The Remarkable “Curvature Blindness” Illusion

By Neuroskeptic | December 8, 2017 2:54 am

A new optical illusion has been discovered, and it’s really quite striking. The strange effect is called the ‘curvature blindness’ illusion, and it’s described in a new paper from psychologist Kohske Takahashi of Chukyo University, Japan.

Here’s an example of the illusion:

curvature-blindness-Takahashi

A series of wavy horizontal lines are shown. All of the lines have exactly the same shape – a sine curve. However, half of the lines appear to have a much more triangular, “zig-zag” shape, when they are superimposed on a grey background. This “zig-zag” appearance is an illusion. (I checked – it really is.)

Takahashi notes the unusual strength of this effect:

As the effect magnitudes are quite strong, unless one carefully stares at the region that looks like a corner, it is hard to find that all lines are physically wavy. Despite the simplicity and effect magnitudes, to the best of our knowledge, no one has reported about this phenomenon.

So what’s going on here? Takahashi proposes that the brain’s visual system may default to seeing corners when there ambiguity over whether a line is a smooth curve or not:

The underlying mechanisms for the gentle curve perception and those of obtuse corner perception are competing with each other in an imbalanced way and the percepts of corner might be dominant in the visual system

The “zig-zag” lines in the illusion are the ones in which the color of the wavy line changes from dark grey to light grey at the ‘corners’ i.e. the peaks and troughs of the curve. It is only seen against a medium grey background however, suggesting that what matters is that the color of the wavy lines shifts from being lighter than the background, to being darker than it.

Takahashi notes that the illusion involves a sense of depth: the “zig-zag” lines look a bit like a surface, or wall, going into and out of the page, and the changing color of the wavy line suggests shadows. However, further experiments revealed that depth perception is not the driving force behind the effect.

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  • nik

    Why is the effect alternate pairs?

    • http://www.mazepath.com/uncleal/qz4.htm Uncle Al

      Look at albedo phasing. Middle angular junctions contrast two albedos, curved junctions are one albedo. One is curious whether the effect obtains using color contrast at uniform albedo. Can retinal rod response be separated from cone response?

    • James Hall

      Look at where the light and dark sections start. It seems jaggy when it changes from light to dark or vise versa at the top or bottom of the arc, instead of at the inflection point.

  • Kevin Klein

    Looks to me like this could be more an artifact of digital anti-aliasing than an actual optical illusion.

    • Luke Zieba

      anyone got a printer?

    • Jimmy Olivo

      Yeah, I’m sure Associate Professor Takahashi from Chukyo University totally overlooked that and neglected to print it.

      Or…any aliasing you see is a result of the journalists who resized and/or compressed the image for the web. If you follow the link to the original paper, you’ll find images there which are less likely to have such digital artifacts.

      • Carrick

        Once I trained my eyes for what I was looking at (by zooming in), I don’t see sharp corners (optical illusions don’t work like that normally).

        My guess the effect comes down to the finite resolution of the image. Corners have an infinite derivative = infinite spatial frequencies. They would have needed to over sample and run the image through a smoothing (anti-alias) filter if they wanted to eliminate the possibility of this class of error.

        [Several edits]

        • BorisTheHoris

          My personal experience is that this is not true. Often I find it easier to see the true pattern of an illusion when I know what I’m looking for.

        • Raven Woods

          Zoom out and you will see it. It is about the relationship between the light and the dark lines that are tried to be made corners when they meet.

        • Mark Syman

          I zoomed in on my browser and those sections are nearly straight, very slight curvature, which is also noticeable at normal zoom.

    • twoElectric

      What’s interesting is that the compression algorithm has naturally created reduction in the curvature in the image above. This might indicate that there is a fundamental explanation in computation. However, it should be extremely obvious that there is a lot more to the illusion than just a bit of compression artifacts (or anti aliasing). Just draw it by hand and see if it’s a problem.

