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.. _sphx_glr_auto_examples_plot_otda_linear_mapping.py:
============================
Linear OT mapping estimation
============================
.. code-block:: python
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
import numpy as np
import pylab as pl
import ot
Generate data
-------------
.. code-block:: python
n = 1000
d = 2
sigma = .1
# source samples
angles = np.random.rand(n, 1) * 2 * np.pi
xs = np.concatenate((np.sin(angles), np.cos(angles)),
axis=1) + sigma * np.random.randn(n, 2)
xs[:n // 2, 1] += 2
# target samples
anglet = np.random.rand(n, 1) * 2 * np.pi
xt = np.concatenate((np.sin(anglet), np.cos(anglet)),
axis=1) + sigma * np.random.randn(n, 2)
xt[:n // 2, 1] += 2
A = np.array([[1.5, .7], [.7, 1.5]])
b = np.array([[4, 2]])
xt = xt.dot(A) + b
Plot data
---------
.. code-block:: python
pl.figure(1, (5, 5))
pl.plot(xs[:, 0], xs[:, 1], '+')
pl.plot(xt[:, 0], xt[:, 1], 'o')
.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_001.png
:align: center
Estimate linear mapping and transport
-------------------------------------
.. code-block:: python
Ae, be = ot.da.OT_mapping_linear(xs, xt)
xst = xs.dot(Ae) + be
Plot transported samples
------------------------
.. code-block:: python
pl.figure(1, (5, 5))
pl.clf()
pl.plot(xs[:, 0], xs[:, 1], '+')
pl.plot(xt[:, 0], xt[:, 1], 'o')
pl.plot(xst[:, 0], xst[:, 1], '+')
pl.show()
.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_002.png
:align: center
Load image data
---------------
.. code-block:: python
def im2mat(I):
"""Converts and image to matrix (one pixel per line)"""
return I.reshape((I.shape[0] * I.shape[1], I.shape[2]))
def mat2im(X, shape):
"""Converts back a matrix to an image"""
return X.reshape(shape)
def minmax(I):
return np.clip(I, 0, 1)
# Loading images
I1 = pl.imread('../data/ocean_day.jpg').astype(np.float64) / 256
I2 = pl.imread('../data/ocean_sunset.jpg').astype(np.float64) / 256
X1 = im2mat(I1)
X2 = im2mat(I2)
Estimate mapping and adapt
----------------------------
.. code-block:: python
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))
# %%
Plot transformed images
-----------------------
.. code-block:: python
pl.figure(2, figsize=(10, 7))
pl.subplot(2, 2, 1)
pl.imshow(I1)
pl.axis('off')
pl.title('Im. 1')
pl.subplot(2, 2, 2)
pl.imshow(I2)
pl.axis('off')
pl.title('Im. 2')
pl.subplot(2, 2, 3)
pl.imshow(I1t)
pl.axis('off')
pl.title('Mapping Im. 1')
pl.subplot(2, 2, 4)
pl.imshow(I2t)
pl.axis('off')
pl.title('Inverse mapping Im. 2')
.. image:: /auto_examples/images/sphx_glr_plot_otda_linear_mapping_004.png
:align: center
**Total running time of the script:** ( 0 minutes 0.635 seconds)
.. only :: html
.. container:: sphx-glr-footer
.. container:: sphx-glr-download
:download:`Download Python source code: plot_otda_linear_mapping.py <plot_otda_linear_mapping.py>`
.. container:: sphx-glr-download
:download:`Download Jupyter notebook: plot_otda_linear_mapping.ipynb <plot_otda_linear_mapping.ipynb>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_
|
