What do you see within the stripes?
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"This is the strength of federated, federatable social media – it disciplines enshittifiers by lowering switching costs, and if enshittifiers persist, it makes it easy for users to escape unshitted, because they don't have to solve the collective action problem. Any user can go to any server at any time and stay in touch with everyone else."
From https://pluralistic.net/2025/01/20/capitalist-unrealism/
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@troy_s
I now return to the issue of achromatic colour matching and how it relates to the figure-ground problem.
In particular, in this recent post (https://mathstodon.xyz/@TonyVladusich/113891497059243315) I argued that achromatic colour matches are generally not possible.
But why not?
My original take on this issue was embodied in the framework of gamut relativity; namely, the assumption that an achromatic colour is represented as a point in blackness-whiteness space.
For a given background luminance, as the luminance of a target varies from low to high in some prescribed range, the achromatic colour varies along a straight line, called a gamut line, in this space.
Here's the rub though, these lines are not the same for targets seen against black and white backgrounds, respectively, as depicted in the figure below.
The reason one cannot generally establish a satisfactory match between targets seen against black and white backgrounds, then, is that there is only one point of intersection between gamuts.
So that seems like a clear prediction: set the luminance of a target to the predicted intersection and folks should be able to match across backgrounds!
But alas, that does not seem to happen. Either the theory is wrong or we are missing something critical that prevents those matches.
I've struggled with this problem for over a decade now, and I think I have a solution that I find satisfactory.
This brings us back to the figure-ground issue: I no longer believe an achromatic colour can, in general, be represented as a single point. Rather, they are represented as pairs of points, corresponding to the opponent figure and ground projections given by the local contrast. And this makes matches generally impossible!
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I'm going to riff off this post here (https://mastodon.art/@troy_s/113896047444652213) by @troy_s.
The point I want to make is that, even for the simplest stimuli, such as a picture of a "disk" on a uniform "background", vision science really has not come to grips with the immense complexity of the perceptual "parsing" that occurs.
Even the usage of the words "disk" and "background" here are not theoretically neutral: they are laden with the baggage of our cognition of "thing" and "other".
What I want to say here, though, is that one cannot speak of the achromatic colour, or grey shade, of a "thing" or "region" without considering how the visual system (A) demarcates the border between figure and ground, and (B) represents the implicit relations of "foreground" and "background".
Consider the figure below, where physically identical targets are perceived completely differently because of the differing luminance of the surrounding areas.
What is a clearly demarcated black or white "foreground" region in one context becomes a greyish "background" seen through a "fuzzy" foreground layer.
And this is one of the simplest stimuli that vision scientists work with!
We really have not the slightest fucking clue how vision works.
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I've just permanently deleted all my social media accounts.
I've also put a strong filter on keywords for topics that I have no interest in hearing about on Mastodon.
I encourage folks to do likewise.
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Almost 20 years ago I published a paper that set me on the path towards developing a general theory of achromatic colour perception (black, white, grey).
The main idea of that paper was to study "edge integration"; namely, how the visual system integrates edge information across the visual field to represent surface colours interior to those edges.
One of the central themes was how simultaneous contrast effects from local (immediately adjacent edges to a surface region) are integrated with assimilation effects from remote edges (NOT immediately adjacent edges to a surface region).
You can appreciate the idea in the picture below, where the traditional simultaneous contrast display is augmented with additional nearby edges to form a bullseye pattern.
The bullseye patterns elicits percepts that are a mixture of simultaneous contrast and assimilation effects.
Yet it is easy to show that the effects don't cancel: one can never adjust the luminance of one of the grey rings to match the achromatic colour of any other ring.
It was this "failure of additivity" that eventually led me to the idea of blackness (darkness) and whiteness (brightness) being represented as separate dimensions and hence the theory of gamut relativity.
This is the original paper (https://jov.arvojournals.org/article.aspx?articleid=2121847).
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LinkedIn is actually a fucking hoot! The comments thread has 8000 replies, mostly either castigating the OP for posting satire or for failing to live thrifty. The split seems about 50/50. You can't buy this sort of entertainment for less than 340k a year!
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Just sayin’, folks are late to this party …
https://www.flyingpenguin.com/?p=49582
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Y’all just light meters! I want to hear from the one person who voted for B though!
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Does the grey shade of the disk in B, C or D best match the disk in A?
