Notebook source code:
notebooks/how_to/09_functional_from_pointwise.ipynb
Run it yourself on binder
How to compute a functional map from a pointwise map?#
In [1]:
import geomstats.backend as gs
import numpy as np
from geomfum.convert import FmFromP2pBijectiveConverter, FmFromP2pConverter
from geomfum.dataset import NotebooksDataset
from geomfum.shape import TriangleMesh
In [2]:
dataset = NotebooksDataset()
mesh_a = TriangleMesh.from_file(dataset.get_filename("cat-00"))
mesh_b = TriangleMesh.from_file(dataset.get_filename("lion-00"))
mesh_a.n_vertices, mesh_b.n_vertices
Out [2]:
(7207, 5000)
Set Laplace eigenbasis for each mesh.
In [3]:
mesh_a.laplacian.find_spectrum(spectrum_size=6, set_as_basis=True)
mesh_b.laplacian.find_spectrum(spectrum_size=6, set_as_basis=True)
mesh_b.basis.use_k = 5
Assume we have a valid pointwise map between mesh_a and mesh_b (which for demonstration purposes, we instantiate randomly).
In [4]:
p2p_12 = gs.from_numpy(np.random.choice(mesh_a.n_vertices, size=mesh_b.n_vertices))
p2p_12.shape
Out [4]:
(5000,)
Compute functional map.
In [5]:
fm_converter = FmFromP2pConverter()
fmap_matrix = fm_converter(p2p_12, mesh_a.basis, mesh_b.basis)
fmap_matrix.shape
Out [5]:
(5, 6)
The pseudo_inverse can be used instead.
In [6]:
fm_converter.pseudo_inverse = True
fmap_matrix = fm_converter(p2p_12, mesh_a.basis, mesh_b.basis)
fmap_matrix.shape
Out [6]:
(5, 6)
The bijective method can be used using a different converter.
In [7]:
p2p_21 = gs.from_numpy(np.random.choice(mesh_b.n_vertices, size=mesh_a.n_vertices))
p2p_21.shape
Out [7]:
(7207,)
In [8]:
fm_bij_converter = FmFromP2pBijectiveConverter()
fmap_matrix = fm_bij_converter(p2p_21, mesh_a.basis, mesh_b.basis)
fmap_matrix.shape
Out [8]:
(5, 6)