In an attempt to understand what you are asking, I searched for "Bart Simpson, epicycles" on Google and found a YouTube Video which I think is related to your question. Let me summarize.
We have a line drawing in the complex plane. We parametrize the drawing as F(t), where t goes from 0 to 2*Pi. Then we expand F(t) into the complex Fourier series, and interpret the partial sums of the series as depicting a planet, a moon, a moon of that moon, and so on. Thus, the Fourier series approximation of F(t) may be viewed as the orbit of the last moon in the sequence of the moons.
In the attached Maple worksheet I show how to animate the moons as they trace the curve corresponding to F(t), which, for the sake of illustration I have taken to be a square. The animation below corresponds to picking 7 terms of the Fourier series, and consequently the target square (drawn in green) is rendered with rounded corners (rendered in red).
Download worksheet: mw.mw
You may replace the square with any other drawing provided that you can obtain a parametric representation for it. I understand that you are looking for a method of extracting the data for a given curve from an image, and then parametrizing it. That's a rather complex operation. I haven't given it much thought. The video quoted above suggests using a traveling salesman algorithm to connect points extracted from a graph.
Added Dec 5:
Here I have replaced the square with an F-shape: