# 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>
#
import os
from pathlib import Path

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

## Data preparation

The four distributions are constructed from 4 simple images

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

## Barycenter computation and visualization

```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()
```

Total running time of the script: ( 1 minutes 43.297 seconds)

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