'weighted mean value' that is spread out over a population of neurons

I'm struggling with understanding of this sentence:
"Oppel-Kundt illusion is considered a physiological phenomenon that arises as a consequence of the inherent properties of the visual system - which prompts the brain to calculate a 'weighted mean value' that is spread out over a population of neurons, and leads the observer to overestimate the divided distance in comparison to the undivided one."

It's quite a technical article, so it's not easy to understand it. Here is more context if it helps: Oppel-Kundt illusion

Can someone, please, paraphrase the sentence using different words to make it more clear?

Any help appreciated.
Thanks in advance.
  • bennymix

    Senior Member
    I think you need a book on the physiology and neurology of vision. 'Weighted means' are a commonplace calculation.
    I think it's pretty well-known that there's complicated processing of signals from the neurons in the eye, to arrive at distances, sizes, etc. It's not surprising if signals from individual neurons are given different weights rather than simply averaged.

    The quotation has many technical terms which probably should be preserved. If you're translating it, that should make it easier than a paragraph from a novel.

    The brain uses the input from neurons to estimate distance; it's hardwired, so to say.
    The input is averaged, but using weights; some input is more important than others.

    There is something about this averaging mechanism which gives different answers for a undivided and an divided segment, presumably because the small segments' lengths (in the latter) are overestimated.
    Last edited:


    Senior Member
    English - England
    Good advice from Julian and Benny.

    For what it's worth, I'll have a go at explaining what I think it means.

    The optical illusion revolves around the fact that the human visual system overestimates a distance which is sub-divided by something such as regular vertical lines, as opposed to the same distance which has no vertical lines along it.

    oppel-kundt illusion - Google Search:

    The reason "weighted mean value" is in inverted commas is because it isn't really a weighted mean, but acts like one. A weighted mean puts greater emphasis on certain elements in a calculation, rather than others, based on the deemed importance of each element.

    The human visual system therefore places greater emphasis on a distance which is sub-divided by vertical lines rather than one which isn't, because it deems each of those vertical lines to be important to it when calculating distance. It therefore gives the distance covered by those lines more emphasis than it should, and therefore overestimates that total distance.
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    Senior Member
    Trochfa makes a good point. There is no process, as in Julian's handy article. The brain is wetware. IF we imagine the brain as a central processor, as in a computer, we can IMAGINE it having retinal sensors, yielding signals (as in robotic perception). Presumably the processor would treat the various signals in a 'weighted' way, say, assigning a multiplier to each initial value.
    Unless the authors can actually isolate microscopic signals, they are making an analogy, not describing a calculation process that actually happens.


    Senior Member
    English (UK then US)
    (Human vision is quite complex and some of what Benny is describing has been done From this pdf of a Scientific American article, fascinating insight if you are interested in such things:
    The retina does much more than pass simple signals to the brain. Surprisingly, it extracts a dozen distinct representations of a visual scene—sophisticated, ghostlike movies formed by relatively few types of neurons.
    The brain uses these abstractions to build a visual world sharp with detail and rich in meaning.
    Thanks all of you for your answers!
    I've already got a rough idea what it wants to say, still cannot see it in the given sentence, but I will trust you native speakers. :D (I don't know, the sentence is just strange I can't help it.)

    Anyway, this would be my explanation based on yours and other stuff I've read (and perhaps mostly on my logical view), can you tell me if it can somehow arise from the article I referenced?

    "The brain puts more emphasis on the subdivided line, because it is "more going on here", and when it comes to calculating the total length, it is done by adding up estimated lengths of subdivided parts of the line, which results in overestimation of the total length."

    OK I can't really see this in the article, but it seems logical, doesn't it? :D
    ...or more like "length of the subdivided part is estimated erroneously because of the noise made of extra vertical lines"? this is the most simple explanation I can think of.

    based on this fragment of another study:


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