This is your post I replied to: None of those people were alive when LEDs were invented, for starters. All of them defined their vector spaces etc in terms of wavelength. But accepting your shift of reference to something else, moving on: LEDs do not emit specific colors. They emit specific wavelengths. The color perception these wavelengths elicit depends on various circumstances, and varies for any given wavelength or combination thereof. The pixels reliably emit particular wavelengths, as you accurately specify. They do not emit specific colors - the colors one sees in their emissions vary by circumstance. To predict what colors will be elicited by those wavelengths, one must specify the circumstances in which they are seen, and a few other factors (genetic variation in the viewers, perceptual fatigue, etc). That is because wavelengths are not colors. To repeat: The colors "generated" by these wavelength emitting pixels vary according to various circumstances, such as background colors and ambient light and perceptual fatigue and the object represented and so forth. The author's vector space is defined over wavelengths. I agree that they refer to these wavelengths as "colors" - but that is valid only because they have carefully defined what they mean by "color" - namely: certain wavelengths. Since such authors have defined "color" in terms of wavelength, they have established by definition the correspondence with wavelengths that is necessary for referring to a wavelength vector space as one of "colors". One should remember that although "colors" defined in this way often share names with traditional colors, such as "red" or "violet", the visual perception of them will vary widely in traditional color depending on circumstance (For example: A wavelength combination the author has assigned the label "orange" may actually appear yellow, red, grey, brown, etc, depending on circumstances.). You mean wavelength vectors. Everything I've read and everything you have linked defines all that stuff - the algebras, the vector spaces, etc - in terms of wavelengths. You have linked nothing that approaches color analysis in any other way (there are other approaches: Goethe wrote on the topic, Newton invented a color wheel, more recent visual artists such as Mondrian developed fairly elaborate theories, and there is always one of the standard painter's approaches (https://www.thesprucecrafts.com/color-theory-for-painting-2578070) which of course vary considerably from the wavelength approach favored by engineers.) One major difference, for example, is the choice of "primary" or fundamental colors - the non-wavelength approaches usually base their analyses on red, blue, and yellow; the wavelength approaches normally choose the wavelengths to which the cone cells in the fovea centralis are tuned (I've seen different color name sets for these wavelengths: green and blue and red, green and green and red, grue and grue and maroon, etc) Another significant difference between wavelength approaches and perceived color approaches is the common arrangement of colors in a "color wheel"; which is accurate and useful in its description of real world color properties important for painters or fashion designers or stained glass workers or the like, but troublesome to the point of impossible as a basis of mathematical analysis. https://drawpaintacademy.com/a-comprehensive-guide-to-color-theory-for-artists/ https://www.artistsnetwork.com/art-techniques/rational-color-theory/ All the vector spaces (let alone the distance functions) in every single one of your links are defined over wavelengths, with color labels assigned to the wavelengths according to the convenience of the engineer or analyst or whoever is doing the analysis etc. I quoted your link to that effect, above. It's explicit, and perfectly clear.
Well that's erm, illuminating. You say my perception of colors from LEDs is actually a perception of wavelengths? That makes very little actual sense. In my universe, if something emits visible light then it must be colored light, even if it's colored white. I know that the white color I can see in a computer display is actually a mixture of three different colors. I can actually see this up close by magnifying it so I'm quite sure that white is a composition of three different colors. These must have different wavelengths; LEDs emit light with an energy determined by a band-gap, so I know the output is fairly narrow-band, almost a spike. Given the visible spectrum is an extremely narrow part of the overall EMR spectrum, it makes sense that narrow-band EMR will be perceived as a single color; this is why the average human sees the same color from a blue LED, albeit there is some dependence on the viewing angle. But given three fixed colors (with fixed wavelengths), you can assign 255 'intensity values' to each of them (the magnitude of each vector varies from 0 to 255); this is a vector space. It can be embedded in Euclidean 3-space (a cube of color). The red and green LEDs in my display are the basis of the CIE diagram (for me and my perception); they are red and green color basis vectors of a 2-dimensional slice of the affine cone over the visible spectrum, or 'spectral cone'. The apex of this cone is the "color" black, i.e. the 0-vector. Thus, the 2-d CIE diagram is at an intensity which is an affine distance from the apex (because intensity is defined over an arbitrary number of levels; 8 bits is a convenience, a choice made by human designers).
Well, I think that's somewhat inaccurate at least. Would you at least agree that color is a function of wavelength? Would you also agree that it's difficult to assign a power output to . . . a wavelength? You really need the wave as well (propagating in the time domain), even though it has this wavelength property?
He's saying - and has been saying for some time now - that your perception of colors from LEDs (and everything else) is not in a one-to-one correspondence with the wavelengths of light emitted from them. The emitted wavelengths alone do not determine what color you perceive.
The problems with color perception not being in a 1-1 correspondence with wavelengths, is there a way around this? Will it ever be possible to manufacture a device that does output light at a wavelength which appears to be fixed to the average human? That is, which stays the same color over a reasonable distance and angle, for a human perceiver? Or should we just give up? If I buy a can of blue paint, will it be blue every time I open the can, or should I expect something else? Dumb question, I know. Or is this one of those "nobody really knows" things?
They didn't. No light source stays the same color under all viewing conditions and for all observers.
In what sense has this problem been resolved by display manufacturers, movie makers, painters etc? Why is it that a theatre full of people all see the same movie (assuming they each have a normal perceptive visual response), or a gallery full of people who all walk past the same painting and look at it under the same ambient light? What's the secret?
It hasn't. Look: Please Register or Log in to view the hidden image! The square labelled "A" is emitting the same wavelengths towards your eyes as the square labelled "B". But would you argue that the two squares are the same colour? What makes you think that a theatre full of people will all perceive the same colours in the movie? You don't have any direct access to measure what they perceive. Same goes for the painting in the gallery. Or any other colour perception.
