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The Curious Phenomenon of Stochastic Resonance (medium.com)
72 points by iQuercus on June 16, 2015 | hide | past | web | favorite | 17 comments

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.

Yes, as described in the article, this is just dithering. I've never heard of "stochastic resonance", but from what I can discern from the wikipedia article, it's essentially the same thing except applied to systems that are merely "nonlinear" and "bistable", as opposed to outright quantized.

It appears we are not the first to note the connection: http://www.ncbi.nlm.nih.gov/pubmed/11046260

In effect yes they are essentially the same thing. One of the (potentially annoying) things you'll see going through the literature is that the term has very broad meaning. Other times it'll be a very narrow term. The broadest is basically "random noise can be used to improve signal." Under that definition, dithering would be a form of stochastic resonance. This biology article actually touches on the definition issues.(http://journals.plos.org/ploscompbiol/article?id=10.1371/jou...)

There's also a case to be made that the definition of SR should be narrowed, and a lot of what's called resonance isn't resonance at all.(http://www.nipslab.org/files/PRE1995-SR-and-dithering-p4691_...)

> 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?

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.


This video (23min) explains, among other things, how dithering of audio signals works in the frequency domain. Note: the main subject of the video is about digital vs analog signals, but he explains dithering as well. It's also just a very well done video, I like the way he presents and explains things.

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


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.

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.

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.

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.

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

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...

It's also used in cochlear implants.

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.

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?

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

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

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