pyFM.spectral.convert

Python implementation of:

[1] - “Deblurring and Denoising of Maps between Shapes”, by Danielle Ezuz and Mirela Ben-Chen.

Functions

FM_to_p2p(FM_12, evects1, evects2[, ...])	Obtain a point to point map from a functional map C.
mesh_FM_to_p2p(FM_12, mesh1, mesh2[, ...])	Wrapper for FM_to_p2p using TriMesh class
mesh_FM_to_p2p_precise(FM_12, mesh1, mesh2)	Computes a precise pointwise map between two meshes, that is for each vertex in mesh2, gives barycentric coordinates of its image on mesh1.
mesh_p2p_to_FM(p2p_21, mesh1, mesh2[, dims, ...])	Compute a Functional Map from a vertex to vertex maps (with possible subsampling).
p2p_to_FM(p2p_21, evects1, evects2[, A2])	Compute a Functional Map from a vertex to vertex maps (with possible subsampling).

pyFM.spectral.convert.p2p_to_FM(p2p_21, evects1, evects2, A2=None)

Compute a Functional Map from a vertex to vertex maps (with possible subsampling). Can compute with the pseudo inverse of eigenvectors (if no subsampling) or least square.

Parameters:

• p2p_21 –

  (n2,) vertex to vertex map from target to source.

  For each vertex on the target shape, gives the index of the corresponding vertex on mesh 1. Can also be presented as a (n2,n1) sparse matrix.

• eigvects1 – (n1,k1) eigenvectors on source mesh. Possibly subsampled on the first dimension.

• eigvects2 – (n2,k2) eigenvectors on target mesh. Possibly subsampled on the first dimension.

• A2 – (n2,n2) area matrix of the target mesh. If specified, the eigenvectors can’t be subsampled

Returns:

FM_12 –

(k2,k1) functional map corresponding to the p2p map given.

Solved with pseudo inverse if A2 is given, else using least square.

Return type:

np.ndarray

pyFM.spectral.convert.mesh_p2p_to_FM(p2p_21, mesh1, mesh2, dims=None, subsample=None)

Compute a Functional Map from a vertex to vertex maps (with possible subsampling).

Parameters:

• p2p_21 –

  (n2,) vertex to vertex map from target to source.

  For each vertex on the target shape, gives the index of the corresponding vertex on mesh 1. Can also be presented as a (n2,n1) sparse matrix.

• mesh1 (TriMesh) – source mesh for the functional map. Requires enough processed eigenvectors.

• mesh2 (TriMesh) – target mesh for the functional map. Requires enough processed eigenvectors.

• dims (int, or 2-uple of int) –

  Dimension of the functional map to return.

  If None uses all the processed eigenvectors. If single int k , returns a (k,k) functional map If 2-uple of int (k1,k2), returns a (k2,k1) functional map

• subsample – None or size 2 iterable ((n1’,), (n2’,)). Subsample of vertices for both mesh. If specified the p2p map is between the two subsamples.

Returns:

FM_12 – (k2,k1) functional map corresponding to the p2p map given.

Return type:

np.ndarray

pyFM.spectral.convert.FM_to_p2p(FM_12, evects1, evects2, use_adj=False, n_jobs=1)

Obtain a point to point map from a functional map C. Compares embeddings of dirac functions on the second mesh Phi_2.T with embeddings of dirac functions of the first mesh Phi_1.T

Either one can transport the first diracs with the functional map or the second ones with the adjoint, which leads to different results (adjoint is the mathematically correct way)

Parameters:

• FM_12 – (k2,k1) functional map from mesh1 to mesh2 in reduced basis

• eigvects1 –

  (n1,k1’) first k’ eigenvectors of the first basis (k1’>k1).

  First dimension can be subsampled.

• eigvects2 –

  (n2,k2’) first k’ eigenvectors of the second basis (k2’>k2)

  First dimension can be subsampled.

• use_adj – use the adjoint method

• n_jobs – number of parallel jobs. Use -1 to use all processes

Returns:

p2p_21 –

(n2,) match vertex i on shape 2 to vertex p2p_21[i] on shape 1,

or equivalent result if the eigenvectors are subsampled.

Return type:

np.ndarray

pyFM.spectral.convert.mesh_FM_to_p2p(FM_12, mesh1, mesh2, use_adj=False, subsample=None, n_jobs=1)

Wrapper for FM_to_p2p using TriMesh class

Parameters:

• FM_12 – (k2,k1) functional map in reduced basis

• mesh1 (TriMesh) – source mesh for the functional map

• mesh2 (TriMesh) – target mesh for the functional map

• use_adj (bool) – whether to use the adjoint map.

• subsample (None or size 2 iterable ((n1',), (n2',)).) – Subsample of vertices for both mesh. If specified the p2p map is between the two subsamples.

• n_jobs (int) – number of parallel jobs. Use -1 to use all processes

Returns:

p2p_21 – (n2,) match vertex i on shape 2 to vertex p2p_21[i] on shape 1

Return type:

np.ndarray

pyFM.spectral.convert.mesh_FM_to_p2p_precise(FM_12, mesh1, mesh2, precompute_dmin=True, use_adj=True, batch_size=None, n_jobs=1, verbose=False)

Computes a precise pointwise map between two meshes, that is for each vertex in mesh2, gives barycentric coordinates of its image on mesh1. See [1] for details on notations.

[1] - “Deblurring and Denoising of Maps between Shapes”, by Danielle Ezuz and Mirela Ben-Chen.

Parameters:

• FM_12 – (k2,k1) Functional map from mesh1 to mesh2

• mesh1 – Source mesh (for the functional map) with n1 vertices

• mesh2 – Target mesh (for the functional map) with n2 vertices

• precompute_dmin –

  Whether to precompute all the values of delta_min.

  Faster but heavier in memory

• use_adj – use the adjoint method

• batch_size – If precompute_dmin is False, projects batches of points on the surface

• n_jobs – number of parallel process for nearest neighbor precomputation

Returns:

P_21 – (n2,n1) - precise point to point map from mesh2 to mesh1

Return type:

scipy.sparse.csr_matrix