How much decimation is too much? A varifold perspective#

Before, we asked the question How much decimation is too much?.

Here, we provide a different perspective using a varifold distance.

[1]:

import numpy as np
from matplotlib import pyplot as plt

import polpo.preprocessing.dict as ppdict
from polpo.mesh.surface import PvSurface
from polpo.mesh.varifold.tuning import SigmaFromLengths
from polpo.preprocessing import BranchingPipeline, IdentityStep
from polpo.preprocessing.load.pregnancy.jacobs import MeshLoader
from polpo.preprocessing.mesh.decimation import PvDecimate

[KeOps] Warning : CUDA was detected, but driver API could not be initialized. Switching to CPU only.

[2]:

session_subset = np.random.choice(np.arange(1, 27))

mesh_loader = (
    MeshLoader(
        subject_subset=["01"],
        struct_subset=["L_Hipp"],
        session_subset=[session_subset],
        derivative="enigma",
        as_mesh=True,
    )
    + ppdict.ExtractUniqueKey(nested=True)
    + PvSurface
)

raw_mesh = mesh_loader()

session_subset

[2]:

np.int64(6)

[3]:

decimation_targets = [0.99, 0.95, 0.9, 0.8, 0.6, 0.5, 0.2, 0]


multi_decimation_pipe = BranchingPipeline(
    [
        (
            PvDecimate(target_reduction=target_reduction, volume_preservation=True)
            + PvSurface
            if target_reduction
            else IdentityStep()
        )
        for target_reduction in decimation_targets
    ],
    merger=lambda data: dict(zip(decimation_targets, data)),
)

meshes = multi_decimation_pipe(raw_mesh)


[mesh.n_points for mesh in meshes.values()]

[3]:

[27, 127, 252, 502, 1002, 1252, 2002, 2502]

We select the varifold kernel using characteristic lengths.

[4]:

sigma_search = SigmaFromLengths(
    ratio_charlen_mesh=2.0,
    ratio_charlen=0.25,
)

sigma_search.fit([raw_mesh])

metric = sigma_search.optimal_metric_

[5]:

dists = [metric.squared_dist(raw_mesh, mesh) for mesh in meshes.values()]

[6]:

_, ax = plt.subplots()


ax.plot(decimation_targets, dists)
ax.set_ylim(0, 10)

ax.set_xlabel("Target reduction")
ax.set_ylabel("Varifold distance");

../../../_images/_generated_notebooks_tutorials_varifold_decimation_charlen_dist_7_0.png

These values become particularly relevant when we start looking at datasets.

How much decimation is too much? A varifold perspective#

Further reading#