Making CAPTCHA

Create and transform a CAPTCHA image.

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Learn Mathematics Calculus

Question

How can mathematical transformations distort text while keeping it readable to a person?

Coordinate transformations change the geometry of an image without changing the underlying text.
Coordinate transformations change the geometry of an image without changing the underlying text.
A CAPTCHA image made from four distorted blue characters.
A CAPTCHA produced in the original project materials.

Goals

  • Represent image positions with coordinates, vectors, and matrices.
  • Create a CAPTCHA image by transforming and recombining pixels.

Method

Begin with a clear text image and change the coordinates of its pixels.

  • Store the image as a grid and identify the foreground pixels.
  • Apply rotations, shears, stretches, or other coordinate transformations.
  • Add controlled noise and check that the result remains readable.