範例十二: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。

  1. 建立一個100x100的影像包含四個不同半徑的圓
  2. 透過np.indices改變影像顏色複雜度
  3. 用spectral_clustering區分出各個不同區域特徵

(一)引入函式庫

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
  1. import numpy as np
  2. import matplotlib.pyplot as plt
  4. from sklearn.feature_extraction import image
  5. from sklearn.cluster import spectral_clustering

(二)建立要被區分的重疊圓圈影像

  • 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。
  1. l = 100
  2. x, 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
  1. center1 = (28, 24)
  2. center2 = (40, 50)
  3. center3 = (67, 58)
  4. center4 = (24, 70)
  6. radius1, radius2, radius3, radius4 = 16, 14, 15, 14
  8. circle1 = (x - center1[0]) ** 2 + (y - center1[1]) ** 2 < radius1 ** 2
  9. circle2 = (x - center2[0]) ** 2 + (y - center2[1]) ** 2 < radius2 ** 2
  10. circle3 = (x - center3[0]) ** 2 + (y - center3[1]) ** 2 < radius3 ** 2
  11. circle4 = (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img
  • img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
  1. # 4 circles
  2. img = circle1 + circle2 + circle3 + circle4
  3. mask = img.astype(bool)
  4. img = img.astype(float)
  6. 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
  1. graph = image.img_to_graph(img, mask=mask)
  3. 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

  1. labels = spectral_clustering(graph, n_clusters=4, eigen_solver='arpack')
  2. label_im = -np.ones(mask.shape)
  3. label_im[mask] = labels
  5. plt.matshow(img)
  6. plt.matshow(label_im)

EX 12:Spectral clustering for image segmentation - 图1
EX 12:Spectral clustering for image segmentation - 图2

(三)完整程式碼

Python source code:plot_segmentation_toy.py

http://scikit-learn.org/stable/_downloads/plot_segmentation_toy.py

  1. print(__doc__)
  3. # Authors:  Emmanuelle Gouillart <emmanuelle.gouillart@normalesup.org>
  4. #           Gael Varoquaux <gael.varoquaux@normalesup.org>
  5. # License: BSD 3 clause
  7. import numpy as np
  8. import matplotlib.pyplot as plt
  10. from sklearn.feature_extraction import image
  11. from sklearn.cluster import spectral_clustering
  13. ###############################################################################
  14. l = 100
  15. x, y = np.indices((l, l))
  17. center1 = (28, 24)
  18. center2 = (40, 50)
  19. center3 = (67, 58)
  20. center4 = (24, 70)
  22. radius1, radius2, radius3, radius4 = 16, 14, 15, 14
  24. circle1 = (x - center1[0]) ** 2 + (y - center1[1]) ** 2 < radius1 ** 2
  25. circle2 = (x - center2[0]) ** 2 + (y - center2[1]) ** 2 < radius2 ** 2
  26. circle3 = (x - center3[0]) ** 2 + (y - center3[1]) ** 2 < radius3 ** 2
  27. circle4 = (x - center4[0]) ** 2 + (y - center4[1]) ** 2 < radius4 ** 2
  29. ###############################################################################
  30. # 4 circles
  31. img = circle1 + circle2 + circle3 + circle4
  32. mask = img.astype(bool)
  33. img = img.astype(float)
  35. img += 1 + 0.2 * np.random.randn(*img.shape)
  37. # Convert the image into a graph with the value of the gradient on the
  38. # edges.
  39. graph = image.img_to_graph(img, mask=mask)
  41. # Take a decreasing function of the gradient: we take it weakly
  42. # dependent from the gradient the segmentation is close to a voronoi
  43. graph.data = np.exp(-graph.data / graph.data.std())
  45. # Force the solver to be arpack, since amg is numerically
  46. # unstable on this example
  47. labels = spectral_clustering(graph, n_clusters=4, eigen_solver='arpack')
  48. label_im = -np.ones(mask.shape)
  49. label_im[mask] = labels
  51. plt.matshow(img)
  52. plt.matshow(label_im)
  54. ###############################################################################
  55. # 2 circles
  56. img = circle1 + circle2
  57. mask = img.astype(bool)
  58. img = img.astype(float)
  60. img += 1 + 0.2 * np.random.randn(*img.shape)
  62. graph = image.img_to_graph(img, mask=mask)
  63. graph.data = np.exp(-graph.data / graph.data.std())
  65. labels = spectral_clustering(graph, n_clusters=2, eigen_solver='arpack')
  66. label_im = -np.ones(mask.shape)
  67. label_im[mask] = labels
  69. plt.matshow(img)
  70. plt.matshow(label_im)
  72. plt.show()