      • https://www.facebook.com/app_scoped_user_id/1026609730/ Jim Balter

        Take a look at Jeremy Scharlack’s gif below. The notion that the optical illusion isn’t really one is plain stupid.

    • foljs

      That’s because you know the term “digital anti-aliasing” but didn’t know it’s irrelevant here, but you still wanted to sound clever.

      • Kevin Klein

        Anti aliasing is irrelevant here on my digital display device? Silly me.

        • http://j1ngo.blogspot.com/ Joshua

          .png images aren’t anti-aliased, ya goof.
          They’re a static grid of colored squares. .svgs and other vector-based graphics are, but this isn’t that.
          You’re trying too hard to sound smart when you’re ignorant.

          People don’t publish papers on weirdly aliased sine waves.

          • Kevin Klein

            So if I render a SVG on my device using anti-aliasing algorithms, take a screen capture, and save it as a PNG, my image is somehow no longer anti-aliased? What magic makes that happen?
            And people publish papers about all kinds of BS. Things like…”vaccines cause autism” just for one example.

          • http://j1ngo.blogspot.com/ Joshua

            “So if I render a SVG on my device using anti-aliasing algorithms, take a screen capture, and save it as a PNG, my image is somehow no longer anti-aliased?”

            That is correct. It doesn’t matter how you got to the static image. Now, if you’re saying instead that the author created a vector image (knowing there was no illusion at all), turned on anti-aliasing (producing the zigzags), then took a screenshot of the result and published that in a professional setting after adding pages and pages of descriptions and examples, well, I think your estimation of PhDs is irrationally cynical to the point of genuine silliness.

            As for papers on vaccines causing autism, well–unless I’m mistaken, there was a single study done that observed some possibility of correlation but which is now regarded as a fluke based on many further studies. (https://academic.oup.com/cid/article/48/4/456/284219) The key difference between that failure and the failure you think is possible here is that you can easily test this effect on your own on paper with a simple protractor or compass. Or you can actually take a few seconds to look at the underlying pixel coordinates. Or you can do some simple photo manipulation like Neuroskeptic did.

            https://uploads.disquscdn.com/images/2100d9629d0284a32c9d7d4f5de33dccac7128cb706c7077b5eb449810153c7e.png

            Do it yourself and see. I know you’re trying to be a good skeptic but you have to use your brain first. Skepticism is not the same as rationality.

          • Kevin Klein

            So let me get this straight: If I render a solid white circle on a black background without AA, I get only white pixels and black pixels and “jagged” edges on the circle. If I turn on AA, I still get mostly white and black but now also some gray pixels were AA smooths out the jagged look. You’re saying if I take a screen capture of this and save it as a PNG all the gray pixels are lost?

            If that’s what you think, well, I can see why this discussion is pointless.

    • Phil Shaffer

      This should be VERY Easy to test – do it totally analog – Draw smooth curves, change the grey levels of the line, then superimpose a grey background.

    • Phil Shaffer

      you may have something here.
      I did this – in my spreadsheet program, got 100 points for the sin function from 0 to 180 – one “hump”. Then I graphed them connected by a line, and I changed the gray scale of the line as he did, and put different backgrounds against it. Cannot see the effect. Try it yourself…..There are a lot of parameters to manipulate.

      https://uploads.disquscdn.com/images/3c2d05dec22e600a4efbea69f123a3c00d88b46c341adea118fd5a5435a9db37.jpg

      • https://www.facebook.com/app_scoped_user_id/1026609730/ Jim Balter

        “you may have something here”

        No, it’s ridiculous.

        “I did this”

        Your chart is irrelevant. See Jeremy Scharlack’s gif below.

        • Phil Shaffer

          Thank you for referring me to his post. There ARE some interesting things here. Precise parameters of the graphic will change the effect, apparently. Now – A comment on your post – I get that this is the internet and we are all supposed to turn up the hostility to – you know – keep up the tradition. But really, you don’t need to. Words like ridiculous and irrelevant could easily be replace by more civil phrases like “Interesting, but check what Jeremy Scharlack did”
          And I see your replies to others are similarly contentious. Why? And that is a real question. Why would you do that?

          • https://www.facebook.com/app_scoped_user_id/1026609730/ Jim Balter

            I prefer honesty over civility. Now FOAD.

          • Shannon Massman

            It’s a shame you have only sufficient cognitive resources to afford one or the other.

          • https://www.facebook.com/app_scoped_user_id/1026609730/ Jim Balter

            It’s a shame that you’ve made an erroneous inference.

    • https://www.facebook.com/app_scoped_user_id/1026609730/ Jim Balter

      Someone always has to be the most stupid and intellectually dishonest person in the room.

      Take a look at Jeremy Scharlack’s gif below and try to explain away that effect as “digital anti-aliasing”.

      • Kevin Klein

        I don’t see what’s so intellectually dishonest about a little bit of skepticism. Jeremy’s gif is much higher quality, so I’ll happily admit that my skepticism may have been misplaced. I’m still curious to know if the illusion is just as strong in a purely analog medium.

        • http://j1ngo.blogspot.com/ Joshua

          Ignorant skepticism is just ignorance. Read the source paper before going for the debunking angle. If you have actual criticism to offer after doing the legwork, by all means do so.

          In other words, be skeptical but first be rational, then critical. Blind skepticism is just as bad as anything.

          • Kevin Klein

            “Ignorant” would be if I wasn’t a software engineer who has worked in computer graphics and understood something about how digital images are rendered. It was just a comment on an Internet board, not a PNAS paper. Get a grip…

          • http://j1ngo.blogspot.com/ Joshua

            As a fellow software engineer who can claim the same, you’re an embarrassment to software engineers who have worked in computer graphics.

            It was “just a comment”? Okay, well it was just bullshit and you should just admit you were wrong instead of deflecting to me. No one is impressed that you know what anti-aliasing is. Everyone who has ever been into games or media is at least generally aware of what it does.

            You claim to be a professional and yet immediately question the professionals involved in publishing the paper, on the grounds that they all somehow failed to realize during the months of collaborative labor that their damn computer screens were just playing tricks on them. It’s silly and irrational.

            To you it’s just a comment but you’re spreading misinformation and a bad form of skepticism. What would I like to see you do? Amend an edit to your original comment explaining that you were wrong to doubt and that you hadn’t thought it all the way through. We need that sort of thing.

          • Kevin Klein

            Dude, I already admitted that I was less skeptical after seeing someone else’s higher quality example. (And I was never all that skeptical to begin with) What more do you want? A promise to never ever question anything anyone with a PhD says ever again?
            It’s not like I’m questioning global warming or trashing vaccines or calling evolution false or something significant like that. I made an “are you sure?” comment about a damned optical illusion. Again, get a grip.

    • Igor

      And the antialiasing works differently depending on the color of the background?

  • Jan-Erik Vinje

    My suspicion goes towards the parts in the brain that percieves the shape of objects by how light falls. The two shades are sharp and not gradual so when such shades flips over from one uniform shade to another the same time it changes direction this is how the light would behave at the corner of a straight or flat shape. If the color change is gradual instead of sharp i would expect the illusion to go away

    • Orlin Pettit

      I remember seeing a photograph of a street scene several weeks ago from near the equator where twice a year the Sun is directly overhead at noon.. an it’s looks very peculiar. Estimating distance and the actual size of objects is not easy as there are no shadows.

  • Tibor Koos

    I think the explanation lies in 2 fact: (a) the illusion only exists when the grey background creates different dark-light polarity directions for the line segments corresponding to the light grey and black parts of the curves (b) that it only works when the coloring of the sine wave changes at the pi/2 phases (peak points).

    My explanation would be that the curvature analysis system works after segmentation of the sine wave. The segmentation is qualitatively different against the middle grey background because the light grey and dark segments have the opposite contrast polarity. In this situations the light grey and black segments are not integrated into a single entity but are analyzed separately.

