TITLE: Curvature Blindness Illusion: Any mathematical explanation?
QUESTION [6 upvotes]: Takahashi, Kohske. "Curvature Blindness Illusion." i-Perception 8.6 (2017): 2041669517742178. (Journal link)


           


       
"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?

REPLY [3 votes]: 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.