.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/segmentation/plot_hausdorff_distance.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_segmentation_plot_hausdorff_distance.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_segmentation_plot_hausdorff_distance.py:


==================
Hausdorff Distance
==================

This example shows how to calculate the Hausdorff distance between two sets of
points. The `Hausdorff distance
<https://en.wikipedia.org/wiki/Hausdorff_distance>`__ is the maximum distance
between any point on the first set and its nearest point on the second set,
and vice-versa.

.. GENERATED FROM PYTHON SOURCE LINES 13-91



.. image-sg:: /auto_examples/segmentation/images/sphx_glr_plot_hausdorff_distance_001.png
   :alt: plot hausdorff distance
   :srcset: /auto_examples/segmentation/images/sphx_glr_plot_hausdorff_distance_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from skimage import metrics

    shape = (60, 60)
    image = np.zeros(shape)

    # Create a diamond-like shape where the four corners form the 1st set of points
    x_diamond = 30
    y_diamond = 30
    r = 10

    fig, ax = plt.subplots()
    plt_x = [0, 1, 0, -1]
    plt_y = [1, 0, -1, 0]

    set_ax = [(x_diamond + r * x) for x in plt_x]
    set_ay = [(y_diamond + r * y) for y in plt_y]
    plt.plot(set_ax, set_ay, 'or')

    # Create a kite-like shape where the four corners form the 2nd set of points
    x_kite = 30
    y_kite = 30
    x_r = 15
    y_r = 20

    set_bx = [(x_kite + x_r * x) for x in plt_x]
    set_by = [(y_kite + y_r * y) for y in plt_y]
    plt.plot(set_bx, set_by, 'og')

    # Set up the data to compute the Hausdorff distance
    coords_a = np.zeros(shape, dtype=bool)
    coords_b = np.zeros(shape, dtype=bool)
    for x, y in zip(set_ax, set_ay):
        coords_a[(x, y)] = True

    for x, y in zip(set_bx, set_by):
        coords_b[(x, y)] = True

    # Call the Hausdorff function on the coordinates
    metrics.hausdorff_distance(coords_a, coords_b)
    hausdorff_point_a, hausdorff_point_b = metrics.hausdorff_pair(coords_a, coords_b)

    # Plot the lines that shows the length of the Hausdorff distance
    x_line = [30, 30]
    y_line = [20, 10]
    plt.plot(x_line, y_line, 'y')

    x_line = [30, 30]
    y_line = [40, 50]
    plt.plot(x_line, y_line, 'y')

    # Plot circles to show that at this distance, the Hausdorff distance can
    # travel to its nearest neighbor (in this case, from the kite to diamond)
    ax.add_artist(plt.Circle((30, 10), 10, color='y', fill=None))
    ax.add_artist(plt.Circle((30, 50), 10, color='y', fill=None))
    ax.add_artist(plt.Circle((15, 30), 10, color='y', fill=None))
    ax.add_artist(plt.Circle((45, 30), 10, color='y', fill=None))

    # Annotate the returned pair of points that are Hausdorff distance apart
    ax.annotate(
        'a',
        xy=hausdorff_point_a,
        xytext=(35, 15),
        arrowprops=dict(facecolor='red', shrink=0.005),
    )
    ax.annotate(
        'b',
        xy=hausdorff_point_b,
        xytext=(35, 5),
        arrowprops=dict(facecolor='green', shrink=0.005),
    )

    ax.imshow(image, cmap=plt.cm.gray)
    ax.axis((0, 60, 60, 0))
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.138 seconds)


.. _sphx_glr_download_auto_examples_segmentation_plot_hausdorff_distance.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-image/scikit-image/v0.23.2?filepath=notebooks/auto_examples/segmentation/plot_hausdorff_distance.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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


.. only:: html

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

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