I think I lost the code, but it was initially a genetic algorithm that randomly placed overlapping polygons, but the later improved method had connected polygons that shared points - which was far more computationally cheaper.
Another method I explored was to compose a representative image via a two-colour binarised bitmap, which provided a pixelated version of the image as a placeholder.
The core idea is that you drop the image as a small Data URI straight into the page, and then fetch the high-detail version later. From the user's perspective, they are getting a very usable web page early on, even on poor connections.
For Bézier curves in particular, iteratively constraining the search around initial matches seems key to retaining detail (see the “rep” argument in Fogleman’s work), for example in the eyes of the Vermeer portrait in the OP.