EX 12: Spectral clustering for image segmentation
http://scikit-learn.org/stable/auto_examples/cluster/plot_segmentation_toy.html
此範例是利用Spectral clustering來區別重疊的圓圈，將重疊的圓圈分為個體。
建立一個100x100的影像包含四個不同半徑的圓
透過
np.indices改變影像顏色複雜度用
spectral_clustering區分出各個不同區域特徵
引入函式庫如下： 1. numpy:產生陣列數值 2. matplotlib.pyplot:用來繪製影像 3. sklearn.feature_extraction import image:將每個像素的梯度關係圖像化 4. sklearn.cluster import spectral_clustering:將影像正規化切割
import numpy as npimport matplotlib.pyplot as pltfrom sklearn.feature_extraction import imagefrom sklearn.cluster import spectral_clustering
產生一個大小為輸入值得矩陣(此範例為100x100)，其內部值為沿著座標方向遞增(如:0,1,...)的值。
l = 100x, y = np.indices((l, l))
建立四個圓圈的圓心座標並給定座標值
給定四個圓圈的半徑長度
將圓心座標與半徑結合產生四個圓圈圖像
center1 = (28, 24)center2 = (40, 50)center3 = (67, 58)center4 = (24, 70)radius1, radius2, radius3, radius4 = 16, 14, 15, 14circle1 = (x - center1[0]) ** 2 + (y - center1[1]) ** 2 < radius1 ** 2circle2 = (x - center2[0]) ** 2 + (y - center2[1]) ** 2 < radius2 ** 2circle3 = (x - center3[0]) ** 2 + (y - center3[1]) ** 2 < radius3 ** 2circle4 = (x - center4[0]) ** 2 + (y - center4[1]) ** 2 < radius4 ** 2
將上一段產生的四個圓圈影像合併為
img使其成為一體的物件mask為布林形式的imgimg為浮點數形式的img用亂數產生的方法將整張影像作亂數處理
# 4 circlesimg = circle1 + circle2 + circle3 + circle4mask = img.astype(bool)img = img.astype(float)img += 1 + 0.2 * np.random.randn(*img.shape)
接著將產生好的影像化為可使用spectral_clustering的影像
image.img_to_graph用來處理邊緣的權重與每個像速間的梯度關聯有關用類似Voronoi Diagram演算法的概念來處理影像
graph = image.img_to_graph(img, mask=mask)graph.data = np.exp(-graph.data / graph.data.std())
最後用spectral_clustering將連在一起的部分切開，而spectral_clustering中的各項參數設定如下:
graph: 必須是一個矩陣且大小為nxn的形式n_clusters=4: 需要提取出的群集數eigen_solver='arpack': 解特徵值的方式
開一張新影像label_im用來展示spectral_clustering切開後的分類結果
labels = spectral_clustering(graph, n_clusters=4, eigen_solver='arpack')label_im = -np.ones(mask.shape)label_im[mask] = labelsplt.matshow(img)plt.matshow(label_im)
Python source code:plot_segmentation_toy.py
http://scikit-learn.org/stable/_downloads/plot_segmentation_toy.py
print(__doc__)# Authors: Emmanuelle Gouillart <emmanuelle.gouillart@normalesup.org># Gael Varoquaux <gael.varoquaux@normalesup.org># License: BSD 3 clauseimport numpy as npimport matplotlib.pyplot as pltfrom sklearn.feature_extraction import imagefrom sklearn.cluster import spectral_clustering###############################################################################l = 100x, y = np.indices((l, l))center1 = (28, 24)center2 = (40, 50)center3 = (67, 58)center4 = (24, 70)radius1, radius2, radius3, radius4 = 16, 14, 15, 14circle1 = (x - center1[0]) ** 2 + (y - center1[1]) ** 2 < radius1 ** 2circle2 = (x - center2[0]) ** 2 + (y - center2[1]) ** 2 < radius2 ** 2circle3 = (x - center3[0]) ** 2 + (y - center3[1]) ** 2 < radius3 ** 2circle4 = (x - center4[0]) ** 2 + (y - center4[1]) ** 2 < radius4 ** 2################################################################################ 4 circlesimg = circle1 + circle2 + circle3 + circle4mask = 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 voronoigraph.data = np.exp(-graph.data / graph.data.std())# Force the solver to be arpack, since amg is numerically# unstable on this examplelabels = spectral_clustering(graph, n_clusters=4, eigen_solver='arpack')label_im = -np.ones(mask.shape)label_im[mask] = labelsplt.matshow(img)plt.matshow(label_im)################################################################################ 2 circlesimg = circle1 + circle2mask = 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] = labelsplt.matshow(img)plt.matshow(label_im)plt.show()