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Takahashi, Kohske. "Curvature Blindness Illusion." i-Perception 8.6 (2017): 2041669517742178. (Journal link)

            CurvIllusion
        "All lines are identical sine waves. [...] A wavy line is perceived as a zigzag line."

Q. I wonder if there is some mathematical hypothesis (as opposed to a strictly physiological hypothesis) that can help explain this remarkable (newly discovered) illusion?

Joseph O'Rourke
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2 Answers2

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My percept matches what you would get if you replaced each segment with its best-fitting circular arc.

For the zigzag case the best-fitting circular arc has zero curvature, i.e. it is a straight line segment.

If this hypothesis is correct, in the other case the curve should appear more "rounded" than a usual sine wave, and to be honest it kind of does.

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    May be just me, but I only "see" the zigzags in the middle stripe with gray background, so there must be more to it than just curvature. Could have something to do with the wave colors being both lighter or both darker than the background in the outer stripes. – dxiv Dec 10 '17 at 02:44
  • I think the colours only matter to the extent that they cause the segments to be interpreted as different objects rather than as parts of the same curve. I would expect the same illusion to appear with, for example, red and blue segments on a white background. If it does not, then I will concede that something more complicated is going on. –  Dec 10 '17 at 03:42
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Looks simple enough to me. The darker bands are interpreted as shadows when they end right in the middle of the curve top or bottom, and that makes you reinterpret the curve as a corner (because the "shadow" ends so abruptly. And conversely, when the darker band continues through the middle, your brain will not interpret it as a corner because it knows that shadows are not in the habit of turning corners like that. At least that's my first impression.

Manuel Maduro
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