editor, which works in HSL. It points out that only for L=0.5 can we set S as high as 1.0. For lower or higher values of L the range of S is correspondingly reduced. That sure fits the bicone notion. But doesn't at all match the RGB to HSL equations.

One possibility is that this is some other color model altogether, the two accidentally sharing the same name. But many of the authors who put forth the same equations I have used for my testing still speak of (and in some cases illustrate) the bicone (or bi-hexcone).

So I am still baffled.

Best regards,

Doug

 

[Asher Kelman]

So Doug,

Is the Munsel paradigm just a simple representation of HSL or what?

Asher

 

[Doug Kerr]

Hi, Asher,

So Doug,

Is the Munsel paradigm just a simple representation of HSL or what?

I haven't yet thought about the relationship between these color notation systems and various mathematical color models (such as HSL). I'll think about that as soon as I clear my head of this "bicone" thing, which I think I have just cracked.

Let me try and nail that, and then I'll look into Messrs. Munsell etc.

Best regards,

Doug

 

[Doug Kerr]

The cones

I think I have cracked the mystery of the "bicone" presentation of the HSL color space.

Indeed, the gamut of the HSL color space, plotted in the cylindrical coordinates H, S, L, is a cylinder.

The "bicone" figure is not in the HSL coordinate system. The "vertical" axis is in fact L, and the angle axis is H, but the "radius" axis is something else (never mentioned). Let me develop the concept.

First, suppose that the radial axis were actual colorimetric saturation (not the S of HSL). I'll call that CS.

The highest luminance for which we can have a fully-saturated color (CS=1.0) has an HSL L value of 0.5. (An example would be RGB 255,0,0). (The actual luminance of such a color, Y, varies with the hue.)

At higher luminances (L>0.5), the maximum attainable CS declines. As we approach the maximum luminance (for which L=1.0), the range of CS shrinks to no range at all (CS=0 only).

Thus, our gamut plot (in H, CS, and L), from the L=0.5 level upwards, becomes something like a cone. (I'm not sure of the exact shape, but it is certainly cone-oid. Calculating CS is a little painful, which I why I don't yet know the exact shape. And I doubt that any of the figures we are discussing are actually rigorously determined anyway.)

But, from L=0.5 downward, the range of CS does not shrink. That is, we can have a color of very low luminance (and thus very low L) for which CS, the true colorimetric saturation, can still be any value up to 1.0.

Thus in fact, the HSL gamut, plotted in cylindrical coordinates H, CS, L would be a cone atop a cylinder.

So we still don't have the entire answer to the infamous "bicone".

But there is this notion that a "100% saturation" color at a low luminance is not as "punchy" as a 100% saturation color at a higher luminance. So evidently somebody decided that for luminances lower than the highest luminance for which we can have 100% saturation (that is, colors for which L is less than 0.5) saturation should be "discounted". I'll call this "discounted saturation" DS.

I have no formal definition for it; my guess is that it is SS*(L/0.5) for 0<=l<=0.5, and just SS above that.

Under this notion, as we approach zero luminance (and L=0), the available range of DS shrinks (just as CS does as we rise toward L=1) (and in fact DS follows this as well).

Thus, if we plot the HSL gamut in the cylindrical coordinate system H, DS, L, we get something that is generally shaped like two cones base-to-base, the top cone reflecting the actual decline in available colorimetric saturation as we approach maximum luminance (and thus maximum L) and the lower cone representing the decline in this fanciful property of "punch" (DS) as we approach black.

Now whether these are actually cone-oids or hexagonal prism-oids I haven't yet ascertained. Some people describe the figure as a "bi-hexcone" (where by "hexcone" I assume they mean a hexagonal pyramid). I have to look into the actual reckoning of SS to find out is this is true.

You can perhaps grasp what happens here on this grid of variations of color with S and L for a given H (0: red):

(This is actually adapted from a figure in the CSS3 color specification, where HSL is a recognized color notation.)

Note that for L=0.125, the rightmost cell (S=1.0) has a genuine colorimetric saturation of 100% (the RGB coordinates are 64,0,0), but doesn't seem very - well, "punchy". So perhaps its "DS" is only about 0.25.

