Teach (and learn) the Fourier transform geometrically! - Deepstash

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## 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.

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## 2. Reorder to minimize distance between sequential points

Now, we need to order the points to make the progression as smooth as possible. In practice, I’ve found ordering to minimize the difference from one point to the next is a good approach!

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## 3. Call the Fourier transform

We’ll now apply the Fourier transform to extract the magnitude and phase information associated with each frequency. As visualizing all the oscillators is slow, we’ll filter out all the frequency components above self._n_oscillators .

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