光谱聚类在图像分割中的应用¶
在此示例中，生成了具有连通圆的图像，并使用光谱聚类方法将圆分离。
在这种情况下，光谱聚类方法解决了所谓的“‘normalized graph cuts’”问题：将图像看作是连通体素图，而光谱聚类算法则是选择图切分定义区域，同时最小化割集的梯度比率和区域体积。
当算法试图平衡体积(即平衡区域大小)时，如果采用不同大小的圆圈，则分割失败。
此外，由于图像的灰度或梯度中没有有用的信息，我们选择在只有弱梯度信息的图上进行光谱聚类。这接近于执行图的Voronoi分割。
此外，我们使用对象的掩码将图形限制在对象的轮廓上。在本例中，我们感兴趣的是将对象从一个对象和另一个对象中分离出来，而不是从背景中分离出来。
print(__doc__)
# Authors: Emmanuelle Gouillart <emmanuelle.gouillart@normalesup.org>
# Gael Varoquaux <gael.varoquaux@normalesup.org>
# License: BSD 3 clause
import numpy as np
import matplotlib.pyplot as plt
from sklearn.feature_extraction import image
from sklearn.cluster import spectral_clustering
l = 100
x, y = np.indices((l, l))
center1 = (28, 24)
center2 = (40, 50)
center3 = (67, 58)
center4 = (24, 70)
radius1, radius2, radius3, radius4 = 16, 14, 15, 14
circle1 = (x - center1[0]) ** 2 + (y - center1[1]) ** 2 < radius1 ** 2
circle2 = (x - center2[0]) ** 2 + (y - center2[1]) ** 2 < radius2 ** 2
circle3 = (x - center3[0]) ** 2 + (y - center3[1]) ** 2 < radius3 ** 2
circle4 = (x - center4[0]) ** 2 + (y - center4[1]) ** 2 < radius4 ** 2
# #############################################################################
# 4 circles
img = circle1 + circle2 + circle3 + circle4
# We use a mask that limits to the foreground: the problem that we are
# interested in here is not separating the objects from the background,
# but separating them one from the other.
mask = img.astype(bool)
img = img.astype(float)
img += 1 + 0.2 * np.random.randn(*img.shape)
# Convert the image into a graph with the value of the gradient on the
# edges.
graph = image.img_to_graph(img, mask=mask)
# Take a decreasing function of the gradient: we take it weakly
# dependent from the gradient the segmentation is close to a voronoi
graph.data = np.exp(-graph.data / graph.data.std())
# Force the solver to be arpack, since amg is numerically
# unstable on this example
labels = spectral_clustering(graph, n_clusters=4, eigen_solver='arpack')
label_im = np.full(mask.shape, -1.)
label_im[mask] = labels
plt.matshow(img)
plt.matshow(label_im)
# #############################################################################
# 2 circles
img = circle1 + circle2
mask = img.astype(bool)
img = img.astype(float)
img += 1 + 0.2 * np.random.randn(*img.shape)
graph = image.img_to_graph(img, mask=mask)
graph.data = np.exp(-graph.data / graph.data.std())
labels = spectral_clustering(graph, n_clusters=2, eigen_solver='arpack')
label_im = np.full(mask.shape, -1.)
label_im[mask] = labels
plt.matshow(img)
plt.matshow(label_im)
plt.show()
脚本的总运行时间：(0分0.721秒)
