Average stroke from a fill

I would like to generate an average stroke from a given compound enclosed path, or fill, in Adobe Illustrator CC or Inkscape.

Sorry I don't know the mathematical function name to achieve this. I've come upon a couple bizarre hacks involving Photoshop, but it stands to reason there is a simpler way to achieve this within a vector program. Unfortunately Illustrator's path averaging collapses my example into a single point, likely because it has both horizontal and vertical aspects.