So that seems to be the story, gang. The "bicone" is the gamut plotted in a cylindrical coordinate system where the radius is "punch". But that is never mentioned.

Finally, please remember that the gamut of the HSL color space is no differetn than the gamut of (some) RGB color space. If we think of the colors as described by their RGB coordinates, we tend to call it the "RGB gamut". If we think of the colors as described by their HSL coordinates, we tend to call it the "HSL gamut". But it is the same gamut of colors (just as the extent of my home lot is the same whether described in terms of latitude and longitude or in "grid" notation).

There is a good possibility that the parameter of interest here is actually the magnitude of chrominance (a different concept from chromaticity). I'll look into that shortly.

Yes, this is my day job.

Best regards,

Doug

 

[Doug Kerr]

Aha - chrominance

Upon further reflection, I believe that the "radial" axis of the coordinate system in which the infamous HSL gamut bicone is plotted is magnitude of chrominance (and in fact the radius-angle plane is a plane of chrominance).

*************

Let me give some background on chrominance (which is a parameter different from chromaticity).

There is a class of color models called "luminance-chrominance" models. In these, we essentially describe a color in terms of a fanciful "recipe": we start with a dose of "white" light (that is, light whose chromaticity is the refernce white of the color space) in an amount corresponding to the luminance of the color being described. Then we add a "colorant": light of a certain hue in an amount that brings the overall color to the color being described.

For example, the YIQ color space (the basis of NTSC color TV signal encoding) is one of the earliest prominent examples of a luminance-chrominance color model. (In it nonlinear forms of both luminance and chrominance are used, which complicates things a little.)

And in fact, the L*a*b* color space (and its cousins) are Luminance-chrminance models (again with the wrinkle of nonlinear representation I spoke of a bit ago in connection with the YIQ color space). The a*b* plane is a chrominance plane.

We can describe the chrominance component in either Cartesian form or polar form. In polar form, we have a radius (how much "colorant" is involved) and an angle (what is its hue). The radius can be thought of as the "magnitude" of the colorant (chrominance) "vector".

Now, here is a key distinction between chrominance and chromaticity. Suppose we start with some color, having a certain luminance and a certain chromaticity (and a certain chrominance). We now "attenuate" it (imagine a neutral density filter). Its luminance is lower. Its chromaticity is unchanged (we did nothing to change it). But its chrominance is now lower (in magnitude) - actually proportional to the luminance.

I use this homey analogy. Imagine that we are to mix up one gallon of paint of a certain "color". We start with almost a gallon of "white", and add a certain number of ounces of various colorant ingredients.

Now, to mix up a quart of the same "color", we start with almost a quart of "white" and add 1/4 of much of the various colorant ingredients.

(Note that in this analogy, the "quantity" of point is analogous to the luminance of the color in our color model case, and the amount and composition of the "colorant dose" is analogous to the chrominance in our color model case.)

You might wonder why adding the colorant does not increase the overall luminance, above the value for the color being described, since that luminance is already accounted for in the "white light" base. A brief explanation is that the colorant has hue and "potency" but zero luminance. Obviously no physical light component can be this way. But the "colorant recipe" paradigm is just abstract - we don't really "produce" light that way (we actually make it by RGB or whatever). So "physically-unrealizable" colorants fit fine into the paradigm.)

*************

Now, back to HSL.

We will start with a color of some arbitrary hue (red, perhaps) at the highest luminance for which we can have 100% saturation (colorimetric saturation, not "S"). That will always turn out to have L=0.5 (and S=1). (An example is RGB=255,0,0.)

If we hold the same saturation (thus the same chromaticity, since we hold hue constant), but reduce L (thus reducing actual luminance, proportionately), the magnitude of the chrominance also decreases proportionately.

Thus the maximum chrominance we can have (which is always the one for 100% colorimetric saturation) will decrease as L decreases. This gives the "lower cone" of the dreaded bicone.

