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‎dev/_downloads/07fcc19ba03226cd3d83d4e40ec44385/auto_examples_python.zip

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‎dev/_downloads/9cdba5635a180cdcca7d23b9cf18ffac/plot_segmentation_toy.py

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# Gael Varoquaux <gael.varoquaux@normalesup.org>
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# License: BSD 3 clause
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# %%
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# Generate the data
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# -----------------
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import numpy as np
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import matplotlib.pyplot as plt
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from sklearn.feature_extraction import image
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from sklearn.cluster import spectral_clustering
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l = 100
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x, y = np.indices((l, l))
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circle3 = (x - center3[0]) ** 2 + (y - center3[1]) ** 2 < radius3**2
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circle4 = (x - center4[0]) ** 2 + (y - center4[1]) ** 2 < radius4**2
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# #############################################################################
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# 4 circles
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# %%
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# Plotting four circles
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# ---------------------
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img = circle1 + circle2 + circle3 + circle4
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# We use a mask that limits to the foreground: the problem that we are
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img = img.astype(float)
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img += 1 + 0.2 * np.random.randn(*img.shape)
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# %%
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# Convert the image into a graph with the value of the gradient on the
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# edges.
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from sklearn.feature_extraction import image
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graph = image.img_to_graph(img, mask=mask)
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# Take a decreasing function of the gradient: we take it weakly
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# dependent from the gradient the segmentation is close to a voronoi
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# %%
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# Take a decreasing function of the gradient resulting in a segmentation
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# that is close to a Voronoi partition
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graph.data = np.exp(-graph.data / graph.data.std())
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# Force the solver to be arpack, since amg is numerically
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# unstable on this example
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# %%
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# Here we perform spectral clustering using the arpack solver since amg is
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# numerically unstable on this example. We then plot the results.
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from sklearn.cluster import spectral_clustering
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import matplotlib.pyplot as plt
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labels = spectral_clustering(graph, n_clusters=4, eigen_solver="arpack")
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label_im = np.full(mask.shape, -1.0)
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label_im[mask] = labels
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plt.matshow(img)
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plt.matshow(label_im)
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fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(10, 5))
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axs[0].matshow(img)
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axs[1].matshow(label_im)
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plt.show()
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# %%
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# Plotting two circles
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# --------------------
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# Here we repeat the above process but only consider the first two circles
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# we generated. Note that this results in a cleaner separation between the
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# circles as the region sizes are easier to balance in this case.
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# #############################################################################
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# 2 circles
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img = circle1 + circle2
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mask = img.astype(bool)
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img = img.astype(float)
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label_im = np.full(mask.shape, -1.0)
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label_im[mask] = labels
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plt.matshow(img)
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plt.matshow(label_im)
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fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(10, 5))
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axs[0].matshow(img)
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axs[1].matshow(label_im)
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plt.show()

