Documentation of algorithm and approach (questions)
Interesting work! This is mainly a documentation issue.
My use case is to assign a significance/priority to any peak in OSM in order e.g. to generalize (filter) a map when zooming out. Prominence and/or topographic isolation output such measures.
I now quite don't understand your algorithm, nor do I see any (filter / range?) parameters in find_extremals.m.
Question 1: Does your algorithm assign any measures (which one could assign to all peaks as aka priority) and if yes, which one(s)?
Q2: Which input/filter parameters did you use when producing the map show case, if any?
Q3: When looking at the map show case, it shows only few peaks e.g. in the alps but many in northern europe. So it seems IMHO that the algorithm (or implementation?) favors flat (or sea level?) topographic regions! Any explanations?