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Quiz time!
Which grey disk surrounded by a black donut best matches the grey shade of the disk inside the white donut?
Poll in thread because Masto doesn't seem to allow both a poll and a pic in the same post.
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America, you are beyond a fucking joke!
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Rubin's face-vase display is a famous example of figure-ground perception and the multi-stability of human vision.
Here's an analysis of how the percept can switch from a pair of black faces on a white ground to a central face on a black ground.
The main ingredients of the analysis are that either the black or white regions can "own" the border but not both.
The region that owns the border adds a "contrast boost" to the luminance-defined point representing each region.
This boost breaks the symmetry between the black and white regions to allow grouping into occluding figure and occluded ground layers.
The grouping rule is simple: given a point formed by the intersection of the projections of the black and white regions, this will be closer to the un-boosted black or white point, meaning the region defined as ground. Hence the ground will be represented as an opaque occluded surface (the origin of the decomposition being the point itself.)
The bi-stability of the display is then explained by the "decision" of whether the black or white regions "own" the contrast defined at the boundary between regions.
(We can model the integration of the differential signal at the boundary over the enclosed regions as a PDE problem, namely, as a solution to the Laplace equation with Neumann boundary conditions.)
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A bit of a depressing watch but how long can we continue to bury our heads in the proverbial sand?
https://www.youtube.com/watch?v=P6EMJlt_Dsw
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In the limiting case, where the grey targets all join up to form a single rectangle, the only difference is whether the short side of the rectangle abuts the black or white bars. Then the effect is entirely eliminated, perhaps even reversed?
But what is interesting is we start to see local simultaneous contrast effects along the vertical borders, with small variations in blackness and whiteness, similar to the grating induction effect.
These local inductions are the signature of PDE integration that has long been postulated to mediate contribution of local contrast to surface appearance.
cc @troy_s
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Introducing the "fat" White's display, which virtually eliminates the White's effect.
This variant is motivated by my previous posts, in which I analysed the White's effect in terms of figure-ground representation.
In particular, I conjectured that the white's effect (and simultaneous contrast) is a manifestation of a scission computation that supports the representation of an occluding figure over an occluded background.
The collinearity of the grey targets with the surrounding black or white stripes supports one configuration of figure-ground, which favours the effect.
In this variant the collinearity is eliminated, and the effect is consequently greatly reduced.
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@wlumley gets it.
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Analysis of figure-ground representation and simultaneous contrast / White's effect in terms of gamut relativity.
Represented as points in blackness/whiteness space, the grey targets are vectorially decomposed into pairs of points representing the occluding grey figures and occluded black or white bars.
The points belonging to the background forms (black or white stripes) are projections of the grey targets onto constraint lines (falling on the blackness and whiteness axes themselves in this example) given by the backgrounds themselves.
The vector decomposition can be thought of as a type of Newton's third law, whereby the completion of the black or white stripes behind the grey occluded must be accompanied by an equal and opposite "force" that adds whiteness or blackness.
The decomposition has a probabilistic interpretation, whereby the linearity of the grey targets and surround black or white stripes dictates the most likely occluded background form.
One can thus interpret both simultaneous contrast and White's effect as manifestations of the processes by which the visual system represents figure-ground relationships.
This leaves us in the remarkable position of being able to write a simple conservation law for a key aspect of human visual perception.
My previous work has hinted at such a law but believe this result allows use to state the general form of the law.
It remains to discover how to derive this law directly from a principle of least action, but I would suggest it should be fairly straightforward.
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Further along the figure-ground path, we should be able to break White's effect by manipulating the grouping of the grey targets with surrounding elements.
Here I've added a subtle manipulation to induce grouping of elements to form transparent vertical figural surfaces appearing in front of the white/black stripes.
Although the transparent figures appear blackish and whitish respectively, the elements aligned along the white stripes in A and the black stripes in B are themselves quite similar, far more so than in the original display.
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Unlike science, the advance of LLMs proceeds excrementally, rather than incrementally.
I'm looking forward to the imminent collapse of LLMs.
I predict that, when the end comes, it will come swiftly and completely.
They have already begun to re-ingest their own excremental outputs.
Fancy releasing into the wild an organism so vicariously virulent and voracious that it eats its own shit.
All for the profit of a few already staggeringly rich sociopaths.
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text/gemini
