
The Curious Phenomenon of Stochastic Resonance - iQuercus
https://medium.com/the-craftsman/the-curious-phenomenon-of-stochastic-resonance-b263449486eb
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luismarques
Isn't this (just) dithering noise?

AFAIK, the reason it's so effective in the example is that adding the noise
helps the quantization process in the posterization better represent the
original color spectrum. Without the dithering the quantization error can keep
adding up in a way that the posterization filter cannot control (but which the
image author can engineer to be problematic, as surely was the case here).
With the dithering you have a statistical guarantee that the quantization
errors average out.

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jessriedel
> With the dithering you have a statistical guarantee that the quantization
> errors average out.

Could you point me towards somewhere this statement is made precise?

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yummyfajitas
I don't know where to link you to, but here is a more detailed statement,
which I think could be straightforwardly expanded into something precise.

Consider a signal S[i], i=1...N. The human eye isn't actually perceiving S[i],
it's perceiving some convolution of it S[i] \conv w[i] (for a window function
w). I.e., an area with 50% white pixels and 50% black pixels appears grey.

Suppose for simplicity w[i] = 1/k on i=0...k.

Now add noise g[i] to the signal in a region where S[i] = alpha. Then S[i] +
g[i] = alpha + g[i]. The number of pixels above a threshold T within the
window are then 1-cdf(T-alpha), where cdf is the cdf of the distribution of g.

Assuming your cdf is approximately linear near T, then 1-cdf(T-alpha) \approx
C + alpha.

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vvanders
Your eye already does this naturally to help you determine detail. There's a
fascinating article about it here:

[http://accidentalscientist.com/2014/12/why-movies-look-
weird...](http://accidentalscientist.com/2014/12/why-movies-look-weird-
at-48fps-and-games-are-better-at-60fps-and-the-uncanny-valley.html)

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klodolph
What's happening is the added noise causes the spectrum of the error to
change. With uniform uncorrelated noise (and some constraints), you can prove
that the error is also uniform + uncorrelated, which means that the signal
distortion must be zero (because otherwise the error would not be
uncorrelated).

You can see that this gives you a discernible image with only 1 bit of depth.
The same technique gives digital audio extra range and lower distortion.

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asgard1024
The phenomenon is interesting, although the connection to UI is a little
vague. Still, I think author has a good point.

Take bevels for instance. They may be considered a visual "noise", and in flat
design they are frowned upon, but how do I know where I can click (push a
button)?

Similar thing for window shadows, they help to recognize the window boundary.

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wodenokoto
If it communicates something helpful or necessary it cannot be considered
noise.

The idea behind flat design is that we don't need to have a wooden texture to
understand that something is a button.

The problem is when you forget to communicate that something is
clickable/interactive, which seems to be a major issue with current flat
design implementations.

But let's not forget that back in the day it was fashionable to only show that
items were interactive through mouse hover. So the problem with designers
forgetting useability is hardly something new.

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antognini
There's a related phenomenon in astronomy called Eddington Bias. If you're
doing a survey of stars in the sky, often times you are limited by the
brightness of the stars, so there's some brightness below which you don't
detect any stars.

Because photons arrive at your detector randomly, sometimes a few more photons
arrive at the detector from a particular star than average, and sometimes
fewer. One therefore sees small random fluctuations in the brightness of the
star.

Because there are many more faint stars than bright stars, it is much more
likely for a star just below your detection threshold to fluctuate up above
your detection threshold than for a star just above your detection threshold
to fluctuate down below your detection threshold. This ends up biasing the
inferred median luminosity to higher values.

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wahsd
I'm not sure how he makes the association to UI, but I agree that the
minimalist and flat designs are way too far gone to be useful. Sure, I despise
noisy and cluttered and fake leather bound UI too, but that doesn't mean we
need to go full bi-polar swing and jettison everything.

Regarding noise and this post, I could see it as a metaphor against Google's
tendency to significantly reduce the information density by adding white-space
to every frigging things, everywhere, at all times. Take the bookmark
boondoggle that they just backpedaled on; guess what Google, I would like to
see more than 8 bookmarks per view and I don't see how a miniature thumbnail
of the site really helps anyone. I want the "noise" in that case, which
consists of density of information, which hopefully is of the relevant type. I
want a quick overview with as much information as possible, but I also need it
to be visually distinguishable. That is another big problem which this post
maybe addresses, visual hierarchy, which is another one of those principles
that has been jettisoned with the minimalist and flat design binge. The user
should be able to pic out content and interactions in a relevant sequence
without significant gaps in visual progression; each level of visual hierarchy
should be an equal or relevantly spaced distance apart without significant
gaps. /my2cent

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murbard2
This is also reminiscent of the Gumbel trick[1] If your noise is Gumbel noise,
you can actually get the probability to exceed the threshold to be
proportional to the intensity of the pixel.

[1] [https://hips.seas.harvard.edu/blog/2013/04/06/the-gumbel-
max...](https://hips.seas.harvard.edu/blog/2013/04/06/the-gumbel-max-trick-
for-discrete-distributions/)

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hrnnnnnn
It's also used in cochlear implants.

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msandford
My dad actually did some work on this. When I was younger I couldn't believe
that such a thing was true. Now that I'm much older and got a couple of
engineering degrees and have worked for a while, it doesn't surprise me much
at all.

The older I get the more I recognize that shit is weird. Intuition is
extremely useful for "simple" deterministic systems. Once biology gets
involved, though, intuition (at least in an engineering sense) tends to go
right out the window.

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lukeforehand
Could someone expand on this phenomenon as it relates to noise machines? They
normally help people sleep but could they actually make certain sounds more
distracting based on this phenomenon?

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mechanician
Professor Bart Kosko at USC is an active publisher in this area.

Example: sipi.usc.edu/~kosko/TSP_May2009.pdf

