[HN Gopher] The non-Riemannian nature of perceptual color space ...
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The non-Riemannian nature of perceptual color space (2022)
Author : cpach
Score : 77 points
Date : 2024-07-31 08:45 UTC (3 days ago)
(HTM) web link (www.pnas.org)
(TXT) w3m dump (www.pnas.org)
| bbor wrote:
| The paper in PDF:
| https://www.pnas.org/doi/pdf/10.1073/pnas.2119753119?downloa...
| there's a lot of math symbols but IMO the usage is pretty
| straightforward for anyone familiar with linear algebra and
| proofs. Ramsay (30) suggests that the principle
| of diminishing returns or its opposite may have been spuriously
| identified by otherresearchers (daringly including his PhD
| advisor, Helm) because of experimental procedures (successive
| intervals, paired compar-isons) ill suited to the task. Indeed,
| open-ended and criterion-dependent tasks give less accurate
| measures of similarity because of individual factors and the
| difficulty of the task... Instead, we use a more reliable
| two-alternative forced choice (2AFC) task, where the participant
| simply answers the following question: "Which is more different?"
| Specifically, we use a triad arrangement of stimuli with the
| reference in the middle and one test on either side. Each of 320
| triads covering the neutral axis was judged by at least 250
| different participants in a crowdsourced study on Amazon
| Mechanical Turk (MTurk) (52).*
|
| The core of it seems strong, IMO. I would have liked a bit more
| cognitive science / philosophy to distinguish between an ideal
| color space and whatever imperfect model is created by individual
| human's neural software, and skipping Goethe and Schopenhauer in
| the intro was downright criminal, but that's more on me than
| them.
|
| Color has long been a convenient "entry point" into the study of
| human unconscious and subconscious data transformations, most
| notably through Wittgenstein's musings about red squares. I look
| forward to this technique being extended to other spaces, even
| ones as abstract as "moral space" or "valence space"!
| robwwilliams wrote:
| Great comment. You made me laugh out loud on the other spaces
| we HAVE TO NAIL DOWN. You would get a kick out of Winograd and
| Flores 1986.
| piannucci wrote:
| I love the drama of how the abstract is written, but TBH I don't
| think this is a surprise. I believe it's well-known among color
| theorists that large perceptual distances are inconsistent with
| sums of small differences. So maybe the most generous thing to
| say here is, good on them for bringing awareness of this subtlety
| to a broader audience.
| robwwilliams wrote:
| Yep: color space is a pragmatic kludge not a "real thing"
| divorced from the human neural network that is its fundamental
| basis.
| mpweiher wrote:
| Not only that, it is also well known that the smallest
| perceptible color difference (DE=1) is not actually consistent,
| even in the "perceptually uniform" color spaces.
|
| So DE is actually 1 in some parts of the space, but up to 4 in
| others. However, that is "good enough" for the purpose for
| which these color spaces were created: quality standards for
| color ("can I buy more of the same color and it will look the
| same?"). If your measured and computed DE is below one, the
| difference will not be perceptible by most humans regardless.
|
| And last I checked, new and improved "perceptually uniform"
| color spaces are proposed every couple of years.
| jimsimmons wrote:
| Is it non Riemann or non Eucliden
| OvbiousError wrote:
| Both
| robwwilliams wrote:
| Neither! Or perhaps Darwinian. It is an idiosyncratic space all
| in our brains. It is our own learned synaptic weights and
| embeddings that allows each of us to effectively/efficiently
| use some of the data generated by our photoreceptors.
|
| Sure, color space can be reformulated many other ways for
| applications but all just operational kludges.
| yccs27 wrote:
| It's non Riemannian and therefore also non Euclidean.
|
| In Riemannian space, the distance between points is the length
| of the shortest path between them. Euclidean space is a subtype
| of Riemannian space, where angles in every triangle sum to
| 180deg.
| Sniffnoy wrote:
| While this phrases things in terms of Riemannian geometry, it
| seems to me like this is really about more fundamental metric
| properties, but I find its terminology a bit unclear. Would it be
| correct to summarize this as saying is that color space is not a
| length space / geodesic space? (See e.g.
| https://en.wikipedia.org/wiki/Intrinsic_metric )
|
| (Yes "length space" (or "path space") and "geodesic space" are
| not exactly the same thing, but "length space but not geodesic
| space" doesn't exactly seem like a very likely possibility.)
