范例十二:Spectral clustering for image segmentation
http://scikit-learn.org/stable/auto_examples/cluster/plot_segmentation_toy.html
此范例是利用Spectral clustering来区别重叠的圆圈，将重叠的圆圈分为个体。
- 建立一个100x100的影像包含四个不同半径的圆
- 透过
np.indices改变影像颜色複杂度 - 用
spectral_clustering区分出各个不同区域特徵
(一)引入函式库
引入函式库如下：
numpy:产生阵列数值matplotlib.pyplot:用来绘製影像sklearn.feature_extraction import image:将每个像素的梯度关系图像化sklearn.cluster import spectral_clustering:将影像正规化切割
import numpy as np
import matplotlib.pyplot as plt
from sklearn.feature_extraction import image
from sklearn.cluster import spectral_clustering
(二)建立要被区分的重叠圆圈影像
- 产生一个大小为输入值得矩阵(此范例为100x100)，其内部值为沿著座标方向递增(如:0,1,...)的值。
l = 100
x, y = np.indices((l, l))
- 建立四个圆圈的圆心座标并给定座标值
- 给定四个圆圈的半径长度
- 将圆心座标与半径结合产生四个圆圈图像
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
- 将上一段产生的四个圆圈影像合併为
img使其成为一体的物件 mask为布林形式的imgimg为浮点数形式的img- 用乱数产生的方法将整张影像作乱数处理
# 4 circles
img = circle1 + circle2 + circle3 + circle4
mask = img.astype(bool)
img = img.astype(float)
img += 1 + 0.2 * np.random.randn(*img.shape)
接著将产生好的影像化为可使用spectral_clustering的影像
image.img_to_graph用来处理边缘的权重与每个像速间的梯度关联有关- 用类似Voronoi Diagram演算法的概念来处理影像
graph = image.img_to_graph(img, mask=mask)
graph.data = np.exp(-graph.data / graph.data.std())
最后用spectral_clustering将连在一起的部分切开，而spectral_clustering中的各项参数设定如下:
graph: 必须是一个矩阵且大小为nxn的形式n_clusters=4: 需要提取出的群集数eigen_solver='arpack': 解特徵值的方式
开一张新影像label_im用来展示spectral_clustering切开后的分类结果
labels = spectral_clustering(graph, n_clusters=4, eigen_solver='arpack')
label_im = -np.ones(mask.shape)
label_im[mask] = labels
plt.matshow(img)
plt.matshow(label_im)
(三)完整程式码
Python source code:plot_segmentation_toy.py
http://scikit-learn.org/stable/_downloads/plot_segmentation_toy.py
print(__doc__)
# Authors: Emmanuelle Gouillart <[email protected]>
# Gael Varoquaux <[email protected]>
# 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
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.ones(mask.shape)
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.ones(mask.shape)
label_im[mask] = labels
plt.matshow(img)
plt.matshow(label_im)
plt.show()