Now, back to our stating color (L=0.5, 100% saturation). As we increase L (thus increasing luminance), we find that we can no longer attain 100% saturation (as one of teh R,G,B is already at its maximum); the maximum saturation declines as we increase L. Now, for any given saturation, the chrominance increases with increasing luminance. But the maximum saturation decreases faster than that, and the net effect is that the maximum available chrominance declines with L. This gives us the upper cone of the dreaded bicone.

Thus I conclude that the "bicone" is plotted in a cylindrical coordinate system where, essentially, the vertical axis is L, the radius is (the magnitude of) chrominance, and the angle is hue (and thus the whole angle-radius plane is chrominance).

Now this may not be exact (and since we have not seen any equations for the bicone, there is no such thing)!. But I suspect this is the underlying concept.

Best regards,

Doug

 

[Jack_Flesher]

Glad you finally got your arms around the bi-cone. Now that we're together there, let's try visualizing the "bi-cone" instead as an arbitrary irregular spheroid 3D "plot" of human vision, viewed in HSL component plot form... It should now be easier to visualize the pure bright white point at the very tip and the pure solid black point at the very base point of this spheroid; gray values become a line (likely irregular) connecting the two endpoints somewhere along a quasi-central axis of the spheroid; maximum saturation colors run along the circumference of an irregular quasi-equator of the spheroid; the highest saturated colors available in the system at any given luminance value form the irregular surface of the spheroid; and finally, any values less than the full saturation of any hue for any given luminance value form the internal volume of the spheroid. Clear as mud now, right? LOLOLOLOL!!!

Frankly, this is why I keep my teaching of color management for photographers basic and somewhat over-simplified. But I do tell them what I'm about to explain is not 100% technically correct before I teach it. (It's also why when they ask me to post my color management for digital photographers powerpoint presentation online, I refuse -- I don't need the headache debates over my not-completely-accurate over-simplifications!) BUT, at the end of the day, these folks leave understanding the RELEVANT components of color science for digital imaging. IMO giving the scientifically accurate and full explanations for each concept would take too long and over-complicate what they really need to understand, and frankly is way more information than a typical photographer needs. As a color scientist, one needs to understand this for sure, but I suspect for 90% of photographers out there they've already seen more color science discussed here than they care to attempt to comprehend...

So, should we move on to explaining conversion and assigning profiles, rendering intents and black-point compensation? LOLOLOLOL!!!

Cheers,

 

[Asher Kelman]

Doug,

I'm up to post # 48. Excellent imagination to conceive how the biconal model might have been derived from it's corresponding RGB gamut (but which one?)

If one wants to create a color, one can use 3 perfect RGB lights and measure the flux from each one and then mix the light in some perfect way.

With that light being reflected from an illuminated color card, I'm struggling with understanding how the L is measured.

First, is the maximum luminance in any of the 3D models described/defined in terms of reflected flux of the particular wavelength mix of incoming light (color temp) or the light reflected back from a flat surface* of the particular color material (presumably not shiny).

IOW, how bright is "brightest" in "L" in these 3D models? Is there an measured figure we can use even if it has to be hue and sat dependent.

Asher







If one uses a flat surface it would have to be "large", by which I mean large enough so that measurements from the center and "nearby" would be uniform.

 

[Doug Kerr]

Hi, Asher,

Doug,

I'm up to post # 48. Excellent imagination to conceive how the biconal model might have been derived from it's corresponding RGB gamut (but which one?)

Any one you care to choose (and of course, mention). I don't think that the HSL convention itself presupposes any particular RGB space. But as specified for cascading style sheets for HTML and XML documents, sRGB is presupposed as the underlying basis.

If one wants to create a color, one can use 3 perfect RGB lights and measure the flux from each one and then mix the light in some perfect way.

Well, regarding "perfect" RGB lights - each standard RGB color space among other things prescribes R, G, and B primaries of specified chromaticity (different between different sub-families of the RGB clan). There is no "inherent" set of primary chromaticities.

With that light being reflected from an illuminated color card, I'm struggling with understanding how the L is measured.

I assume you mean the "L" of HSL.

