I made a simple web UI[1] for generating images like this. It uses a Go library by Michael Fogleman[2] for all the heavy lifting—hat’s off to him.

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.

[1]: https://github.com/kevin-hanselman/primitive-web-ui

[2]: https://github.com/fogleman/primitive

The project references Geometrize: https://github.com/Tw1ddle/geometrize and I find both insanely cool!

Back in the 00s or early 10s a friend and I played with the idea of using genetic programming and random line segments to approximate images (ie. maintain a population of candidates, take the best n percent, "breed" them to create the next generation, add some "mutations", repeat). This implementation seems to use a basic hill-climbing algorithm to reach a local optimum – something like simulated annealing might improve both quality and speed of convergence.

I wrote something similar years ago, which would instead convert an image into a mesh of polygons. The idea was to have a vector low-size SVG that could be used as an image placeholder or background for web pages.

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 historic reference, back in 2008, Roger https://www.rogeralsing.com/2008/12/07/genetic-programming-e... kicked this off by attempting to reproduce the Mona Lisa using evolved polygons.

https://news.ycombinator.com/item?id=389727