Largest Empty Rectangle (Square actually)

I'm not much of a mathematician, but looking around wikipedia, I figured I need something like a Largest Empty Circle/Rectangle algorithm to solve my problem:

I would like to find the largest square that fits inside a roughly circular, closed, planar curve.

These curves are usually almost a circular shape, but could be more oval or mushroom shaped - it is different from one job to another. Imagine the silhouettes of various fruits (excluding bananas).

Following a paper I found online, I've broken the curve up into 100 points, and used grasshopper to create a Voronoi diagram from them. I'm struggling to follow the paper from there on.

Maybe there is a simpler solution anyway?