Based on this paper.

Elephant from paper with just 8 parameters:

Fancy elephant with more parameters:

How does it work?

Given arrays of parameters A_k^x, B_k^x, A_k^y, B_k^y, a curve, parameterized by t, is calculated and the Adam optimizer is used to fit the curve to given data points p_i describing the contour of an elephant:

  x(t) = \sum_{k=0} (A_k^x cos(kt) + B_k^x sin(kt))
  y(t) = \sum_{k=0} (A_k^y cos(kt) + B_k^y sin(kt))
  
  min_{A_k^x, B_k^x, A_k^y, B_k^y} \sum_i ((x(t) - p_i^x)^2 + (y(t) - p_i^y)^2)

Or more simply put, you can approximate a sequence of values with a Fourier series. For example, see this graph of a house approximated with truncated Fourier series:

If you do that with both x- and y-coordinates, you can approximate a contour.

I want to make my own elephants!

You can make your own elephants by edditing the binary mask in fancy_elephant.png (make sure the elphant has a single contour!) and then run:

1. python contour_from_image.py This will find the contour of the binary mask and save the points in points_fancy_elephant.npy.
2. python elephant.py This will fit Fourier coefficients to the elephant.

Note that this repository is about as serious as FizzBuzz in TensorFlow.