Evolution: The Simple Polygon

Just watch, this is what evolution is all about. In the beginning the fish is what can easily be recognized as one, but as the number of lines in the polygon are reduced, it becomes more an more abstract.

Check out the math behind the method!

Important properties of the discrete curve evolution:

  1. This evolution method is translation, rotation, reflection, and scaling invariant.
  2. It leads to the simplification of shape complexity, in analogy to evolutions by diffusion equations, with no blurring effects and no distortion of relevant features.(compare to [2])
  3. It is stable with respect to noisy deformations, since noise elimination takes place in the early stages of the evolution.
  4. It allows us to find digital line segments in noisy images, due to the relevance order of the repeated process of digital linearization.