    This in itself is not enough to explain the illusion because of the phase sensitivity (point b above). But consider that when the boundaries of the line segments are on the pi/2 points the segments are from peak to peak and correspond to segments for which the line integral of the signed curvature is zero. In contrast when the segments are between the degree points the line integrals of the signed curvatures are either positive finite for upper halves or negative finite for lower halves. The result of all this is that the segment phase in the first case with lead to a construction for the form of the whole line as a zig zag while it will be a curved line in the second situation.

    The best indication that this explanation is on the right track is to notice that the apparent spatial frequency of the sine wave increases against the grey background (when there is no zig zag illusion). This would be expected if the curvature estimator summed curvature values only among the same kind segments and if the curvature values near the transition points have less input to the final (because of their proximity to the transition point)

    • Michael Mullins

      Well done I think you nailed it. Could you clarify why this effect is only in the gray area?

  • et

    Well… I cut out a single line of the zig-zag-looking “sine wave” and isloated it in its own image file. It STILL looks like a zig-zag, leading me to believe that if it’s still a zig-zag divorced from its visual context, this could be a hoax.

    https://uploads.disquscdn.com/images/32f221fb9dd258b89c49b32e5733945d425ae3ae58f17306b86961dbf552bd1f.jpg

    • Jan-Erik Vinje

      No hoax sir, just zoom in much closer 😉

      • Allen Joseph

        It’s no hoax. I’ve recreated it and it does that exactly, even at different wave heights.

        • Mark Syman

          I zoomed in and you can that some of the lines are nearly straight. The Dr. made a mistake.

          • https://www.facebook.com/app_scoped_user_id/1026609730/ Jim Balter

            You’re a mistake.

    • kwoolery
    • https://www.facebook.com/app_scoped_user_id/1026609730/ Jim Balter

      You’re a hoax. See Jeremy Scharlack’s gif above.

  • Dan Montgomery

    The sections with inflection points approximate a straight line much more closely than the semi-circular sections. I think that’s the main effect. The grey background color is adding to it, but even with no background, the difference is there. In other words, if you circumscribed the smallest rectangle onto each section, the semi-circular section would have a notably narrower rectangle than the s-shaped section.

    • Cory Kiser

      “All of the lines have exactly the same shape – a sine curve.”

      • Dan Montgomery

        Here’s what I’m trying to describe (thumb-sketched on my phone but hopefully you get the idea):

        https://imgur.com/gallery/z3YuH

        • Sławomir Borymski

          I agree. This was my first thought as well.

  • PedsAnesthesia.Net

    Way outside my bailiwick but…curious what happens if darker segment of line is moved in smaller increments (does this abolish the effect?) And how does color (rather than B/W/Gray shade impact?

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  • Julia Keren-Detar

    https://uploads.disquscdn.com/images/bf7b715e5f739b8433e1b7f91467507ed504761590976755b7890cbc55c5f2e0.jpg This is cool! It reminds me of similar effects made by traditional American quilts. One pattern has the opposite effect where straight lines seem to curve. Photo credit: Traditional Quiltworks issue no 64: “Long May She Wave” by Judy Martin

    • John Thompson

      I can only see the curves on the quilt with my periphery vision.
      My understanding is your actual focused vision is about the size of your thumbnail at arms length (don’t let your eyes dart around and look just at and notice that the other letters in this post are blurry.
      It’s amazing to me that a mere 1.5-2% of our field of vision is what we actually have in sharp focus.
      Our eyes do dart around, but it’s our brain that makes us think we see much more than we actually do. We are still able to have a mental image of a larger view despite the actual info coming from our eyes being almost all very limited and blurry.

