107 lines
3.9 KiB
Python
107 lines
3.9 KiB
Python
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"""
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================================================
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Segmenting the picture of greek coins in regions
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================================================
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This example uses :ref:`spectral_clustering` on a graph created from
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voxel-to-voxel difference on an image to break this image into multiple
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partly-homogeneous regions.
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This procedure (spectral clustering on an image) is an efficient
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approximate solution for finding normalized graph cuts.
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There are three options to assign labels:
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* 'kmeans' spectral clustering clusters samples in the embedding space
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using a kmeans algorithm
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* 'discrete' iteratively searches for the closest partition
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space to the embedding space of spectral clustering.
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* 'cluster_qr' assigns labels using the QR factorization with pivoting
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that directly determines the partition in the embedding space.
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"""
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# Author: Gael Varoquaux <gael.varoquaux@normalesup.org>
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# Brian Cheung
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# Andrew Knyazev <Andrew.Knyazev@ucdenver.edu>
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# License: BSD 3 clause
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import time
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import matplotlib.pyplot as plt
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import numpy as np
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from scipy.ndimage import gaussian_filter
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from skimage.data import coins
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from skimage.transform import rescale
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from sklearn.cluster import spectral_clustering
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from sklearn.feature_extraction import image
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# load the coins as a numpy array
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orig_coins = coins()
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# Resize it to 20% of the original size to speed up the processing
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# Applying a Gaussian filter for smoothing prior to down-scaling
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# reduces aliasing artifacts.
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smoothened_coins = gaussian_filter(orig_coins, sigma=2)
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rescaled_coins = rescale(smoothened_coins, 0.2, mode="reflect", anti_aliasing=False)
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# Convert the image into a graph with the value of the gradient on the
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# edges.
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graph = image.img_to_graph(rescaled_coins)
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# Take a decreasing function of the gradient: an exponential
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# The smaller beta is, the more independent the segmentation is of the
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# actual image. For beta=1, the segmentation is close to a voronoi
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beta = 10
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eps = 1e-6
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graph.data = np.exp(-beta * graph.data / graph.data.std()) + eps
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# The number of segmented regions to display needs to be chosen manually.
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# The current version of 'spectral_clustering' does not support determining
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# the number of good quality clusters automatically.
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n_regions = 26
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# %%
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# Compute and visualize the resulting regions
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# Computing a few extra eigenvectors may speed up the eigen_solver.
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# The spectral clustering quality may also benefit from requesting
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# extra regions for segmentation.
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n_regions_plus = 3
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# Apply spectral clustering using the default eigen_solver='arpack'.
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# Any implemented solver can be used: eigen_solver='arpack', 'lobpcg', or 'amg'.
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# Choosing eigen_solver='amg' requires an extra package called 'pyamg'.
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# The quality of segmentation and the speed of calculations is mostly determined
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# by the choice of the solver and the value of the tolerance 'eigen_tol'.
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# TODO: varying eigen_tol seems to have no effect for 'lobpcg' and 'amg' #21243.
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for assign_labels in ("kmeans", "discretize", "cluster_qr"):
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t0 = time.time()
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labels = spectral_clustering(
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graph,
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n_clusters=(n_regions + n_regions_plus),
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eigen_tol=1e-7,
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assign_labels=assign_labels,
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random_state=42,
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)
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t1 = time.time()
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labels = labels.reshape(rescaled_coins.shape)
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plt.figure(figsize=(5, 5))
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plt.imshow(rescaled_coins, cmap=plt.cm.gray)
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plt.xticks(())
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plt.yticks(())
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title = "Spectral clustering: %s, %.2fs" % (assign_labels, (t1 - t0))
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print(title)
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plt.title(title)
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for l in range(n_regions):
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colors = [plt.cm.nipy_spectral((l + 4) / float(n_regions + 4))]
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plt.contour(labels == l, colors=colors)
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# To view individual segments as appear comment in plt.pause(0.5)
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plt.show()
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# TODO: After #21194 is merged and #21243 is fixed, check which eigen_solver
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# is the best and set eigen_solver='arpack', 'lobpcg', or 'amg' and eigen_tol
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# explicitly in this example.
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