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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>`_