Recovering polygons from the 2-persistence representation

[HugoHenneuse]

First, thank you for this very nice package, it's been a pleasure to work with it.

I have a question regarding the 2-persistence representation you propose, based on the interval decomposition techniques implemented in the multiparameter_module_approximation module. The resulting "persistent polygons" provide a very elegant and informative visualization.

My question is: beyond the visual rendering, is it possible to access or extract the individual polygons ? for instance, as a shapely polygon or a similar representation? I imagine this could be straightforward, but I haven’t managed to figure out how to do it from the docs. Any pointers or suggestions would be greatly appreciated!

Best,
Hugo Henneuse.

[DavidLapous]

Hey Hugo,

Thank you for these kind words and your interest in multipers !
It's totally possible to recovers these coordinates. Basically a module approximation is iterable on its summand, i.e., shape.
So something like the following should work:

import multipers as mp
from multipers.data.synthetic import noisy_annulus


X = noisy_annulus(500,500)
s = mp.filtrations.DelaunayCodensity(points = X, bandwidth=.1, reduce_degree=1)
m = mp.module_approximation(s)

for summand in m:
    print(summand.get_birth_list())
    print(summand.get_death_list())
    break

# or 
print(m[73].get_birth_list())

The birth_list $B$ correspond to the lower corners of the shape, while the death_list $D$ correspond to the upper corners of the shape, such that $I = \bigcup_{b,d \in B\times D} [b,d]$ where $[b,d] = \{ x\in \mathbb R^n \mid b\le x \le d\}$

This interface could be improved, but I didn't find something significantly better than this for the moment.
There is also some code to have the corners in a differentiable way (if the input has a gradient ofc), but the interface is clearly not ready yet

[HugoHenneuse]

Oh, okay, I get it now. I hadn't understood it that way before. Thanks, that's really helpful!