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Note

Example updated in release: 0.9.1.

# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License

# sphinx_gallery_thumbnail_number = 2

import os
from pathlib import Path

import numpy as np
from matplotlib import pyplot as plt
import ot

Generate data

n = 1000
d = 2
sigma = 0.1

rng = np.random.RandomState(42)

# source samples
angles = rng.rand(n, 1) * 2 * np.pi
xs = np.concatenate((np.sin(angles), np.cos(angles)), axis=1) + sigma * rng.randn(n, 2)
xs[: n // 2, 1] += 2


# target samples
anglet = rng.rand(n, 1) * 2 * np.pi
xt = np.concatenate((np.sin(anglet), np.cos(anglet)), axis=1) + sigma * rng.randn(n, 2)
xt[: n // 2, 1] += 2


A = np.array([[1.5, 0.7], [0.7, 1.5]])
b = np.array([[4, 2]])
xt = xt.dot(A) + b

Plot data

plt.figure(1, (5, 5))
plt.plot(xs[:, 0], xs[:, 1], "+")
plt.plot(xt[:, 0], xt[:, 1], "o")
plt.legend(("Source", "Target"))
plt.title("Source and target distributions")
plt.show()
Source and target distributions

Estimate linear mapping and transport

Plot transported samples

plt.figure(2, (10, 5))
plt.clf()
plt.subplot(1, 2, 1)
plt.plot(xs[:, 0], xs[:, 1], "+")
plt.plot(xt[:, 0], xt[:, 1], "o")
plt.plot(xst[:, 0], xst[:, 1], "+")
plt.legend(("Source", "Target", "Transp. Monge"), loc=0)
plt.title("Transported samples with Monge")
plt.subplot(1, 2, 2)
plt.plot(xs[:, 0], xs[:, 1], "+")
plt.plot(xt[:, 0], xt[:, 1], "o")
plt.plot(xstgw[:, 0], xstgw[:, 1], "+")
plt.legend(("Source", "Target", "Transp. GW"), loc=0)
plt.title("Transported samples with Gaussian GW")
plt.show()
Transported samples with Monge, Transported samples with Gaussian GW

Load image data

Estimate mapping and adapt

Plot transformed images

plt.figure(3, figsize=(14, 7))

plt.subplot(2, 3, 1)
plt.imshow(I1)
plt.axis("off")
plt.title("Im. 1")

plt.subplot(2, 3, 4)
plt.imshow(I2)
plt.axis("off")
plt.title("Im. 2")

plt.subplot(2, 3, 2)
plt.imshow(I1t)
plt.axis("off")
plt.title("Monge mapping Im. 1")

plt.subplot(2, 3, 5)
plt.imshow(I2t)
plt.axis("off")
plt.title("Inverse Monge mapping Im. 2")

plt.subplot(2, 3, 3)
plt.imshow(I1tgw)
plt.axis("off")
plt.title("Gaussian GW mapping Im. 1")

plt.subplot(2, 3, 6)
plt.imshow(I2tgw)
plt.axis("off")
plt.title("Inverse Gaussian GW mapping Im. 2")
Im. 1, Im. 2, Monge mapping Im. 1, Inverse Monge mapping Im. 2, Gaussian GW mapping Im. 1, Inverse Gaussian GW mapping Im. 2
Text(0.5, 1.0, 'Inverse Gaussian GW mapping Im. 2')

Total running time of the script: (0 minutes 2.175 seconds)

Gallery generated by Sphinx-Gallery