We determine the RGB coordinates of the reflected light, and then convert to HSL with a set of standard transform equations. (Did I answer the right question?)

In reality, our colorimeter probably doesn't read in RGB, so we have to take the color space in which it works and convert that to RGB.

And note in that regard that the "luminance" readings of the meter aren't on a relative basis of 0-100% (as we have in a color space), but in absolute terms (in cd/m^2, for example). Thus we must decide what luminance we will consider "100%" (as for example, would be considered 100 points as L* in L*a*b*, or Y=1.0 in xyY).

First, is the maximum luminance in any of the 3D models described/defined in terms of reflected flux of the particular wavelength mix of incoming light (color temp) or the light reflected back from a flat surface* of the particular color material (presumably not shiny).

In fact, if we are being rigorous, we examine the spectrum and determine its color in terms of the CIE XYZ color space. Then we transform that to the color space we are interested in (often having to choose a white point if one is not inherent in the space definition).

If in fact the "destination" color space is HSL, we must convert first from XYZ to (the appropriate flavor of) RGB, and then to HSL (although of course one could construct equations that did it all in one step).

Note that this makes no presumption about how that spectrum came to exist - for reflected light, what was the spectrum of the incident light, what was the reflectivity spectrum of the surface, was specular reflection involved, etc., or in the case of "emitted" light, what was it emitted by and what was its angular distribution. It is just based on what is the spectrum of the light that arrives at our "instrument".

IOW, how bright is "brightest" in "L" in these 3D models? Is there an measured figure we can use even if it has to be hue and sat dependent.

Well, just as I said a minute ago (sorry to get out in front of the questions), what actual luminance (in cd/m^2) we treat as an L of 100 in HSL (or an L* of 100 in L*a*b) is wholly arbitrary (and those are both hue dependent - even L* is a pseudo-luminance).

A reminder of that is that, for a scene item with a certain luminance (as we would measure it with a photometer), the RGB value in the digital image (and thus the implicit "relative luminance") depends on exposure (in the sense of shutter speed and effective relative aperture) and ISO sensitivity.

If one uses a flat surface it would have to be "large", by which I mean large enough so that measurements from the center and "nearby" would be uniform.

Sure, and that all depends on the "acceptance angle" of the photometer. One can get photometers whose field of view is very tiny.

But technically, luminance and chromaticity can exist at a "point" on a surface (we must consider an infinitesimal area centered on that point to get any flux to measure, however).

Best regards,

Doug

 

[Asher Kelman]

Doug,

I am interested in providing a simple physics basis for the maximum brightness and saturation in various 3D color spaces. I really have always been pained by the concepts of 255. The deep "colors" are perceptual phenomena we experience from childhood. Let's consider we have colored monchromatic lasers for every layman's color hue. That wavelength can be given in nm of the light wave or else in terms of kev energy of the photon particle. Either way hues can be represented thus.

That was easy! Saturation? That's a degree to which a hue is dominant in a particular light beam. How is it defined scientifically? What are the units? Let me just suggest that one could say that saturation is the increasing proportion (probably normalized by some functions) of the perceived hue in a mixture of white light (of a "standard" temp).

We can get that particular color light in a number of ways. One would be, by using mixed beams of primary colors Red, Green and Blue. Here however, we have the advantage, for the sake of discussion of a perfect light mixer with a red laser source and a white light source which can be increase in output without altering the color temp! At least we can use this setup within these operational bounds.

So let's now increase luminance and maintain very high saturation, of 99% monochromatic red laser and 1% of our standard white light, each with the same flux of photons. To me it appears that the light beam landing on a white surface would appear equally saturated at all levels of brightness that did not cause eye discomfort. If it did we can simply record that image with a super high speed camera and show that the saturation was indeed constant.

Tell me where am I misunderstanding the 3D spaces.

I can describe colors by the energy of a photon and how much white light is added to that. That gives me 2 dimensions. The 3rd dimension must be in units of energy/unit area/sec and I cannot see where that is in the models we use? Yes there is "Luminance" but how does that relate to physical measurements of photon flux?