| woopsn wrote:
| That's an interesting related thought that is not quite the
| same as the paper. They claim that what we perceive as "color
| similarity" is not a metric at all. That would be required in
| order to define arclength and geodesy.
|
| I agree with others that it is not surprising and is a
| technicality. If you put that aside then the situation is much
| closer to your intuition.
| Sniffnoy wrote:
| Are you sure it's claiming that? Looking quickly I didn't see
| anything to indicate that, I didn't see anything claiming
| triangle inequality violations. (But this is why I wish it
| had been phrased explicitly in these terms, instead of
| talking about whether it's specifically Riemannian!)
| mannykannot wrote:
| At one point, the article says "importantly, [the principle
| of diminishing returns] holds even along geodesics, making
| it distinct from and stronger than the triangle
| inequality." Later, they say "it is not trivial to verify
| whether any given path through color space is a geodesic.
| We chose the neutral axis because it is the one path on
| which all available data agree that it is indeed a
| geodesic", and go on to argue (if I am following it
| correctly) that it is unlikely that their principle of
| diminishing returns is just an artifact from this choice.
|
| I do not know if the authors are claiming that what we
| perceive as color similarity is not a metric at all, but
| personally, I would not be surprised if it were not. See my
| other post for how my subjective perception of color
| differences seems to me.
| Sniffnoy wrote:
| > stronger than the triangle inequality
|
| That's not a violation -- "stronger than" is the
| _opposite_ of a violation!
| woopsn wrote:
| You're right, I misinterpreted. I don't know what they get
| out of calling the space non-Riemannian if not to say the
| inner product fails. Good idea, ignoring that term.
| Sniffnoy wrote:
| I mean, what they mean by "non-Riemannina" specifically
| is that it's a metric that can't be realized as the
| metric on a Riemannian manifold. But while that much is
| clear, getting beyond that is not. Which is why I'm
| asking, are they saying it's not a length space...
| srean wrote:
| My thoughts exactly. It made me wonder if color space has any
| interesting topology. Topological semigroup might be a way of
| looking at it.
| yccs27 wrote:
| Yes, it's important to note the measure of distance (metric)
| used. Quoting from the paper: Humans are not
| good at judging questions of the type "How big is the
| difference?" that form the basis for many large difference
| experiments.
|
| Instead, the authors use data from decisions of "which color
| step is larger". They find that as the steps get larger, you
| need a higher difference in color steps to reach the same
| certainty.
|
| This is not that surprising, since people generally get worse
| at noticing small differences as the absolute quantities get
| larger. Unfortunately, the model of perception uncertainty used
| in the paper (Thurstone's theory of Gaussian perceptual
| process) does not take this effect into account.
| ucarion wrote:
| > Consequently, we need to adapt how we model color differences,
| as the current standard, DE, recognized by the International
| Commission for Weights and Measures, does not account for
| diminishing returns in color difference perception.
|
| This isn't to reduce the notability of the article, but isn't
| BIPM's interest in any color-perception stuff basically limited
| to making lightbulbs roughly equally bright? (i.e.
| https://en.wikipedia.org/wiki/Luminous_efficiency_function) I
| guess I don't see how even nonlinearity in perceptual space
| matters for that purpose.
| contravariant wrote:
| Changing the triangle inequality to a strict one and claiming
| that the result is non-Riemannian is a bit dubious.
|
| First of all the difference between a strict and a non-strict
| inequality is not that big, stating two things are never
| _exactly_ equal is nigh impossible to measure, especially for
| something subjective.
|
| Secondly that could happen simply by reporting distances in some
| non-linear fashion, and who cares if the _unit_ of distances is
| non-linear? If there is a metric that correctly identifies which
| colour is _closer_ then we 're in business, nobody ever said this
| had to correspond _linearly_ to whatever measure of perceptual
| distance someone came up with.
| yccs27 wrote:
| Yes, it's important to note the measure of distance used.
| Quoting from the paper: Humans are not good
| at judging questions of the type "How big is the difference?"
| that form the basis for many large difference experiments.
|
| Instead, the authors use data from decisions of "which color
| step is larger". They find that as the steps get larger, you
| need a higher difference in color steps to reach the same
| certainty.
|
| This is not that surprising, since people generally get worse
| at noticing small differences as the absolute quantities get
| larger. Unfortunately, the model of perception uncertainty used
| in the paper (Thurstone's theory of Gaussian perceptual
| process) does not take this effect into account.