No, not unless I look up close, then I can see that the pixels are "illuminated" the same amount. But there are three colors in each pixel, so although at a distance I see two shades of grey, I also know these are a combination of red green and blue "wavelengths" in the light coming out of the screen. I have incontrovertible proof; I could also use some instrumentation other than my own eyes to capture spectral information, i.e. a spectral power curve. Moreover, the effect is not because my eyes respond differently, the effect is due to my visual cortex, and doesn't exist until after my brain processes the 'primary' visual response. I can model all the biology with lab equipment and a computer program; I might even be able to claim I can reproduce the above optical illusion on a machine, up to an approximation.
But for well over a century now, people have been tested for their individual responses to different colors and optical illusions by asking them what they see.
arfa brane: Your claim is that you are somehow able to map colours onto a vector space. I'm content to let you have that argument out with iceaura. The fact that you now admit that the visual cortex and other features of individual human brains are involved in colour processing shows that your initial claim that colour = wavelength, essentially, is hopelessly naive. I will leave it there.
Not just me either, lots of other people know this can be done. This is sciforums though, so I guess all I can expect here is mostly pathetic argument from a bunch of ignorant people who not only haven't done their homework, they aren't going to.
It looks to me like iceaura has done his homework on this. You - not so much. I'm not really interested in debating this topic with you, and iceaura is already doing an excellent job in showing you up, so I'll leave him to it.
Well I'm glad for you and iceaura both. Unfortunately you're both pretty lost with this subject and I'm not really interested in the idea that you're both right. Meaning Maxwell was wrong, Young and Helholtz too, and many, many thousands of people who use color models in computer imaging and analysis. Yeah, right. QuarkHead probably knows more about this than he wants to admit, but he's pretty much a heckler on the sidelines. I guess someone has to.
In the real world you aren't given three fixed colors for your three fixed wavelengths. The engineers and other wavelength analysis employers must - and do (as we read in your links ) - fix the colors (assign them to wavelengths and combinations thereof) by well motivated definition and careful specification or arrangement of circumstance. All of those people use wavelength vector spaces etc in their analyses and computer imaging. Not one of them uses colors except as defined by wavelengths or categories of wavelength etc. All of their "colors" are defined as (and therefore limited to) certain wavelengths and combinations thereof - that's how they bring the powerful (and digitally employable) mathematical machinery of vector spaces and so forth to bear, which would be impossible if dealing with colors themselves. The processes by which colors are assigned to the wavelengths used in the analyses etc are explicitly described in your own links. Why not read them? They are often detailed and clear. I quoted excerpts, above. - - - - Meanwhile: In the links I posted to examples of other approaches - analyses of "color space" based on colors and combinations of colors rather than the wavelengths of the EMR spectrum - one often finds "color wheels". These seem interesting and relevant to this thread, more than to the tangential argument I carelessly granted too much attention above (I was intending to use them to illustrate the impossibility of defining a suitable distance function over the space of colors - their variety, for one thing, and the fact that the distances around the wheel depend on direction as well as an essentially arbitrary spacing, but mainly their illustration of the fact that colors in the color space are not ordered - yellow is between red and blue, and red is between yellow and blue, both.). And also this came up: https://printninja.com/printing-res...ced-concepts/cmyk-vs-rgb-advanced-explanation https://printninja.com/printing-res...-academy/advanced-concepts/pantone-spot-color The takehome seems to be that the answer to "what is color" will not emerge easily from a consideration of how colors are generated or produced, how color perceptions are elicited, or similar cookbook comprehension.
Could you show me how to define a vector space of wavelengths, given that wavelengths are scalar and correspond to real numbers. I have never seen this in electronics so I'm quite keen to see someone (try to) do it. I have read them, they assign wavelengths to colors by defining color as a 'spectral' function of wavelength, have you not seen this? So any attempt to reproduce the human perception of colors with devices, radiometers or photon counters, is a waste of time, it will not tell us anything? There goes nearly 200 years of research? But perhaps more importantly, the Commission Internationale de l'éclairage system (see any CIE diagram) is simply a cooked up "book" with little real use? They should hang their heads in shame?
James R posted an image which my display has (he must assume) reproduced faithfully and which he claims is evidence that engineers haven't solved a certain problem with human visual response. What he seems to have skipped over entirely, is that the image is a solution (it presents an optical illusion and is therefore a solution to a problem). It has been carefully programmed, it's the result of some well-defined (and understood) visual response models . . . If he and I see the same illusion, what does that say about the image? And, why ask me what I can see? What's the point, if human visual responses are so varied and subject to all kinds of discrimination errors? Why did James expect me to see an illusory shading in the image? Huh?
I quoted your links, above, specifically doing exactly that. You posted them as examples of analysts setting up vector spaces etc, and I noted that they were doing that with wavelengths, not colors. As I posted above: They assign color names to wavelengths (it's the colors they are defining). They all define colors in terms of wavelengths, regardless of whatever a human eye would see in any particular circumstance (see post 129 for the latest example posted here). That partial translation into wavelengths, although a significant oversimplification and distortion of human color perception, allows them to bring in all that mathematical machinery that cannot be used to analyze colors themselves - the distortions and limitations involved in dealing with wavelengths instead of colors are worth it, for the benefit of being able to use the otherwise inapplicable mathematics. That's why I quoted a couple of those passages for you - you seemed to have overlooked them. That's why I posted examples of common and important "color space" analyses that did not begin by translating color space into wavelength space - so you could compare them. Apparently that's not the problem. So what's your point?
