OT for domain adaptation with image color adaptation [6] with mapping estimation [8].
[6] Ferradans, S., Papadakis, N., Peyre, G., & Aujol, J. F. (2014). Regularized discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882.
[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, “Mapping estimation for discrete optimal transport”, Neural Information Processing Systems (NIPS), 2016.
# Authors: Remi Flamary <remi.flamary@unice.fr>
# Stanislas Chambon <stan.chambon@gmail.com>
#
# License: MIT License
# sphinx_gallery_thumbnail_number = 3
import os
from pathlib import Path
import numpy as np
from matplotlib import pyplot as plt
import ot
rng = np.random.RandomState(42)
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)
Generate data Domain adaptation for pixel distribution transfer
# EMDTransport
ot_emd = ot.da.EMDTransport()
ot_emd.fit(Xs=Xs, Xt=Xt)
transp_Xs_emd = ot_emd.transform(Xs=X1)
Image_emd = minmax(mat2im(transp_Xs_emd, I1.shape))
# SinkhornTransport
ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)
ot_sinkhorn.fit(Xs=Xs, Xt=Xt)
transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=X1)
Image_sinkhorn = minmax(mat2im(transp_Xs_sinkhorn, I1.shape))
ot_mapping_linear = ot.da.MappingTransport(
mu=1e0, eta=1e-8, bias=True, max_iter=20, verbose=True
)
ot_mapping_linear.fit(Xs=Xs, Xt=Xt)
X1tl = ot_mapping_linear.transform(Xs=X1)
Image_mapping_linear = minmax(mat2im(X1tl, I1.shape))
ot_mapping_gaussian = ot.da.MappingTransport(
mu=1e0, eta=1e-2, sigma=1, bias=False, max_iter=10, verbose=True
)
ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt)
X1tn = ot_mapping_gaussian.transform(Xs=X1) # use the estimated mapping
Image_mapping_gaussian = minmax(mat2im(X1tn, I1.shape))
It. |Loss |Delta loss
--------------------------------
0|1.797245e+02|0.000000e+00
1|1.758014e+02|-2.182822e-02
2|1.757026e+02|-5.620752e-04
3|1.756521e+02|-2.875691e-04
4|1.756218e+02|-1.725224e-04
5|1.756015e+02|-1.153553e-04
6|1.755868e+02|-8.348118e-05
7|1.755759e+02|-6.234582e-05
8|1.755673e+02|-4.893582e-05
9|1.755604e+02|-3.942771e-05
10|1.755547e+02|-3.206000e-05
11|1.755500e+02|-2.695056e-05
12|1.755460e+02|-2.307154e-05
13|1.755426e+02|-1.944208e-05
14|1.755395e+02|-1.715960e-05
15|1.755369e+02|-1.515613e-05
16|1.755345e+02|-1.367864e-05
17|1.755324e+02|-1.197885e-05
18|1.755305e+02|-1.071067e-05
19|1.755303e+02|-9.898122e-07
It. |Loss |Delta loss
--------------------------------
0|1.842001e+02|0.000000e+00
1|1.780145e+02|-3.358084e-02
2|1.778490e+02|-9.296544e-04
3|1.777841e+02|-3.648247e-04
4|1.777495e+02|-1.948923e-04
5|1.777284e+02|-1.184075e-04
6|1.777135e+02|-8.396988e-05
7|1.777027e+02|-6.059322e-05
8|1.776945e+02|-4.619816e-05
9|1.776880e+02|-3.672789e-05
10|1.776827e+02|-2.971430e-05
Plot original images Plot pixel values distribution
plt.figure(2, figsize=(6.4, 5))
plt.subplot(1, 2, 1)
plt.scatter(Xs[:, 0], Xs[:, 2], c=Xs)
plt.axis([0, 1, 0, 1])
plt.xlabel("Red")
plt.ylabel("Blue")
plt.title("Image 1")
plt.subplot(1, 2, 2)
plt.scatter(Xt[:, 0], Xt[:, 2], c=Xt)
plt.axis([0, 1, 0, 1])
plt.xlabel("Red")
plt.ylabel("Blue")
plt.title("Image 2")
plt.tight_layout()
Plot transformed images
plt.figure(2, figsize=(10, 5))
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(Image_emd)
plt.axis("off")
plt.title("EmdTransport")
plt.subplot(2, 3, 5)
plt.imshow(Image_sinkhorn)
plt.axis("off")
plt.title("SinkhornTransport")
plt.subplot(2, 3, 3)
plt.imshow(Image_mapping_linear)
plt.axis("off")
plt.title("MappingTransport (linear)")
plt.subplot(2, 3, 6)
plt.imshow(Image_mapping_gaussian)
plt.axis("off")
plt.title("MappingTransport (gaussian)")
plt.tight_layout()
plt.show()
Total running time of the script: (0 minutes 22.790 seconds)
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