In the demo there's also a second mode called "Cell" that seems reminiscent of sampling via Poisson Disc, which you can read more about in Mike Bostock's excellent "Visualizing Algorithms" post.[0]
Yep, both delaunay ("Triangle") and voronoi ("Cell") uses "best candidate algorithm" to distribute the points by default. It's similiar to poisson disc.
The "Analyze image" uses JSFeat to apply a computer vision algorithm (feature point detection) to add some "interesting" points based on the image.
Then for each polygon, I take its points (center point or vertices or an arbitrary point) and find the corresponding pixel on the image. Then I extract the rgb color, and use that to fill the polygon (as solid color or gradient).