‎dev/_downloads/e7311e6599ab6ff3129117a6d8c302ec/plot_segmentation_toy.ipynb

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},
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"outputs": [],
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"source": [
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"# Authors: Emmanuelle Gouillart <emmanuelle.gouillart@normalesup.org>\n# Gael Varoquaux <gael.varoquaux@normalesup.org>\n# License: BSD 3 clause\n\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nfrom sklearn.feature_extraction import image\nfrom sklearn.cluster import spectral_clustering\n\nl = 100\nx, y = np.indices((l, l))\n\ncenter1 = (28, 24)\ncenter2 = (40, 50)\ncenter3 = (67, 58)\ncenter4 = (24, 70)\n\nradius1, radius2, radius3, radius4 = 16, 14, 15, 14\n\ncircle1 = (x - center1[0]) ** 2 + (y - center1[1]) ** 2 < radius1**2\ncircle2 = (x - center2[0]) ** 2 + (y - center2[1]) ** 2 < radius2**2\ncircle3 = (x - center3[0]) ** 2 + (y - center3[1]) ** 2 < radius3**2\ncircle4 = (x - center4[0]) ** 2 + (y - center4[1]) ** 2 < radius4**2\n\n# #############################################################################\n# 4 circles\nimg = circle1 + circle2 + circle3 + circle4\n\n# We use a mask that limits to the foreground: the problem that we are\n# interested in here is not separating the objects from the background,\n# but separating them one from the other.\nmask = img.astype(bool)\n\nimg = img.astype(float)\nimg += 1 + 0.2 * np.random.randn(*img.shape)\n\n# Convert the image into a graph with the value of the gradient on the\n# edges.\ngraph = image.img_to_graph(img, mask=mask)\n\n# Take a decreasing function of the gradient: we take it weakly\n# dependent from the gradient the segmentation is close to a voronoi\ngraph.data = np.exp(-graph.data / graph.data.std())\n\n# Force the solver to be arpack, since amg is numerically\n# unstable on this example\nlabels = spectral_clustering(graph, n_clusters=4, eigen_solver=\"arpack\")\nlabel_im = np.full(mask.shape, -1.0)\nlabel_im[mask] = labels\n\nplt.matshow(img)\nplt.matshow(label_im)\n\n# #############################################################################\n# 2 circles\nimg = circle1 + circle2\nmask = img.astype(bool)\nimg = img.astype(float)\n\nimg += 1 + 0.2 * np.random.randn(*img.shape)\n\ngraph = image.img_to_graph(img, mask=mask)\ngraph.data = np.exp(-graph.data / graph.data.std())\n\nlabels = spectral_clustering(graph, n_clusters=2, eigen_solver=\"arpack\")\nlabel_im = np.full(mask.shape, -1.0)\nlabel_im[mask] = labels\n\nplt.matshow(img)\nplt.matshow(label_im)\n\nplt.show()"
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"# Authors: Emmanuelle Gouillart <emmanuelle.gouillart@normalesup.org>\n# Gael Varoquaux <gael.varoquaux@normalesup.org>\n# License: BSD 3 clause"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Generate the data\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import numpy as np\n\nl = 100\nx, y = np.indices((l, l))\n\ncenter1 = (28, 24)\ncenter2 = (40, 50)\ncenter3 = (67, 58)\ncenter4 = (24, 70)\n\nradius1, radius2, radius3, radius4 = 16, 14, 15, 14\n\ncircle1 = (x - center1[0]) ** 2 + (y - center1[1]) ** 2 < radius1**2\ncircle2 = (x - center2[0]) ** 2 + (y - center2[1]) ** 2 < radius2**2\ncircle3 = (x - center3[0]) ** 2 + (y - center3[1]) ** 2 < radius3**2\ncircle4 = (x - center4[0]) ** 2 + (y - center4[1]) ** 2 < radius4**2"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Plotting four circles\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"img = circle1 + circle2 + circle3 + circle4\n\n# We use a mask that limits to the foreground: the problem that we are\n# interested in here is not separating the objects from the background,\n# but separating them one from the other.\nmask = img.astype(bool)\n\nimg = img.astype(float)\nimg += 1 + 0.2 * np.random.randn(*img.shape)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Convert the image into a graph with the value of the gradient on the\nedges.\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"from sklearn.feature_extraction import image\n\ngraph = image.img_to_graph(img, mask=mask)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Take a decreasing function of the gradient resulting in a segmentation\nthat is close to a Voronoi partition\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"graph.data = np.exp(-graph.data / graph.data.std())"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Here we perform spectral clustering using the arpack solver since amg is\nnumerically unstable on this example. We then plot the results.\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"from sklearn.cluster import spectral_clustering\nimport matplotlib.pyplot as plt\n\nlabels = spectral_clustering(graph, n_clusters=4, eigen_solver=\"arpack\")\nlabel_im = np.full(mask.shape, -1.0)\nlabel_im[mask] = labels\n\nfig, axs = plt.subplots(nrows=1, ncols=2, figsize=(10, 5))\naxs[0].matshow(img)\naxs[1].matshow(label_im)\n\nplt.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Plotting two circles\nHere we repeat the above process but only consider the first two circles\nwe generated. Note that this results in a cleaner separation between the\ncircles as the region sizes are easier to balance in this case.\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"img = circle1 + circle2\nmask = img.astype(bool)\nimg = img.astype(float)\n\nimg += 1 + 0.2 * np.random.randn(*img.shape)\n\ngraph = image.img_to_graph(img, mask=mask)\ngraph.data = np.exp(-graph.data / graph.data.std())\n\nlabels = spectral_clustering(graph, n_clusters=2, eigen_solver=\"arpack\")\nlabel_im = np.full(mask.shape, -1.0)\nlabel_im[mask] = labels\n\nfig, axs = plt.subplots(nrows=1, ncols=2, figsize=(10, 5))\naxs[0].matshow(img)\naxs[1].matshow(label_im)\n\nplt.show()"
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]
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}
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],

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