| mannykannot wrote:
| Thanks, that clears up one thing I was puzzling about: if I
| were asked to give a quantitative value to how different two
| colors seem to be, my first problem would be to figure out
| what a number - any number - would mean in this context.
| While 'barely perceivable difference' seems like a reasonable
| unit of measure, I don't think I could judge multiples of
| that unit with any degree of accuracy or consistency, or,
| indeed, in any meaningful way.
|
| On thinking about this issue, it seems to me that I think of
| large differences categorically (red vs. green, for example)
| while thinking of small differences as being on a continuum,
| even when the colors in question lie in the borderlands of
| the above categories.
| robwwilliams wrote:
| At some level the fundamental assumptions of a "color" space as a
| real representation of the human perceptual space is almost
| comical. The color yellow has been an issue for many decades and
| diverse combinations of wavelengths evoke identical conscious
| yellow percepts.
|
| The fundamental "not-geometry" of color space is the output of a
| very complex deep neural net.
|
| Thinking about color space as "real" world is almost nonsensical
| ;-). Trying to map "real" world into brain now has a deservedly
| bad wrap. Modern philosophy has largely given up on Descartes,
| sharp subject-object dichotomies, and the brain and mind as a
| warped mirror of nature.
|
| If puzzling at first then check out Humberto Maturana and F.
| Valera (both experts in color vision electrophysiologist and
| philosophers), Martin Heidegger, Richard Rorty, and Daniel
| Dennett have powerful arguments against representationalism of
| the type implicit in most neuroscience.
|
| Valera, Rorty, Dennett are all readable. Heidegger and Matura are
| more cryptic unless you are a philosopher.
|
| https://en.wikipedia.org/wiki/Francisco_Varela
|
| Valera's "The Embodied Mind: Cognitive Science and Human
| Experience", co-authored with Evan Thompson and Eleanor Rosch, is
| a good intro on this and related concepts.
|
| But for Hacker News readers by far the best intro to this topic
| are chapters 4 and 5 of is the CS classic by Terry Winograd and
| Fernando Flores that is often highlighted on HN. It is a key text
| in understanding both what goes on in our brains and what is and
| may go on in machine brains.
|
| 1986. Understanding Computers and Cognition: A New Foundation for
| Design (with Fernando Flores) Ablex Publ Corp
| BobbyTables2 wrote:
| I've always found it deeply disturbing that we ascribe special
| significance to red/green/blue (that's only what the eye is
| best at detecting) as "primary" colors. Why do we teach this to
| kids?
|
| It's ridiculous that linearly adding "red" and "blue" would
| make "purple" -- all different wavelengths -- without a
| nonlinear effect occurring. CA prism separates these two back
| out and shows us purple didn't exist in such an experiment. But
| we do see "purple" in a rainbow !?!?
|
| We see beautiful pictures on LCD screens but we only sense only
| 3 colors from it? An alien that could see the whole spectrum
| would think we were completely crazy!
| SAI_Peregrinus wrote:
| "Purple" is not a spectral color. Violet is, but the purples
| are a mix of violet & red, or red & blue, or such.
|
| Red/green/blue are one set of primaries. Lots of artists
| working with paint use red/yellow/blue. Inkjet printers use
| cyan/magenta/yellow. Which colors are "primary" depends on
| the medium.
| carlob wrote:
| Not quite RGB or CYM(K) depends on whether you are adding
| or subtracting colors i.e. if the light is transmitted or
| reflected.
| SAI_Peregrinus wrote:
| Yes, that's a change of medium. You can also have color-
| equivalents in non-visible light, such as in frequency-
| division multiplexing in radio links or fiber optics.
| Every broadcast TV channel is a different spectral radio
| color (well, a small range of them).
| DiscourseFan wrote:
| >Heidegger and Matura are more cryptic unless you are a
| philosopher.
|
| I think _The Origin of the Work of Art_ by Heidegger is fairly
| readable. I 'd also add one of Heidegger's classmate's, Walter
| Benjamin, whose early writing was directly about the experience
| of color. There's a book about it called _Walter Benjamin, The
| Colour of Experience_ by Howard Caygill. Though its a bit
| difficult for the layman because it interprets Benjamin through
| his neokantian education (at the Marburg school, with
| Heidegger) and assumes a certain familiarity with Kant.
