Finding topographic prominence of peaks in a 2D heightmap

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Is there a (preferably simple) algorithm for finding topographic prominence of peaks in a 2D heightmap? I'd like to find how prominent each local maximum is. I'm toying with good old terrain generation and I'd like the generator to identify prominent mountains/peaks. Trying to implement this in C++.

Here's a screenshot for clarity White ticks mark the peaks (found by brute force). I want to determine the prominence for each of them.

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