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  • http://giannisarcone.com Gianni Sarcone

    When coloring with contrasting colors the descending and ascending curves of sine waves, the crests look less rounded and more sharp, especially when the background color is the average of the two contrasting colors… I wouldn’t have called it “curvature blindness”, the illusion is mainly due to the fact that the amplitude of the sine waves is very weak and the size of the curves very small.

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  • Jerome Barry

    Optical illusions are fun to look at, more fun to create.

  • Houshalter

    Take a look at the individual segments zoomed in: https://i.imgur.com/H4y4XTH.png

    I think what’s happening is the brain is processing the separate color segments individually, instead of a continuous line. And at an individual segment level, it’s much harder to detect a curve on the bottom pieces than the top. Notice the red line I drew. The bottom pieces fit much closer to a true line than the top pieces.

    • RCPreader

      Very helpful analysis!

    • Dan Montgomery

      I agree and tried to say the same thing in my comment but you said it better!

    • Arny.Plumb

      Your colored line helps demonstrate that when the chord drawn between adjacent transitions is horizontal there is a quarter circle of arc above or below the chord line. When the chord line is sloped at either the positive or negative 22.5degree there is 1/8 of a circle above and below the line so the curvature away from the chord is significantly less. A similar effect can be seen when drawing a square inside a circle, versus drawing an octagon inside a circle.

    • Igor

      Yes, but it is interesting that this only comes into play, very strongly, on the grey background. On white and black backgrounds, there is very little effect.

      • mtwzzyzx

        Probably to do with the fact that against the grey background, light and dark have roughly the same differential of tione, so you see them individually, as opposed to a light or dark background where you see the whole line, not the individual segments as much.

    • Scott Kennedy

      I think you cracked it @Houshalter:disqus ! Indeed, it’s not “harder to detect a curve” on the bottom pieces, but rather there *are* actually less curves once your brain has sufficient contrast to distinguish individual segments. In a way, this is an example of the brain correctly seeing individual shapes, rather than “being fooled” into seeing corners. Because the lower set of lines actually contains much straighter segments than the upper.

  • Nessie509

    Why does it look like every other of the lines is angular instead of curving? How strange and wonderful!

    • https://www.facebook.com/app_scoped_user_id/1026609730/ Jim Balter

      Pay more attention … the lines are different.

      • Chris TMC

        They are not different in shape at all, that is the entire point.

        • https://www.facebook.com/app_scoped_user_id/1026609730/ Jim Balter

          Chris, you seem to be profoundly stupid. Nessie asked why every other line looks different. The reason is that they are colored differently. Yes they are the same shape, but the brain processes them differently because of how the segments are colored.

          • Chris TMC

            I am aware, I read the article. There is no reason for you to be so angry and hostile beacuse I added one simple sentence to what you said just to help Nessie understand.There is no logical reason for hostility over that.

          • https://www.facebook.com/app_scoped_user_id/1026609730/ Jim Balter

            There was every reason for my response, and you are being dishonest. Your comment had nothing to do with helping Nessie to understand … it wasn’t directed at her, it was directed at me, and it was a stupid, ignorant attempt to refute my accurate statement.

          • Chris TMC

            Its sad that a benign sentence which wouldnt reasonably bother anyone had you frothing for days. It was not intended to, which I tried to clarify, but you are too angry to accept that. Over one sentence- one where you were not insulted, belittled, nothing… it still made you so inexplicably angry that you have spent the better part of a week insulting me in some kind of retribution. This I presume is where you yearn to tell me yet again how dishonest, profoundly stupid, ignorant, etc etc etc it was to DARE explain that continuity of shape was the whole point. Ill save you the trouble and live with this horrible, unbelievably terrible sentence that I dared, um, “post at” you for the rest of my natural life.

  • Warren Dew

    It’s not depth perception, but it is 3D perception. It happens against the medium grey background because the lighter and darker grey appearing to be based on angles to incident light reinforce the sharp color change, which overcomes the perception of a curve rather than a corner at the transition.

  • Robert Jensen

    It’s caused by a brain tooo-mer.

