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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>`_
|
