Drawing the longest line segment contained in an area

Inside a rectangle, this line segment would be its diagonal.

Inside a circle, this line segment would be its diameter.

Inside a more "jagged" shape, it would be:

However, suppose we consider an irregular area, such as

The longest possible line segment that can be drawn would not be as intuitive any more. Is there any geometrical approach (hopefully an efficient one) which would allow us to determine this mentioned line segment for any (enclosed) areas, in general?

Just to clarify, the line segment in question is a straight line. The entire line segment must be contained within the area. It cannot cross the boundary.

The final result could be something like this.

Original question from Math StackExchange

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/330389-how-to-find-greatest-and-smallest-diameter-of-an-irregular-shape

Answer 1

[Image Analyst]

My attached demo does almost that. It doesn't check though if the line goes outside the region. You'll have to test for that if you think that's a possibility. Basically uses bwboundaries() and then gets the distance between every pair of points.