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  • D Samuel Schwarzkopf

    I haven’t read the paper but based on the image alone I suspect it has something to do with the phase of the light and dark parts of the waves. For the zig-zag lines they meet at the peaks/troughs of the curves and presumably this is interpreted as corners and straight lines. This should have implications for other shapes and so should be quite testable.

  • Jeremy Scharlack

    I created an animation to explore this:
    https://uploads.disquscdn.com/images/5841aad2995786a84e473982b42ab88d29cdc654b446fd04e800c8b56f8702b4.gif
    Increasing the height (amplitude) reduces the effect. I was surprised how much *more* curved the version with the colors at the top and bottom was. One interpretation – edges in real life are rarely 100% sharp so we will interpret a change in color as an ‘edge’ even if it is curved.

  • Jeremy Scharlack

    I created an animation to explore this:
    https://uploads.disquscdn.com/images/2751ad27fe1eb5d02f6a70c82493068943115ce214db1a488e8f72c2a4809281.gif
    Increasing the height (amplitude) reduces the effect. I was surprised how much *more* curved the version with the colors at the top and bottom was.

    One interpretation – edges in real life are rarely 100% sharp so we will interpret a change in color as an ‘edge’ even if it is curved. I also wonder if it has to do with how we interpret it as being a beveled edge ‘lit’ being by a light in the direction of the white part.

    • https://www.facebook.com/app_scoped_user_id/1026609730/ Jim Balter

      Great animation, that totally refutes the “not an optical illusion” idiocy elsewhere on this page.

    • polistra24

      Great animation! Shows what’s happening better than the original. Still doesn’t explain WHY it happens, but the animation should help more to find the WHY.

    • Jeremy Scharlack

      Tried another animation, this time in 3D to test a theory.

      When the tones are on the sides, it looks like an object being lit from the sides. Indeed it corresponds to a sharp (but not 100% sharp) sawtooth like object from the sides.

      When the tones are on the top and bottom it is clearly just a geometric drawing and we don’t see it as a 3D object.

      Another thing it might be is – as houshalter showed – a sin wave has more curvature at it’s peaks then at the sides.

    • Jeremy Scharlack

      Tried another animation, this time in 3D to test a theory.

      https://uploads.disquscdn.com/images/65a26bdfd47399f3531c1820a3ee7e45fea6d5dd8e7718aed9cc3c6369b2ac30.gif

      When the tones are on the sides, it looks like an object being lit from the sides. Indeed it corresponds to a sharp (but not 100% sharp) sawtooth like object from the sides.

      When the tones are on the top and bottom it is clearly just a geometric drawing and we don’t see it as a 3D object. As I change the lighting on the 3D objects you just see 1 tone.

      Another thing it might be is – as houshalter showed – a sin wave has more curvature at it’s peaks then at the sides.

      • Joe Botha

        Does it work the other way round? Like, if you start with a sawtooth, does it appear as a sine wave when the colours are out of phase?

        • John Thompson

          I noticed that as you magnify the image the effect diminishes.
          At 10X it’s nearly gone – there are some optical illusions that don’t scale up or down.
          I wonder if the limitations to the resolution/focus area of our eyes plays a role.

    • CL

      Nice!
      What if only one segment “moves” across the sinus curve, like a small black snake crawling across, I think MC Echer would like that

    • Dave Julian

      Well done. I think this shows that the modern human brain has been trained to see the meeting of two different coloured edges as a corner. I suspect a brain that has never been exposed to 2d representation of a 3d objects ie to a computer screen or drawing, would not see this effect.

  • Julius Smith

    I would say the brain is inferring the triangular geometry indirectly from shading that is perceived as reflected light

  • Isaac Maxwell

    To me this seems like the defensive mechanism of assuming a pattern is human-made. The presence of right angles indicates the presence of humans, and the presence of humans would indicate a higher threat level than whatever natural objects would present the wavy lines. (Most likely vines)

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  • Michael Mullins

    I’ll give you my evolutionary theory. Visual Illusions on small objects reflect distance perception. They claim this is not but I think it’s how we interpret far objects, not the distance itself.