So how is it we have in all the models, discussed so far, a fixed max L(Luminance) apex when all we need to do is turn up the brightness? Why do you feel that "as brightness increases saturation must decrease". In the set up I describe we can increase the flux of white light and the monochromatic laser light in exact proportions and therefore saturation should not change!

There's a disconnect somewhere and I cannot put my finger on it yet!

Thanks in advance for solving this puzzle for me! Maybe it would be cleared up anyway by some good red wine, LOL!

My pragmatic solution:

I know that the various L (luminance) axes are relative scales.

So we say, "Here is a fixed intensity of illumination. Now map all the colors possible in a 3D space" Then the color seen is not related to actual variances in light arriving to different parts of a scene. I can see that these models normalize for different intensities of incident light.


Asher

 

[Doug Kerr]

Color and color spaces - Part 1

Hi, Asher,

Doug,

I am interested in providing a simple physics basis for the maximum brightness and saturation in various 3D color spaces. I really have always been pained by the concepts of 255. The deep "colors" are perceptual phenomena we experience from childhood. Let's consider we have colored monchromatic lasers for every layman's color hue. That wavelength can be given in nm of the light wave or else in terms of kev energy of the photon particle. Either way hues can be represented thus.

Indeed, each wavelength in the "visible spectrum" conveys a unique hue. (And, just for completeness, we also have the set of non-spectral hues, the purples, but we need not let that derail us for the moment, and I'll ignore them in much of what follows.)

That was easy! Saturation? That's a degree to which a hue is dominant in a particular light beam. How is it defined scientifically? What are the units? Let me just suggest that one could say that saturation is the increasing proportion (probably normalized by some functions) of the perceived hue in a mixture of white light (of a "standard" temp).

That's pretty good. Let me restate it.

We can think of saturation as being measured on a chromaticity plot (perhaps on the CIE x-y plane) along a line running from the chromaticity we choose to arbitrarily call "white" to a monochromatic chromaticity (which, on the plot, lies on the "spectral locus", or "horseshoe". The monochromatic chromaticity can be thought of as a "pure" example of a certain hue.

[See my comment later about "white light of a standard temperature". I don't want to derail the story here.]

At one end of the line (at our white point), the saturation is defined as zero. At the other end of the line (at our monochromatic chromaticity), the saturation is defines as 1.0 (or 100%, if you prefer). Intermediate values of saturation are found linearly along the length of the line.

Thus in fact this outlook on saturation, s you suggested, is a measure of the "purity" of our color, where composition wholly by a monochromatic component represents full purity, but teh addition of "white" light (whatever we consider that to be) to the recipe dilutes that purity, until when the recipe consists wholly of white light the purity is completely gone.

We can get that particular color light in a number of ways. One would be, by using mixed beams of primary colors Red, Green and Blue. Here however, we have the advantage, for the sake of discussion of a perfect light mixer with a red laser source and a white light source which can be increase in output without altering the color temp! At least we can use this setup within these operational bounds.

A useful model. We assume the laser output to be monochromatic (as you stipulated at the outset).

So let's now increase luminance and maintain very high saturation, of 99% monochromatic red laser and 1% of our standard white light, each with the same flux of photons. . . .

Well, perhaps you mean the laser output having 99 times the photon flux of the "white source"

. . .To me it appears that the light beam landing on a white surface would appear equally saturated at all levels of brightness that did not cause eye discomfort.

As to "appear", that is a little dangerous. Human perception of saturation varies with absolute luminance (or rather. luminance relative to the eye's state of luminance adaptation.) But the light would in fact have the same saturation at all levels of brightness.

If it did we can simply record that image with a super high speed camera and show that the saturation was indeed constant.

Not sure why a "super high speed camera" would be needed, but nevertheless, quite so.

Tell me where am I misunderstanding the 3D spaces.

I'm not sure what you mean. What you have said here above is all fine. I guess you mean in regard to what you will say next.

I can describe colors by the energy of a photon and how much white light is added to that. That gives me 2 dimensions. The 3rd dimension must be in units of energy/unit area/sec and I cannot see where that is in the models we use? Yes there is "Luminance" but how does that relate to physical measurements of photon flux?

