.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/cluster/plot_segmentation_toy.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_cluster_plot_segmentation_toy.py>`
        to download the full example code. or to run this example in your browser via Binder

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_cluster_plot_segmentation_toy.py:


===========================================
用于图像分割的谱聚类
===========================================

在这个示例中，生成了一幅包含相连圆形的图像，并使用谱聚类将这些圆形分开。

在这些设置中，:ref:`spectral_clustering` 方法解决了所谓的“归一化图割”问题：图像被视为一个由相连体素组成的图，而谱聚类算法相当于选择定义区域的图割，同时最小化沿割线的梯度与区域体积的比率。

由于算法试图平衡体积（即平衡区域大小），如果我们使用不同大小的圆形，分割将会失败。

此外，由于图像的强度或其梯度中没有有用的信息，我们选择在一个仅由梯度弱信息化的图上执行谱聚类。这接近于对图执行 Voronoi 分区。

另外，我们使用对象的掩码来将图限制在对象的轮廓上。在这个示例中，我们感兴趣的是将对象彼此分开，而不是将它们与背景分开。

.. GENERATED FROM PYTHON SOURCE LINES 17-21

.. code-block:: Python


    # 作者：scikit-learn 开发者
    # SPDX-License-Identifier：BSD-3-Clause








.. GENERATED FROM PYTHON SOURCE LINES 22-24

生成数据
---------

.. GENERATED FROM PYTHON SOURCE LINES 24-42

.. code-block:: Python


    import numpy as np

    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








.. GENERATED FROM PYTHON SOURCE LINES 43-45

绘制四个圆
---------------------

.. GENERATED FROM PYTHON SOURCE LINES 45-54

.. code-block:: Python


    img = circle1 + circle2 + circle3 + circle4

    # 我们使用一个限制在前景的掩码：我们在这里感兴趣的问题不是将物体从背景中分离出来，而是将它们彼此分离。
    mask = img.astype(bool)

    img = img.astype(float)
    img += 1 + 0.2 * np.random.randn(*img.shape)








.. GENERATED FROM PYTHON SOURCE LINES 55-56

将图像转换为图，其中边的值为梯度值。

.. GENERATED FROM PYTHON SOURCE LINES 56-61

.. code-block:: Python


    from sklearn.feature_extraction import image

    graph = image.img_to_graph(img, mask=mask)








.. GENERATED FROM PYTHON SOURCE LINES 62-63

取梯度的递减函数，得到接近于Voronoi分割的分割结果

.. GENERATED FROM PYTHON SOURCE LINES 63-66

.. code-block:: Python


    graph.data = np.exp(-graph.data / graph.data.std())








.. GENERATED FROM PYTHON SOURCE LINES 67-68

在这里，我们使用 arpack 求解器执行谱聚类，因为在这个例子中 amg 在数值上不稳定。然后我们绘制结果。

.. GENERATED FROM PYTHON SOURCE LINES 68-83

.. code-block:: Python


    import matplotlib.pyplot as plt

    from sklearn.cluster import spectral_clustering

    labels = spectral_clustering(graph, n_clusters=4, eigen_solver="arpack")
    label_im = np.full(mask.shape, -1.0)
    label_im[mask] = labels

    fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(10, 5))
    axs[0].matshow(img)
    axs[1].matshow(label_im)

    plt.show()




.. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_segmentation_toy_001.png
   :alt: plot segmentation toy
   :srcset: /auto_examples/cluster/images/sphx_glr_plot_segmentation_toy_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 84-87

绘制两个圆
--------------------
在这里我们重复上述过程，但只考虑我们生成的前两个圆。请注意，这样会导致圆之间的分离更加清晰，因为在这种情况下区域大小更容易平衡。

.. GENERATED FROM PYTHON SOURCE LINES 87-106

.. code-block:: Python


    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, -1.0)
    label_im[mask] = labels

    fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(10, 5))
    axs[0].matshow(img)
    axs[1].matshow(label_im)

    plt.show()



.. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_segmentation_toy_002.png
   :alt: plot segmentation toy
   :srcset: /auto_examples/cluster/images/sphx_glr_plot_segmentation_toy_002.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.395 seconds)


.. _sphx_glr_download_auto_examples_cluster_plot_segmentation_toy.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/cluster/plot_segmentation_toy.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_segmentation_toy.ipynb <plot_segmentation_toy.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_segmentation_toy.py <plot_segmentation_toy.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_segmentation_toy.zip <plot_segmentation_toy.zip>`


.. include:: plot_segmentation_toy.recommendations


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_