How can I create an interior convex set?

(Background): I am working on a code to automate the process of reconstructing arterial networks from medical imaging scans. As these networks can often branch or merge, I've found myself needing to track the centroids of slices throughout the image sequence.

(Problem): I need to identify a point which would be unique to a specific object in a binary image, but also remains within the region area. I initially looked to the centroid using regionprops(); however, in some instances (such as the aortic arch) this point falls "outside" of the region area. While the convex hull would define a polygon with the desired centroid properties, it physically extends the region area (or the centroid of the hull remains outside of the original region), which will not work for me either.

I would like to know... is there any method to determine the smallest set of convex polygons (smallest meaning a set requiring the fewest number of polygons), perhaps within a specified tolerance of the original region area, fitting within a given region in space?