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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
============================
Linear OT mapping estimation
============================
"""
# 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()
##############################################################################
# Estimate linear mapping and transport
# -------------------------------------
# Gaussian (linear) Monge mapping estimation
Ae, be = ot.gaussian.empirical_bures_wasserstein_mapping(xs, xt)
xst = xs.dot(Ae) + be
# Gaussian (linear) GW mapping estimation
Agw, bgw = ot.gaussian.empirical_gaussian_gromov_wasserstein_mapping(xs, xt)
xstgw = xs.dot(Agw) + bgw
##############################################################################
# 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()
##############################################################################
# Load image data
# ---------------
def im2mat(img):
"""Converts and image to matrix (one pixel per line)"""
return img.reshape((img.shape[0] * img.shape[1], img.shape[2]))
def mat2im(X, shape):
"""Converts back a matrix to an image"""
return X.reshape(shape)
def minmax(img):
return np.clip(img, 0, 1)
# Loading images
this_file = os.path.realpath("__file__")
data_path = os.path.join(Path(this_file).parent.parent.parent, "data")
I1 = plt.imread(os.path.join(data_path, "ocean_day.jpg")).astype(np.float64) / 256
I2 = plt.imread(os.path.join(data_path, "ocean_sunset.jpg")).astype(np.float64) / 256
X1 = im2mat(I1)
X2 = im2mat(I2)
##############################################################################
# Estimate mapping and adapt
# ----------------------------
# Monge mapping
mapping = ot.da.LinearTransport()
mapping.fit(Xs=X1, Xt=X2)
xst = mapping.transform(Xs=X1)
xts = mapping.inverse_transform(Xt=X2)
I1t = minmax(mat2im(xst, I1.shape))
I2t = minmax(mat2im(xts, I2.shape))
# gaussian GW mapping
mapping = ot.da.LinearGWTransport()
mapping.fit(Xs=X1, Xt=X2)
xstgw = mapping.transform(Xs=X1)
xtsgw = mapping.inverse_transform(Xt=X2)
I1tgw = minmax(mat2im(xstgw, I1.shape))
I2tgw = minmax(mat2im(xtsgw, I2.shape))
# %%
##############################################################################
# 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")
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