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Topographic relief detection on a slope

Question asked by dave090 on Sep 21, 2020
I am not exactly sure how to describe this. I need to find out what the greatest height is between the perimeter of polygons I have and a point within each polygon that "stands up higher" than anywhere else in the area.  This is for marine bathymetry data. Note that what I am looking for is not necessarily the shallowest point because my polygons are on a slope. So I want to find the highest local maximum I guess. See the very crude drawing I attached (but my example is planner, not linear). I am trying to find the length of the red line in B, for a maximum point within the polygon, even though it isn't the highest point. I need to automate this for various polygons in my data frame. I thought about it like I was rotating the slope so it was level, and THEN trying to find what was the highest point. I believe depending on how far the point is from the perimeter, the height changes more or less when rotated. So I was not sure how to do this or even how to google it.
We originally thought we could find the maximum height in the polygon overall and then subtract from that value the average perimeter of the polygon, but that does not work. The maximum height is usually at the top part of the slope (so not the point in the triangle in my picture but the start of the slope (upper left most point).
Some concepts I thought that might help was local maximum (from graphing) and topographic prominence but I couldn't figure it out more.  
Does anyone have some suggestions?

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