[The following has nothing to do with where you are going, but I just need to mention it for completeness, as we sometimes get misdirected by not recognizing this.]

Let me clarify that we often say that, in luminance-chromaticity color models, one of the coordinates is "relative luminance", but that would be strictly precise only if we were talking about the light reflected from (or emitted by) a finite surface (for which the "potency" property is indeed luminance.. If we were talking about light from a "point source", then the actual physical property would be (relative) luminous intensity; if we were talking about a "beam" of light observed in mid-travel, it would be (relative) luminous flux density. If we were talking about the impact of that beam on a surface, it would be "relative" illuminance.

So we need to remember that "luminance" is just a proxy for any of four different measures of the "potency" of light, depending on the situation. In any of them, it is luminous flux that is the operative ingredient. It's just a difference of "luiminous flux per unit what"?

Now back to the story.

So how is it we have in all the models, discussed so far, a fixed max L(Luminance) apex when all we need to do is turn up the brightness?

If we don't identify a certain luminance as "100% (directly in a luminance-chromaticity color model, implicitly in others) we have an unmanageable situation with regard to "device dependent" models.

Suppose we used the following color space (which is actually what color photometers report in): luminance (absolute) in units of cd/m^2 plus chromaticity (say, on the CIE x-y plane). A 3D plot of this color space would be an extrusion of the areas within the "horseshoe" to an infinite height. (This is the Lxy color space, in fact, where here the over-used symbol "L" has its meaning in popular photometry, actual luminance.)

Now, recall that what we mostly use color models (as particularized in specific color space definitions) to describe the color of pixels in a photographic image. (And their properties in fact take that the realities of that context into account.) Perhaps we decide to do this in our camera in the Lxy color space. Then for each pixel there would need to be three numbers, giving the values of L, x, and y respectively.

Then, strictly, when we photographed a scene, for each pixel in the image, the value of L would be the actual luminance of that point on the scene.

Well, for one thing, L would have to have a gigantic range, since the range of scene luminances in which we are intersted is enormous. And if we wanted to accurately represent the lower values of L, this numbering system would have to have a gigantic "range". And a consequence would be that a very large number of bits would be required per pixel just for luminance. (Of course a "floating point" representation would mitigate this substantially.)

Even more importantly, the camera sensor would have to have s similarly gigantic dynamic range.

Then, what do we do with this image when we display it? To be true to the driving theme of this discussion, we would need to present on a screen, for each pixel, the luminance and chromaticity of each point on the original scene.

Well, firstly, this would require a light source for the display of gigantic output capability. And when we did that in our living room, we would be blinded.

Well, you may say, of course we would want to scale the onscreen output in luminance to suit the viewing environment (and in the process generally allow us to use a practical display mechanism). But when we do that, we squander the gigantic range of luminance carried in the image (at substantial bit expense) and teh gigantic dynamic range of teh camera (at some other great expense).

So of course we "scale" the incoming luminance by controlling aperture and exposure time. And once we have done that, then in our color space, (used for image recording or manipulation purposes), we have no need for an "infinite" scale of luminance.

[continued in part 2]

 

[Doug Kerr]

Color and color spaces - Part 2

[Continued]

Why do you feel that "as brightness increases saturation must decrease".

Note that this is for a particular context: one in which the underlying color space (regardless of the space to which we transform it) is an RGB space, in which the values of R, G, and B have a finite range (typically stated as 0-255). (A similar effect occurs however in the more fundamental color space, CIE XYZ.)

Now, that color space cannot describe at higher luminances colors of large saturation without requiring a value of R, G, and of B that is greater than 255. And that is the limitation. It is not a limitation of "color", but rather of the specific coordinate system we have chosen to represent color.

And of course the real ("historical") source of that limitation is the limitation of an RGB-type display mechanism, which pragmatically inspired the RGB color model.

Now, we could define a color space in which one of the coordinates was actually relative luminance and the other two describe chromaticity. (We might call this an L'xy space, where L' was luminance, normalized to some arbitrary value, as we discussed earlier.

