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+
+
+.. _sphx_glr_auto_examples_plot_convolutional_barycenter.py:
+
+
+============================================
+Convolutional Wasserstein Barycenter example
+============================================
+
+This example is designed to illustrate how the Convolutional Wasserstein Barycenter
+function of POT works.
+
+
+
+.. code-block:: python
+
+
+    # Author: Nicolas Courty <ncourty@irisa.fr>
+    #
+    # License: MIT License
+
+
+    import numpy as np
+    import pylab as pl
+    import ot
+
+
+
+
+
+
+
+Data preparation
+----------------
+
+The four distributions are constructed from 4 simple images
+
+
+
+.. code-block:: python
+
+
+
+    f1 = 1 - pl.imread('../data/redcross.png')[:, :, 2]
+    f2 = 1 - pl.imread('../data/duck.png')[:, :, 2]
+    f3 = 1 - pl.imread('../data/heart.png')[:, :, 2]
+    f4 = 1 - pl.imread('../data/tooth.png')[:, :, 2]
+
+    A = []
+    f1 = f1 / np.sum(f1)
+    f2 = f2 / np.sum(f2)
+    f3 = f3 / np.sum(f3)
+    f4 = f4 / np.sum(f4)
+    A.append(f1)
+    A.append(f2)
+    A.append(f3)
+    A.append(f4)
+    A = np.array(A)
+
+    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))
+
+
+
+
+
+
+
+
+Barycenter computation and visualization
+----------------------------------------
+
+
+
+
+.. code-block:: python
+
+
+    pl.figure(figsize=(10, 10))
+    pl.title('Convolutional Wasserstein Barycenters in POT')
+    cm = 'Blues'
+    # regularization parameter
+    reg = 0.004
+    for i in range(nb_images):
+        for j in range(nb_images):
+            pl.subplot(nb_images, nb_images, i * nb_images + j + 1)
+            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:
+                pl.imshow(f1, cmap=cm)
+                pl.axis('off')
+            elif i == 0 and j == (nb_images - 1):
+                pl.imshow(f3, cmap=cm)
+                pl.axis('off')
+            elif i == (nb_images - 1) and j == 0:
+                pl.imshow(f2, cmap=cm)
+                pl.axis('off')
+            elif i == (nb_images - 1) and j == (nb_images - 1):
+                pl.imshow(f4, cmap=cm)
+                pl.axis('off')
+            else:
+                # call to barycenter computation
+                pl.imshow(ot.bregman.convolutional_barycenter2d(A, reg, weights), cmap=cm)
+                pl.axis('off')
+    pl.show()
+
+
+
+.. image:: /auto_examples/images/sphx_glr_plot_convolutional_barycenter_001.png
+    :align: center
+
+
+
+
+**Total running time of the script:** ( 1 minutes  11.608 seconds)
+
+
+
+.. only :: html
+
+ .. container:: sphx-glr-footer
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Python source code: plot_convolutional_barycenter.py <plot_convolutional_barycenter.py>`
+
+
+
+  .. container:: sphx-glr-download
+
+     :download:`Download Jupyter notebook: plot_convolutional_barycenter.ipynb <plot_convolutional_barycenter.ipynb>`
+
+
+.. only:: html
+
+ .. rst-class:: sphx-glr-signature
+
+    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_