    We should see them as waves by default. But when we see dark on one side of an curve, and light on the other, our brain wants to infer a shadow formed by a peak.

    A curved hill has an oblong shadow further down the sine wave. I bet if you moved the dark area to simulate that, it would look like rolling hills. And voila if you look at Jeremy’s gif, the original sine waves look like snow covered peaks and shaded valleys. – the shadow perception bias translates the image into landscape.

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  • Johan Siverklev

    I think this is a question of contrast. When the lines are alternating in the slopes, the brain registers the opposite slopes, disregarding the low contrast corner, and thus the zig zag is exaggerated. When the lines’ color alternates over the curved part, the curve is highlighted, with high contrast, and thus the brain registers the curves rather than the slopes. Makes sense?

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  • Stephen Malinowski

    I made this video to explore the effect: https://www.youtube.com/watch?v=2VG3lGvSHY0

  • http://akngs.tumblr.com/ Alan Kang

    Here’s an interactive demonstration of the illusion:

    https://bl.ocks.org/akngs/6e8d225d9922bbcb5783d890c45e8430

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  • Erik Bosma

    There seems to be a real threat to certain people’s egos when they are fooled by optical illusions. I’m included in that group. Whenever I see an optical illusion the first thing I try to do is to disprove it. It’s like if I admit to being fooled by the illusion I am also admitting that I am also a fool. After reading ALL of the arguments below I feel that this whole issue has more to do with Psychology than it does with Optics.

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  • Justin Waulters

    I think the 50% grey in the middle has a lot to do with it. I don’t see the effect nearly as much with solid black or white.

  • albertobladerunner

    To me it obvious that having the lines that have light (white-like) and dark (black-like) colors meet at mid wave produces an ABRUPT switch which suggest two surfaces meeting at a sharp angle which are illuminated by a light that frontally illuminates the light segment of the line and leaves the perpendicular dark line in darkness because of the abrupt switch from light to dark as that of the rocks in the Lunar atmosphere. The grey virtual surface provides the contrast to observe such lighted surface in contrast with the surface in the shadows (dark).

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  • http://TapGnomes.com Justin Waulters

    There may be an illusion here, but I took a look at the image in a photo editor and the lines are not the same.
    The round lines are actually a bit rounded due to photo compression.
    Based on close analysis, this image was compressed several times.
    I wonder if the illusion would happen in analogue – or even a better quality image.

  • Barbara Ellison

    If you look closely enough at original image, you can see the curve on all the lines across the image..We register the illusion first and if we skip on by we think we know what we saw..Scrutinizing detail can make illusion disappear..This is cool. Thanks! :)

  • Nathan F. Okun

    This happens at the corners where shades of black and white suddenly change. This is related to the color edge problem: When two distinct colors (red and blue, for example) meet at an edge (two adjacent square tiles with no noticeable crack between them, for example), the edge is sharp ONLY if the shade of grey they become if the color is removed is NOT the same!! If the shade of gray (the “gamma” of the color) is the same, the edge is invisible (blurs as though you need glasses for reading and took them off). It turns out that the “edge-detection” optical circuits in human brains — all human brains and probably all other animals with eyes (though this might not be true with different eyes like those in insects or squids; it should be tested) — are COLOR BLIND and if the color is the only difference between two adjacent points, they blur into one wider point — at least until the eye moves far enough away from the edge to turn off this circuit. There are probably lots of such “holes” in our optical and auditory processing that we do not know about because we literally are “blind” to them!!

