Segmenting the picture of greek coins in regions
This example uses Spectral clustering on a graph created from voxel-to-voxel difference on an image to break this image into multiple partly-homogeneous regions.
This procedure (spectral clustering on an image) is an efficient approximate solution for finding normalized graph cuts.
There are two options to assign labels:
- with ‘kmeans’ spectral clustering will cluster samples in the embedding space using a kmeans algorithm
- whereas ‘discrete’ will iteratively search for the closest partition space to the embedding space.
print(__doc__) # Author: Gael Varoquaux <gael.varoquaux@normalesup.org>, Brian Cheung # License: BSD 3 clause import time import numpy as np from scipy.ndimage.filters import gaussian_filter import matplotlib.pyplot as plt import skimage from skimage.data import coins from skimage.transform import rescale from sklearn.feature_extraction import image from sklearn.cluster import spectral_clustering from sklearn.utils.fixes import parse_version # these were introduced in skimage-0.14 if parse_version(skimage.__version__) >= parse_version('0.14'): rescale_params = {'anti_aliasing': False, 'multichannel': False} else: rescale_params = {} # load the coins as a numpy array 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. smoothened_coins = gaussian_filter(orig_coins, sigma=2) rescaled_coins = rescale(smoothened_coins, 0.2, mode="reflect", **rescale_params) # Convert the image into a graph with the value of the gradient on the # edges. graph = image.img_to_graph(rescaled_coins) # Take a decreasing function of the gradient: an exponential # The smaller beta is, the more independent the segmentation is of the # actual image. For beta=1, the segmentation is close to a voronoi beta = 10 eps = 1e-6 graph.data = np.exp(-beta * graph.data / graph.data.std()) + eps # Apply spectral clustering (this step goes much faster if you have pyamg # installed) N_REGIONS = 25
Visualize the resulting regions
for assign_labels in ('kmeans', 'discretize'): t0 = time.time() labels = spectral_clustering(graph, n_clusters=N_REGIONS, assign_labels=assign_labels, random_state=42) t1 = time.time() labels = labels.reshape(rescaled_coins.shape) plt.figure(figsize=(5, 5)) plt.imshow(rescaled_coins, cmap=plt.cm.gray) for l in range(N_REGIONS): plt.contour(labels == l, colors=[plt.cm.nipy_spectral(l / float(N_REGIONS))]) plt.xticks(()) plt.yticks(()) title = 'Spectral clustering: %s, %.2fs' % (assign_labels, (t1 - t0)) print(title) plt.title(title) plt.show()
Out:
Spectral clustering: kmeans, 3.52s Spectral clustering: discretize, 3.17s
Total running time of the script: ( 0 minutes 7.599 seconds)
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https://scikit-learn.org/0.24/auto_examples/cluster/plot_coin_segmentation.html