Now in that color space, the available saturation does not decline with luminance. We could have a valid representation with L'=1.0 (the maximum) and x and y describing "fully saturated cyan", which in fact would be a spectral (monochromatic) chromaticity (something that a physical RGB dispolay device could not render at any luminance).

But when we fed images in that form to a display chain that would end up with an RGB display, gigantic parts of the color space gamut would be out of the device gamut.

In the set up I describe we can increase the flux of white light and the monochromatic laser light in exact proportions and therefore saturation should not change!

Quite so. But here we are speaking of "making light", not of "describing light in one of our color spaces". And you could describe any light you can make there in a true luminance-hue-saturation color space.

There's a disconnect somewhere and I cannot put my finger on it yet!

The disconnect is that the color spaces we use cannot describe all colors of light that can exist (on an absolute basis), for practical reasons (properties they got based largely on what we use those color spaces for).

My pragmatic solution:

I know that the various L (luminance) axes are relative scales.

So we say, "Here is a fixed intensity of illumination.

I have to interrupt here to caution you about using "intensity" here; that has a specific meaning in photometry, not necessarily the one you mean here. Are you thinking of, for example, luminance (even in its role as "proxy" for various other photometric measures)? I'll proceed as if you do mean that - light of a fixed luminance.

Now map all the colors possible in a 3D space.

Oh, once we have stipulated to a fixed luminance, all possible colors can actually be plotted in 2D space (any chromaticity plane will do). If we use x and y coordinates for chromaticity, then the plot "for all possible colors" would be the area bounded by the familiar "horseshoe".

Or perhaps you mean "light of not over a certain luminance". Then all possible such colors occupy a "gamut solid" in 3D space. Its shape depends on the coordinate system. If that is Lxy, then that shape is an upward extrusion of the "horseshoe" to an altitude of Lmax (the stipulated maximum luminance, if that is what you really mean.

Then the color seen is not related to actual variances in light arriving to different parts of a scene.

I'm not sure I know what you mean by that.

[/quote] I can see that these models normalize for different intensities of incident light.[/quote]

Well, I think you mean that we usually plant the range of color observed by our camera in a workable place in the color space we use (we think of it as planting it in the dynamic range of the camera, which then leads to that) based (typically) upon incident luminance.

But note that the color spaces themselves don't even contemplate that the light being described is "reflected from some surface as a result of some incident light". They just describe the color of light (wherever it came from ). It might have come from one face of a traffic signal.

Let me now (as threatened) return to the matter of "white light (of a 'standard' temp)".

First, if by "temp" you mean "color temperature", note that only "blackbody" chromaticities have a color temperature, and most flavors of white light that are recognized with a "name" are not such. So "D50" does not have a color temperature.

Now, for chromaticities "in the general neighborhood of the blackbody locus" we can assign them a "correlated color temperature", which is the color temperature of the chromaticity on the blackbody locus that is "closest" to the chromaticity of interest (to be precise, "closest" if we are working on the CIE u-v chromaticity plane).

But that correlated color temperature doesn't describe a chromaticity. We must accompany it by an expression of how far the chromaticity of interest lies from the blackbody locus, and in what direction.

My point here is that, unless for some reason we are speaking only of light having a blackbody chromaticity, we should not say "light of some temperature".

***********

Please forgive if this has not been checked for editorial or orthographic errors up to my usual standards. I have to move on to Breakfast 1.

Best regards,

Doug

 

[Asher Kelman]

Thanks so much Doug! I feel comforted in my own ideas on the pragmatic models of gamut. Your addition of cautions in the choice of words like "intensity and "color temp" as well as hinting that not all colors we perceive can be referenced to a wavelength on the visible spectrum are helpful guides.

The last point needs enphasizing in that we can distinguishi some colors that cannot be found and referenced to any one wavelength of light! Such colors need at least two monochrmatic or mixed light sources to be perceived. What a clever thing the human brain is!

Does all this have practical use in our photography? Well understanding color tools might allow wiser choices. Also it may allow us to guess what nature thought was important to our competing in a dangerous but rich planet!

Asher