A demo of structured Ward hierarchical clustering on an image of coins#

Compute the segmentation of a 2D image with Ward hierarchical clustering. The clustering is spatially constrained in order for each segmented region to be in one piece.

# Author : Vincent Michel, 2010
#          Alexandre Gramfort, 2011
# License: BSD 3 clause

Generate data#

from skimage.data import coins

orig_coins = coins()

Resize it to 20% of the original size to speed up the processing Applying a Gaussian filter for smoothing prior to down-scaling reduces aliasing artifacts.

import numpy as np
from scipy.ndimage import gaussian_filter
from skimage.transform import rescale

smoothened_coins = gaussian_filter(orig_coins, sigma=2)
rescaled_coins = rescale(
    smoothened_coins,
    0.2,
    mode="reflect",
    anti_aliasing=False,
)

X = np.reshape(rescaled_coins, (-1, 1))

Define structure of the data#

Pixels are connected to their neighbors.

from sklearn.feature_extraction.image import grid_to_graph

connectivity = grid_to_graph(*rescaled_coins.shape)

Compute clustering#

import time as time

from sklearn.cluster import AgglomerativeClustering

print("Compute structured hierarchical clustering...")
st = time.time()
n_clusters = 27  # number of regions
ward = AgglomerativeClustering(
    n_clusters=n_clusters, linkage="ward", connectivity=connectivity
)
ward.fit(X)
label = np.reshape(ward.labels_, rescaled_coins.shape)
print(f"Elapsed time: {time.time() - st:.3f}s")
print(f"Number of pixels: {label.size}")
print(f"Number of clusters: {np.unique(label).size}")
Compute structured hierarchical clustering...
Elapsed time: 0.177s
Number of pixels: 4697
Number of clusters: 27

Plot the results on an image#

Agglomerative clustering is able to segment each coin however, we have had to use a n_cluster larger than the number of coins because the segmentation is finding a large in the background.

import matplotlib.pyplot as plt

plt.figure(figsize=(5, 5))
plt.imshow(rescaled_coins, cmap=plt.cm.gray)
for l in range(n_clusters):
    plt.contour(
        label == l,
        colors=[
            plt.cm.nipy_spectral(l / float(n_clusters)),
        ],
    )
plt.axis("off")
plt.show()
plot coin ward segmentation

Total running time of the script: (0 minutes 0.373 seconds)

Related examples

Hierarchical clustering: structured vs unstructured ward

Hierarchical clustering: structured vs unstructured ward

Comparing different hierarchical linkage methods on toy datasets

Comparing different hierarchical linkage methods on toy datasets

Feature agglomeration vs. univariate selection

Feature agglomeration vs. univariate selection

Agglomerative clustering with different metrics

Agglomerative clustering with different metrics

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