1. Convert outline to a complex signal

First, we need to get an outline from an image. I decided to use Canny edge detection to extract the edges from an image (in the example above, a drawing of Sherlock Holmes).

This will give us a 2D binary array indicating the edges of the image. Now, we need to represent these points as complex coordinates oriented about the origin. The x-axis will represent the real component, and the y-axis will represent the imaginary component.