Especially the part about sailing over the continental divide… that just sounds slick.

http://www.craftacraft.com/continental_divide

Ok, the algorithm at least needs a way to fill plateaus and find an exit from those, just finding a local descent gets stuck in those as well.

Also the raw data (GLOBE) contains some artefacts, in http://ch.iocl.org/g.png (falsecolor to bring out small-elevation features) near the upper left water (pink) there are a few features that are too rectangular to be of natural origin.

Because I can truncate the minimum search when I encounter an already-colored pixel, I will search long paths for some pixels, but I will only try to find the steepest descent from each pixel one time — when it is not yet colored.

for all pixels of the next-lowest height. . .
remove the next pixel and mark it colored. among all of its adjacent, colored, neighbors, choose that with the greatest height (aka the neighbor with best matching height)
if there is such a neighbor (could be NO neighbors are colored), union the sets of the current pixel and its neighbor
repeat the loop until queue is empty.

Sets now contain the terrain, properly divided up.
Simple, n lg n algorithm due to the priority queue. Everything else is linear time.

A characteristic of an unseeded basin is that any pixel on its rim drains into an area that has not yet been colored. Thus, when the coloring algorithm reaches the lowest point on the rim, the pixels inside the basin will have the property that they are (a) uncolored, and (b) lower than the current “water level”.

Thus, when you color a pixel, you can add a check to see whether it is in fact in the band of elevations that you are expecting to color. If it is below that level, it must be inside an unseeded basin. Thus, you can follow a steepest-descent algorithm to find the spot at the bottom of the basin, place a seed there, and raise the water level on that seed until it reaches the current level.

We know that the steepest-descent algorithm will do the right thing. It won’t run into an existing basin, because that would require there to be an uncolored pixel that is lower than the one we started with, but which is adjacent to an existing basin; this cannot happen because of the order in which basins are colored. Also, any uncolored pixel that the steepest-descent algorithm lands on will be the bottom of a basin; if steepest-descents from all pixels in an uncolored region do not resolve to a unique answer, that means either that the bottom is flat (so it doesn’t matter) or that there are multiple unseeded basins within the region. The basin-filling algorithm should be recursive; if you find another unseeded basin while doing this, you go and fill it in, and then raise the pair up to the main current level.

A relevant observation is that, since the basin is previously-undiscovered, we know that the filling process will not reach a boundary with the existing basins/oceans until we get up to the current level, and thus the result is not different from having placed seeds in the basins a priori.

The continuously varied coastline sounds like a fun idea, but I expect the results will be very similar to what would happen if you put a seed point wherever a river meets an ocean.

Here is a tutorial: http://www.cis.upenn.edu/~jshi/GraphTutorial/

For the multicolor case, an optimal segmentation can be approximated to within a constant factor of optimality using Boykov & Kolmogorov’s method.