| mpweiher wrote:
| The concept of color spaces for human color perception is
| deeply and solidly anchored in the structure of the human
| visual system.
|
| Different kinds of color spaces in different parts of that
| system.
|
| The additive "RGB" colorspace has to do with the fact that we
| have 3 different types of color cones in our eyes, which have
| different spectral sensitivities. Any color perception that we
| can register is a combination of these three signals. Hence a
| three-dimensional space.
|
| https://en.wikipedia.org/wiki/CIE_1931_color_space
|
| The RGB primaries that we choose for monitors do not match
| these color sensitivities, but also map to a space that is made
| to overlap with our perceptual space.
|
| > The color yellow has been an issue for many decades and
| diverse combinations of wavelengths evoke identical conscious
| yellow percepts.
|
| No. Metamerism is a general property of human color perception.
| For each color we can perceive there are a vast number of
| spectral distributions that can produce that particular color.
|
| https://en.wikipedia.org/wiki/Metamerism_(color)
|
| One of the many reasons a purely physical approach is both too
| difficult and insufficient for color management.
|
| In addition to these physical color spaces, there are
| perceptual color spaces, my favorite one being CIE Lab, an
| opponent color space.
|
| With CIE Lab, the L component is overall luminosity, a is a
| red-green difference and b is blue-yellow difference. This
| corresponds to color processing that occurs after the initial
| signal is received and closely matches how humans actually
| subjectively perceive color, philosophical (im)ponderables
| aside.
|
| https://en.wikipedia.org/wiki/CIELAB_color_space
| canjobear wrote:
| > Any color perception that we can register is a combination
| of these three signals. Hence a three-dimensional space.
|
| Only approximately. In the linked article you can see that
| the color gamut is a horseshoe shape that cannot be fully
| spanned by a triangle. So there are color percepts such as
| responses to pure wavelengths that can't be reproduced as
| combinations of real primaries. You could invent imaginary
| primary colors to make it work, hence the XYZ color space.
|
| In any case, the whole point of TFA is that a space is not an
| adequate characterization of color percepts, because there is
| no Riemannian geometry that matches the psychophysical data.
| mpweiher wrote:
| >> Any color perception that we can register is a
| combination of these three signals.
|
| > Only approximately.
|
| No. That is precise, because three color sensors is all we
| (well most of us) have available[1].
|
| >> Hence a three-dimensional space.
|
| > Only approximately.
|
| There was no claim of precision or precise matching for the
| space, only of dimensionality. The point was that it is a
| _three dimensional_ space, and that 's because there are
| three basic components that span it, the three color
| signals coming from the three types of cones. And once you
| have three base vectors, they will span a 3d space (unless
| co-planar).
|
| So quite the opposite of what the poster I was replying to
| claimed, which was that the idea of representing human
| color perception as a "space" is somehow "comical".
|
| > So there are color percepts such as responses to pure
| wavelengths that can't be reproduced as combinations of
| real primaries.
|
| Sure, which is one of the reasons why the matching
| functions can have negative coefficients for some colors /
| colorspaces, something that is, er, more difficult with
| real RGB monitors. Or, as you also noted, you invent
| primaries that cover the space but go outside of reality.
| The spaces are mathematical constructs, after all. However
| they are not _arbitrary_ mathematical constructs. The fact
| that they are 3d spaces is rooted heavily in reality. And
| mathematically they are actually all the same space (as
| distinct from specific regions in that space if you
| constrain the vector components, for example to range
| [0,1]).
|
| > In any case, the whole point of TFA is that a space is
| not an adequate characterization of color percepts, because
| there is no Riemannian geometry that matches the
| psychophysical data.
|
| Not really. The article is a bit fuzzy on some of the
| terminology, but if you read even the abstract closely, it
| is clear that they are talking about _perceptually-uniform_
| color spaces that make a claim about color differences in
| that space matching perceived color differences, our good
| old friend DE.
|
| https://en.wikipedia.org/wiki/Color_difference
|
| I don't see the paper making such a claim for the more
| general concept of a color space that does not claim to be
| perceptually uniform. CIE XYZ for example, does not claim
| to be perceptually uniform. And isn't.
|
| And once again, it is well-known that "perceptually-
| uniform" color spaces are only approximate. Always have
| been. DE varies in different regions of the space. It also
| varies depending on the area of the color swatches[2]. It
| also varies depending on whether the color is a light
| source or reflected. (IIRC, CIE Luv performs better for
| light sources). That these distances don't add is an
| interesting additional wrinkle, but not surprising, given
| all the other oddities and also the fact that the color
| spaces were never intended for having the distances add.
