Is there a function to fit the inner ellipses to a polygon?

I have 2D scattered data in X,Y format and I would like to fit an ellipses to this data. But all the scripts I found are fitting a ellipses over the whole data. I would need a function though that lets me fit the inscripting ellipses, with the maximum volume. Is there a function for this somewhere? Or does anyone know how to best implement this? Thanks in advance.

[Matt J]

A picture, perhaps?

[Torsten]

https://math.stackexchange.com/questions/2456854/finding-the-maximum-volume-inscribed-ellipsoid-using-cvx/2457011

[Image Analyst]

How many points do you have? If it's not too many, then you can do a brute force approach of taking all sets of 5 points that define an ellipse and compute the area of all of them.

[Bruno Luong]

Image Analyst: And how you ensure the ellipse goes through 5 random points are inscripting ellipses to the polygon (data boundary)?

Torsen's pointer is a correct approach.

[Katharina Haase]

That was excatly what I was looking for. Thanks so much. And I have a varring amount of points. It can be between 20 and a 100. Thanks again everyone for the quick help :) But I would also be interested in Image Analysts approach. Would that be still possible with my amount of points?

[Bruno Luong]

There are 75287520 ways to peak out 5 points from 100. If you have very very fast computer you might temp it, but:

Take a look at the picture on Torsen's link, you'll see the inscribing ellipse does not touch any data point (polygon vertex), let alone 5 points.

Now if you impose the constraints that the vertexes are outside the ellipse, then the largest ellipse will be bigger than the previous constraint (inside the polygon), and the minimizing formulation is slightly different.