.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/1_registration/semiLagrangian_scheme.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_1_registration_semiLagrangian_scheme.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_1_registration_semiLagrangian_scheme.py:


.. semiLagrangian_scheme:

Why we should use semi-Lagrangian scheme?
=========================================


In this example I will try to demonstrate to you why we should use the semi-Lagrangian
scheme during geodesic integration rather than Eulerian. Obviously, we could
use even more developed schemes like Runge-Kutta, but semi-Lagrangian is a good
compromise between speed and accuracy.

.. GENERATED FROM PYTHON SOURCE LINES 16-17

Importing the necessary libraries

.. GENERATED FROM PYTHON SOURCE LINES 17-25

.. code-block:: Python

    import matplotlib.pyplot as plt

    import demeter.metamorphosis as mt
    import demeter.utils.reproducing_kernels as rk
    import demeter.utils.torchbox as tb
    from demeter.constants import DLT_KW_IMAGE









.. GENERATED FROM PYTHON SOURCE LINES 26-27

Open images

.. GENERATED FROM PYTHON SOURCE LINES 27-40

.. code-block:: Python


    size = (200,200)
    S = tb.reg_open('08',size=size)
    T = tb.reg_open('m0',size=size)

    fig,ax = plt.subplots(1,3)
    ax[0].imshow(S[0,0].cpu(),**DLT_KW_IMAGE)
    ax[0].set_title('source')
    ax[1].imshow(T[0,0].cpu(),**DLT_KW_IMAGE)
    ax[1].set_title('target')
    ax[2].imshow(tb.imCmp(S,T,'seg'),origin='lower')
    ax[2].set_title('superposition of S and T')




.. image-sg:: /auto_examples/1_registration/images/sphx_glr_semiLagrangian_scheme_001.png
   :alt: source, target, superposition of S and T
   :srcset: /auto_examples/1_registration/images/sphx_glr_semiLagrangian_scheme_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Text(0.5, 1.0, 'superposition of S and T')



.. GENERATED FROM PYTHON SOURCE LINES 41-42

Now we try to register the source to the target using the Eulerian scheme.

.. GENERATED FROM PYTHON SOURCE LINES 42-57

.. code-block:: Python

    kernel_op = rk.GaussianRKHS(sigma=(6, 6))

    momentum_ini = 0
    mr = mt.lddmm(S, T, momentum_ini,
          kernelOperator = kernel_op,
          cost_cst=.0001,
          integration_steps=100,
          n_iter=15,
          grad_coef=1,
          integration_method="Eulerian",
          dx_convention='pixel',
    )
    mr.plot()
    mr.plot_deform()
    mr.mp.plot()
    plt.show()


.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/1_registration/images/sphx_glr_semiLagrangian_scheme_002.png
         :alt: Lambda = 0.0001 rho = 1.0
         :srcset: /auto_examples/1_registration/images/sphx_glr_semiLagrangian_scheme_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/1_registration/images/sphx_glr_semiLagrangian_scheme_003.png
         :alt: source, target, Integrated source image, comparaison deformed image with target
         :srcset: /auto_examples/1_registration/images/sphx_glr_semiLagrangian_scheme_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/1_registration/images/sphx_glr_semiLagrangian_scheme_004.png
         :alt: diffeo = tensor(True)
         :srcset: /auto_examples/1_registration/images/sphx_glr_semiLagrangian_scheme_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/1_registration/images/sphx_glr_semiLagrangian_scheme_005.png
         :alt: t = 0.0, diffeo = tensor(True), t = 0.2, diffeo = tensor(True), t = 0.5, diffeo = tensor(True), t = 0.7, diffeo = tensor(True), t = 1.0, diffeo = tensor(True)
         :srcset: /auto_examples/1_registration/images/sphx_glr_semiLagrangian_scheme_005.png
         :class: sphx-glr-multi-img


.. rst-class:: sphx-glr-script-out

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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    Progress: [##--------]  20.00%  (Ssd : ,4710.3496).ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    Progress: [###-------]  26.67%  (Ssd : ,4710.3496).ic| classic.py:85 in _step_fullEulerian()
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    Progress: [###-------]  33.33%  (Ssd : ,4710.3496).ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    Progress: [####------]  40.00%  (Ssd : ,4710.3496).ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    Progress: [#####-----]  46.67%  (Ssd : ,4710.3496).ic| classic.py:85 in _step_fullEulerian()
        self.rho: 1
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    Progress: [#####-----]  53.33%  (Ssd : ,4710.3496).ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    Progress: [######----]  60.00%  (Ssd : ,4710.3496).ic| classic.py:85 in _step_fullEulerian()
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    Progress: [#######---]  66.67%  (Ssd : ,4710.3496).ic| classic.py:85 in _step_fullEulerian()
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    Progress: [#######---]  73.33%  (Ssd : ,4710.3496).ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    Progress: [########--]  80.00%  (Ssd : ,4710.3496).ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    ic| classic.py:85 in _step_fullEulerian()
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    Progress: [#########-]  86.67%  (Ssd : ,4710.3496).ic| classic.py:85 in _step_fullEulerian()
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    Progress: [#########-]  93.33%  (Ssd : ,4710.3496).ic| classic.py:85 in _step_fullEulerian()
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.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 20.709 seconds)


.. _sphx_glr_download_auto_examples_1_registration_semiLagrangian_scheme.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: semiLagrangian_scheme.ipynb <semiLagrangian_scheme.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: semiLagrangian_scheme.py <semiLagrangian_scheme.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: semiLagrangian_scheme.zip <semiLagrangian_scheme.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_