How much decimation is too much?

Here we show the impact of decimation on the characteristic length of the mesh.

import numpy as np
from matplotlib import pyplot as plt

import polpo.preprocessing.dict as ppdict
from polpo.mesh.geometry import centroid2farthest_vertex
from polpo.mesh.surface import PvSurface
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.

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

np.int64(5)

decimation_targets = [0.95, 0.9, 0.8, 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()]

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

np.amax([np.sum(mesh.volume) for mesh in meshes.values()])

np.float64(3674.2668726564752)

max_edge_lengths = np.array([np.amax(mesh.edge_lengths) for mesh in meshes.values()])
median_edge_lengths = np.array(
    [np.median(mesh.edge_lengths) for mesh in meshes.values()]
)

max_edge_lengths, median_edge_lengths

(array([9.59674358, 7.63264751, 6.4765296 , 5.32241917, 4.82180786,
        2.03753066]),
 array([4.33092594, 2.99716091, 2.11263514, 1.301808  , 1.03224313,
        0.92778929]))

_, ax = plt.subplots()

for target_red, mesh in meshes.items():
    edge_lengths = mesh.edge_lengths
    ax.hist(
        edge_lengths,
        label=target_red,
        alpha=0.6,
        weights=1 / edge_lengths.size * np.ones_like(edge_lengths),
    )


ax.set_xlabel("Edge length")
ax.set_ylabel("Frequency")
ax.legend(title="Reduc", bbox_to_anchor=(1.02, 1), loc="upper left")

<matplotlib.legend.Legend at 0x7d31ba721040>

c2farthest = np.array(centroid2farthest_vertex(meshes.values()))

c2farthest

array([22.66272926, 22.24136734, 22.13410568, 22.11614799, 22.2365303 ,
       22.34024041])

_, ax = plt.subplots()

ax.scatter(decimation_targets, c2farthest / max_edge_lengths, label="max")
ax.scatter(decimation_targets, c2farthest / median_edge_lengths, label="median")

ax.set_ylabel("Ratio")
ax.set_xlabel("Target reduction")

ax.legend(bbox_to_anchor=(1.02, 1), loc="upper left");

Further reading

• How much decimation is too much? A varifold perspective