|
| [1] Some people have reduced function in one or more of the
| cone types, they are color-blind, and some apparently have
| four types of cones.
|
| https://en.wikipedia.org/wiki/Tetrachromacy
|
| [2] The way those color spaces are tested is to give people
| swatches with colors that, I think, they are allowed to put
| next to each other. If they can tell they are different,
| the DE is greater than 1.
| robwwilliams wrote:
| Interesting response and I appreciate the pragmatic utility.
| But reifying this space as "closer to the truth" misses the
| more important point that there is no one color space to rule
| them all.
|
| I have quantified variation in photoreceptor mosaics in
| humans, primates, cats, dogs, and mice. The variation in
| ratios of cone types is impressive. Variation of R:G ratios
| in health human retina is impressive (work by C Cursio). Yes,
| sure, humans still call green green despite the differences,
| but not so true of those with opsin gene variants.
|
| Here are three of my own studies: the first of which re-
| discovered that the nasal periphery of humans is tiled by
| large cones.
|
| https://pubmed.ncbi.nlm.nih.gov/1829378/
|
| https://link.springer.com/article/10.1007/s004290050319
|
| https://onlinelibrary.wiley.com/doi/10.1002/cne.902970404
| JadeNB wrote:
| > The color yellow has been an issue for many decades and
| diverse combinations of wavelengths evoke identical conscious
| yellow percepts.
|
| How can you possibly determine whether different stimuli evoke
| identical percepts? (I don't know a technical definition of
| 'percept,' but am assuming that it carries some additional data
| beyond something that can be directly measured from brain
| activity. If not, then I withdraw my question.)
| gmueckl wrote:
| Historically, this has been determined by presenting stimuli
| simultaneously and asking the subject about their similarity;
| alternatively by presenting a reference stimulus next to a
| tunable stimulus (e.g. red, green and blue monochromatic
| light sources) and asking the subject to match the two
| stimuli as closely as possible.
| _nalply wrote:
| And for animals like dogs and some birds, set up a reward
| system, train the animal, then run tests and deduct what
| can be seen by the behavior of the trained animal.
|
| Dogs see only two colors, this means compared to humans
| they are color-blind (or something like red-green blind).
| turtledragonfly wrote:
| For those interested in such topics, I'm a fan of the "Oklab"[1]
| color space.
|
| It's not perfect, but well documented and discussed, has freely-
| available implementations, efficient shader code, etc. and
| overall works pretty well.
|
| [1] https://bottosson.github.io/posts/oklab/
| woolion wrote:
| This reminds of Poincare's remark that all geometries are wrong,
| they are just useful abstractions of space. The different color
| spaces all have some features they are good at with their own
| algebra.
|
| So, RGB is close to how screen works, but is very un-intuitive as
| its algebra is additive rather than subtractive (like the one we
| have with paints). Then HSV is a middle ground to be more
| practical for humans, as it separates the color into its 3 most
| significant dimensions, that are value, hue, and saturation. It
| does so while being a fast linear transform, but it is not a
| really good mapping with regards to human perception. For example
| a given fixed value will appear as very different when given two
| different hues. Still, it's a nice middle ground that made it a
| good choice for painting and image manipulation software.
|
| There are other spaces that are "more" perceptual, in that
| changing the hue of a color should not affect how its value is
| perceived. This can be useful in design work as a palette could
| be hue-shifted and always stay legible, which was not possible in
| the general case with HSV or RGB. Yet, these fancy color spaces
| are not used a lot because in most practical applications there
| isn't enough justifications to use them. In particular because
| professionals are used to workaround the space deficiencies, so
| there's a cost to re-learn some of the primitives. The only
| really practical application I have ever seen of these perceptual
| models is to simulate 'color blindness', which theoretically give
| the possibility to design charts and maps that are more
| accessible to people. I believe such a validation tool should be
| required for public communications.
|
| The article is interesting and well written, as it gives an
| history of how some of these abstractions were developed, and
| highlight some of its shortcomings.
| fredgrott wrote:
| If you look at the CIE Lab def and the HCT definition that Google
| uses it makes the math more clear....as with HCT there is a
| perception adjustment mathematically calculated
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