An example for 2D and 3D Digital Images

[aranos-tda]

I would like to first thank you for your efforts in building this package.
It would be nice to have an example where the input is a 2D digital Image and plotting the corresponding Multiparameter representation. I searched in the docs/notebooks but could not find one.
I can provide medical images for a notebook to do the multiparameter representation of images and a set of images to do machine learning ( e.g. classification).

Best Wishes
Aras Asaad

P.S. : I could not find an email to directly contact you
I can be contacted by: aras.asaad@maths.ox.ac.uk

[DavidLapous]

Dear Aras,

Thanks for your interest in this library :)
I noticed that I didn't push the code for cubical complexes indeed, I'll do that ASAP;
In the meantime, an easy workaround is simply to triangulate your image into a simplicial complex, i.e.,
do something like this

import gudhi as gd
import multipers as mp
import numpy as np

# Data
num_parameters = 3
res = (10,20,30,num_parameters)
img = np.random.uniform(size=res)

#Triangulation
mesh = np.meshgrid(*[np.arange(r) for r in res[:-1]])
X = np.concatenate(tuple(stuff.ravel()[:,None] for stuff in mesh), axis=1)
ac = gd.AlphaComplex(points = X)
st = ac.create_simplex_tree()
p = np.fromiter((ac.get_point(i) for (i,),f in st.get_skeleton(0)), dtype=np.dtype((int,img.ndim-1)))
assert np.all(p == X) # alpha complex may reorder points, it doesn't seem to be the case here

# To multipers
st = mp.SimplexTreeMulti(st, num_parameters = num_parameters,dtype=np.float64)
for i in range(num_parameters):
    st.fill_lowerstar(img[...,i].ravel(),parameter = i)

which will give you a topologically equivalent simplicial complex. Note that in the 2-parameter case, you'll have access to edge collapses, and minimal presentation, so this shouldn't hurt performance there.
I'll do a notebook once I update this code, I'd be happy to have your images, I'll contact you when I'll have the time to do this.
The rest of the code should be in the notebooks, feel free to ask me if that's not the case.

I currently have some issues with my website, so my email can be hard to find; you can contact me at david.loiseaux@inria.fr

Best,
David

[aranos-tda]

Thanks David, much appreciated.
Best,
Aras

[DavidLapous]

I forgot to mention this notebook in the documentation with the cubical complexes. I don't have a proper dataset at hand at the moment, so it's a bit convoluted, but it should work. Feel free to email me if you have a better example to replace this one.