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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>`_