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I want to mimic and reproduce the noise curves in the captcha images below.

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It seems the curve was generated by a brush on a random curve path. The pattern of the path is like but not simple sin/cos function or a Bessel function.

So, how can I guess the curve paths' pattern?

nn0p
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  • You may be better off fitting a polynomial curve. http://en.wikipedia.org/wiki/Curve_fitting#Fitting_lines_and_polynomial_curves_to_data_points – rayryeng May 10 '15 at 05:03
  • @rayryeng I don't think it's a polynomial function. – nn0p May 15 '15 at 01:14
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    Never said it was. I said you "may be better off". From some of those images it looks like it, but I can't honestly say for sure. The only thing I can really suggest is try it and see how it goes. It could also be piecewise polynomial too. Split up the segments into polynomials of different orders! – rayryeng May 15 '15 at 01:15
  • Thanks for the suggestions. Quite helpful. I'd give a try. @rayryeng – nn0p May 15 '15 at 01:29
  • No problem at all. More on what I was suggesting, figure out how many segments you want to split up the width of the image into, then for each segment, generate a spline or polynomial of a random order and random coefficients... also make sure that the end of one spline serves as the beginning of the next spline and piece them all together. If that works, I wouldn't mind writing an answer and probably with a Python implementation too! Let me know how it goes. – rayryeng May 15 '15 at 01:31

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