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 three options to assign labels:
‘kmeans’ spectral clustering clusters samples in the embedding space using a kmeans algorithm
‘discrete’ iteratively searches for the closest partition space to the embedding space of spectral clustering.
‘cluster_qr’ assigns labels using the QR factorization with pivoting that directly determines the partition in the embedding space.
# Author: Gael Varoquaux <email@example.com> # Brian Cheung # Andrew Knyazev <Andrew.Knyazev@ucdenver.edu> # License: BSD 3 clause import time import numpy as np from scipy.ndimage import gaussian_filter import matplotlib.pyplot as plt from skimage.data import coins from skimage.transform import rescale from sklearn.feature_extraction import image from sklearn.cluster import spectral_clustering # 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", anti_aliasing=False) # 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 # The number of segmented regions to display needs to be chosen manually. # The current version of 'spectral_clustering' does not support determining # the number of good quality clusters automatically. n_regions = 26
Compute and visualize the resulting regions
# Computing a few extra eigenvectors may speed up the eigen_solver. # The spectral clustering quality may also benetif from requesting # extra regions for segmentation. n_regions_plus = 3 # Apply spectral clustering using the default eigen_solver='arpack'. # Any implemented solver can be used: eigen_solver='arpack', 'lobpcg', or 'amg'. # Choosing eigen_solver='amg' requires an extra package called 'pyamg'. # The quality of segmentation and the speed of calculations is mostly determined # by the choice of the solver and the value of the tolerance 'eigen_tol'. # TODO: varying eigen_tol seems to have no effect for 'lobpcg' and 'amg' #21243. for assign_labels in ("kmeans", "discretize", "cluster_qr"): t0 = time.time() labels = spectral_clustering( graph, n_clusters=(n_regions + n_regions_plus), eigen_tol=1e-7, 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) plt.xticks(()) plt.yticks(()) title = "Spectral clustering: %s, %.2fs" % (assign_labels, (t1 - t0)) print(title) plt.title(title) for l in range(n_regions): colors = [plt.cm.nipy_spectral((l + 4) / float(n_regions + 4))] plt.contour(labels == l, colors=colors) # To view individual segments as appear comment in plt.pause(0.5) plt.show() # TODO: After #21194 is merged and #21243 is fixed, check which eigen_solver # is the best and set eigen_solver='arpack', 'lobpcg', or 'amg' and eigen_tol # explicitly in this example.
Spectral clustering: kmeans, 1.57s Spectral clustering: discretize, 1.46s Spectral clustering: cluster_qr, 1.50s
Total running time of the script: ( 0 minutes 5.233 seconds)