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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.

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause

Generate data#

fromskimage.dataimport 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.

importnumpyasnp
fromscipy.ndimageimport gaussian_filter
fromskimage.transformimport 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.

fromsklearn.feature_extraction.imageimport grid_to_graph
connectivity = grid_to_graph(*rescaled_coins.shape)

Compute clustering#

importtimeastime
fromsklearn.clusterimport 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: 0.229s
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.

importmatplotlib.pyplotasplt
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 ()