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  • Riccardo Manzotti

    I totally agree with Jeremy Scharlack, Stephen Malinowski, and Jim Balter. I also made an animation https://uploads.disquscdn.com/images/0cb68b768c00886c9113fabcb20eab7ddddd5268503cd044d70d3b425377aaf1.gif, surely not as good as theirs, but the point is similar.
    It is not literally an illusion insofar as the lines are different and thus we perceive them as being different. You can check here my argument:
    http://www.consciousness.it/CC/Takahashi/Takahashi.php

    • Kohske Takahashi

      Shading and depth perception (may strengthen the illusion but) would not be the cause of the illusion. Please see Experiment 3 in the article. “we see just what is there” absolutely true. And in some cases “what is there” is not perfectly correlated with the 2D inputs into eyes. We usually call this situation “illusion.” cf: https://en.wikipedia.org/wiki/Checker_shadow_illusion

      • Riccardo Manzotti

        The point I wanted to make that to define an illusion (as is usually done) one needs an apriori notion about what one expects one ought to perceive (absolute gray level, orientation, lenght).
        Yet, there are two possible interpretations: either people perceive something different from the assumed property contained in the 2D input, or people perceive something else. In the former case we deploy the traditional notion of illusion (as you did), in the latter case we may use the perceptual case to revise our understanding of what we perceive. I argued on this issue here about Kitaoka’s illusion:
        http://www.nybooks.com/daily/2016/12/08/color-of-consciousness/
        Happy Xmas!

        • https://www.youtube.com/playlist?list=UUwbGJwCdp96FKSLuWpMybxQ Lee Rudolph

          The point I wanted to make that to define an illusion (as is usually done) one needs an apriori notion about what one expects one ought to perceive (absolute gray level, orientation, lenght).

          I have made this point at greater (and possibly tedious…) length in my editorial introduction (with co-author Jaan Valsiner) to Qualitative Mathematics for the Social Sciences (Routledge, 2013).

          Mathematics has been described as “the study of pattern” (Whitehead, 1941, pp. 674, 680) and (not necessarily more ambitiously) as “the science of patterns” (Devlin, 1997; Resnik, 1997; Steen, 1988). It is usual and natural for humans to perceive patterns, even patterns that are not ‘really there’; our perceptual systems create “perceptual illusions” of wholes from configurations of points, corners (Kanizsa, 1969) or sounds (Benussi, 1913). Furthermore, the human mind can contemplate objects that do not exist—a “round triangle” is an example that has fascinated thinkers since the 1880s when Alexius Meinong attempted to understand the nature of such objects in his Gegenstandstheorie (Meinong, 1907, passim; 1915, p. 14).

          In this connection, the traditional use of the word “illusion” is tendentious; it can be disputed along the following lines (see also
          Carini, 2007). Start with the axiom that a ‘whole’ that is perceived is ipso facto ‘correctly’ perceived. Then, for the person who perceives a whole, what is—or may be—‘illusory’ is not the whole: it is the felt need or imposed demand to identify the perceptually present and correctly perceived whole as something else, namely, a certain unperceived whole that is perceptually and physically absent from the present situation of the perceiver (and might even be physically absent from the entire universe, past, present, and future—if, say, it is a “round triangle”). Contrariwise, for a(nother, or the same) person (perhaps a psychologist) who is observing the situation, what is illusory is the conviction that the ‘whole’ known to the perceiver is in some manner or degree less (or more) ‘real’ than the ‘unwhole’ known to the observer, which the perceiver somehow should and would be perceiving—were not the universe (or the observer) somehow setting successful snares. On this view, the ascription of ‘illusion’ is a category error, a failure of the ascriber’s (formal or informal) ontology and epistemology to adequately fit the phenomena of construction by the human mind (starting with the human perceptual system).

  • Morbas

    Human Cognizance is dependent on an heirarchical voting system.

  • S.M. Ryan

    If the lines were the same shape they would distort the same way; they do not. (vertical stretch attached) The illustration for the story is a poor one. Several people below have much better illustrations for this illusion.

    https://uploads.disquscdn.com/images/b8b1674dfd9b44aa4bf04a2aa73e3fdbce66c5b590e302d3b195e9895ca16cd8.png

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