TITLE: Centroid within non-convex 2d polygon
QUESTION [6 upvotes]: The centroid of an object is defined as the arithmetic mean of all points of the object. For non-convex objects, the centroid is often not a part of the object itself:

Is there a definition of a centroid-like point which always lies within the object?

A definition that tackles 2 dimensional polygon objects is sufficient. I could think of something like the following, however, I would prefer a well-known definition if there is one:

Let $s_p(a, b)$ be the shortest path from $a \in p$ to $b \in p$ such that all points of the path are within $p$.
Let $S_p := \{s_p(a, b) | a, b \in p\}$.
Let $d$ be the longest path in $S_p$.
The mid point of $d$ is a centroid-like point and it always lies within $p$.

REPLY [5 votes]: In geography there is an interesting point called Pole of inaccessibility: the most distant internal point from the polygon outline.  
It is found by an iterative method, described in the Methodology section of this paper.  
Links of interest:  
https://sites.google.com/site/polesofinaccessibility/ 
https://github.com/mapbox/polylabel