Moving window KDE

This example shows how to use the moving window KDE to resample the control points of the tow.

Load example dataset

import numpy as np
import polytex as ptx
import matplotlib.pyplot as plt

# Input: parameters
resolution = 0.022  # 0.022 mm
# number of extrema (control points) for contour description
extremaNum, windows, nuggets = 10, 2, [1e-3]

# Load the example dataset
path = ptx.example("sorted coordinate")
coordinatesSorted = ptx.pk_load(path)

Visualize the dataset (a tow contour)

The tow contour is described by a set of control points. The control points can be labeled by its z coordinate (the scanning slices) since the dataset is obtained from Micro CT scanning. The control points are sorted by its z coordinate.

fig = plt.figure()
ax = fig.add_subplot(projection='3d')

x = coordinatesSorted["X"].to_numpy()
y = coordinatesSorted["Y"].to_numpy()
z = coordinatesSorted["Z"].to_numpy()
ax.scatter(x, y, z, s=1, marker="o", c=z)

ax.set_xlabel("X")
ax.set_ylabel("Y")
ax.set_zlabel("Z")
ax.set_title("Control points of a fiber tow")
ax.set_aspect("equal")
plt.show()

Slice number of the tow

slices = np.array(coordinatesSorted["Z"] / resolution, dtype=int)
nslices = np.unique(slices).size  # number of slices

Dataset preparation for moving window kernel density estimation

t_norm = np.vstack((coordinatesSorted["normalized distance"], slices)).T

# bw = np.arange(0.01, 0.03, 0.01)  # specify a range for bandwidth optimization
# initialize the bandwidth according to Scott's rule
bw = 0.01

kdeOutput, cluster_centers = ptx.stats.movingKDE(t_norm, bw, windows, extremaNum)

kdeOutput.plot(x="normalized distance", y="probability density")
plt.show()