.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/barycenters/plot_convolutional_barycenter.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_barycenters_plot_convolutional_barycenter.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_barycenters_plot_convolutional_barycenter.py:


============================================
Convolutional Wasserstein Barycenter example
============================================

This example is designed to illustrate how the Convolutional Wasserstein
Barycenter function of POT works.

.. GENERATED FROM PYTHON SOURCE LINES 12-23

.. code-block:: Python


    # Author: Nicolas Courty <ncourty@irisa.fr>
    #
    # License: MIT License
    import os
    from pathlib import Path

    import numpy as np
    import matplotlib.pyplot as plt
    import ot








.. GENERATED FROM PYTHON SOURCE LINES 24-28

Data preparation
----------------

The four distributions are constructed from 4 simple images

.. GENERATED FROM PYTHON SOURCE LINES 28-53

.. code-block:: Python


    this_file = os.path.realpath('__file__')
    data_path = os.path.join(Path(this_file).parent.parent.parent, 'data')

    f1 = 1 - plt.imread(os.path.join(data_path, 'redcross.png'))[::2, ::2, 2]
    f2 = 1 - plt.imread(os.path.join(data_path, 'tooth.png'))[::2, ::2, 2]
    f3 = 1 - plt.imread(os.path.join(data_path, 'heart.png'))[::2, ::2, 2]
    f4 = 1 - plt.imread(os.path.join(data_path, 'duck.png'))[::2, ::2, 2]

    f1 = f1 / np.sum(f1)
    f2 = f2 / np.sum(f2)
    f3 = f3 / np.sum(f3)
    f4 = f4 / np.sum(f4)
    A = np.array([f1, f2, f3, f4])

    nb_images = 5

    # those are the four corners coordinates that will be interpolated by bilinear
    # interpolation
    v1 = np.array((1, 0, 0, 0))
    v2 = np.array((0, 1, 0, 0))
    v3 = np.array((0, 0, 1, 0))
    v4 = np.array((0, 0, 0, 1))









.. GENERATED FROM PYTHON SOURCE LINES 54-57

Barycenter computation and visualization
----------------------------------------


.. GENERATED FROM PYTHON SOURCE LINES 57-90

.. code-block:: Python


    fig, axes = plt.subplots(nb_images, nb_images, figsize=(7, 7))
    plt.suptitle('Convolutional Wasserstein Barycenters in POT')
    cm = 'Blues'
    # regularization parameter
    reg = 0.004
    for i in range(nb_images):
        for j in range(nb_images):
            tx = float(i) / (nb_images - 1)
            ty = float(j) / (nb_images - 1)

            # weights are constructed by bilinear interpolation
            tmp1 = (1 - tx) * v1 + tx * v2
            tmp2 = (1 - tx) * v3 + tx * v4
            weights = (1 - ty) * tmp1 + ty * tmp2

            if i == 0 and j == 0:
                axes[i, j].imshow(f1, cmap=cm)
            elif i == 0 and j == (nb_images - 1):
                axes[i, j].imshow(f3, cmap=cm)
            elif i == (nb_images - 1) and j == 0:
                axes[i, j].imshow(f2, cmap=cm)
            elif i == (nb_images - 1) and j == (nb_images - 1):
                axes[i, j].imshow(f4, cmap=cm)
            else:
                # call to barycenter computation
                axes[i, j].imshow(
                    ot.bregman.convolutional_barycenter2d(A, reg, weights),
                    cmap=cm
                )
            axes[i, j].axis('off')
    plt.tight_layout()
    plt.show()



.. image-sg:: /auto_examples/barycenters/images/sphx_glr_plot_convolutional_barycenter_001.png
   :alt: Convolutional Wasserstein Barycenters in POT
   :srcset: /auto_examples/barycenters/images/sphx_glr_plot_convolutional_barycenter_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 19.632 seconds)


.. _sphx_glr_download_auto_examples_barycenters_plot_convolutional_barycenter.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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