Photoshop has a lot of cool artistic filters, and I\'d love to understand the underlying algorithms.
One algorithm that\'s particularly interesting is the Cutout filter
Very old question but maybe someone searching for an answer and maybe this helps. Opencv's findcontours and approxPolyDP functions can do this. But we need to prepare the image before main process. First; find most used N colors with k-means. For example find 8 colors.Find contours for each color and then calculate contourArea for all colors one by one (We will have N=8 layers). After that draw filled contours after approxPolyDP for each color from biggest ContourArea to smaller with its pre-calculated color. My another suggestion is eliminate very small contours while calculating contourArea.
Photoshop cutout effects parameters; Number Of Levels=K-Means-find most used N colors. Edge Simplicity=I guess gaussian blur or other removing noise filters like bilateral filter or meanshift filter with edge preserving will be useful for this step.This step can be executed after K-Means and before finding contours. Edge fidelity=openCV's approxPolyDP epsilon parameter.
Maybe not exactly what you are looking for, but if you like knowing how filters work, you could check out the source code of GIMP. I can't say if GIMP has an equivalent of cutout filter you mentioned, but it's worth taking a look if you are truly interested in this field.
From tinkering with it I've found out that:
Altogether it looks like simplified version of Live Trace algorithm from Adobe Illustrator that uses polygons instead of curves.
... or maybe not.