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Transforming several pixel width shape into 1 pixel width.

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Never mind, I got it. All I had to do, was select the "ocean" region, reverse the selection so it would select all the landmass, with AA disabled, delete it. Then globally fill any of the transparent or landmass region with any colour (I selected gray). The result is exactly what I wanted.

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I'm happy you found a solution to your problem. I thought you needed the more general solution of reducing the edges to one-pixel width while maintaining connectivity. That's called "skeletonization" or "thinning." That's more complex, and I'm pretty sure there's no plugin to do that.

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