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+
+#%%
+# -*- coding: utf-8 -*-
+"""
+============================================
+Convolutional Wasserstein Barycenter example
+============================================
+
+This example is designed to illustrate how the Convolutional Wasserstein Barycenter
+function of POT works.
+"""
+
+# 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
+
+
+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
+# ----------------------------------------
+#
+
+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()