.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/registration/plot_lddmm_1_normalization.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_registration_plot_lddmm_1_normalization.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_registration_plot_lddmm_1_normalization.py:


LDDMM with normalized kernel
============================

This notebook illustrates the interest of normalizing the cometric in the LDDMM
model. We consider the registration of two spheres that differ by a translation
first, and then a more complex registration task with a translation and a deformation.

Without normalization, the carpooling artifact occurs: the sphere
is contracted, then translated and finally expanded. in this situation, event if
the morphed shape matches the target, the intermediate shapes are not meaningful
and the extrapolation is not reliable.

Normalizing the kernel adds regularization to the morphing, leanding to prevention
of the carpooling artifact and improvement of the extrapolation to some extent.

Options for normalization are:

* "rows": normalize the rows of the kernel
* "columns": normalize the columns of the kernel
* "both": normalize both the rows and the columns of the kernel (for quare kernels, algorithm 5.7 in https://www.jeanfeydy.com/geometric_data_analysis.pdf)

Further explanation can be found in the p177 and onwards of https://www.jeanfeydy.com/geometric_data_analysis.pdf.

.. GENERATED FROM PYTHON SOURCE LINES 26-36

.. code-block:: Python


    from time import time

    import pyvista as pv
    import torch

    import skshapes as sks

    # sphinx_gallery_thumbnail_number = 9








.. GENERATED FROM PYTHON SOURCE LINES 37-38

Load data

.. GENERATED FROM PYTHON SOURCE LINES 38-68

.. code-block:: Python


    plot_kwargs = {
        "smooth_shading": True,
        "pbr": True,
        "metallic": 0.7,
        "roughness": 0.6,
    }

    cpos = [
        (1.6256104086078755, -9.701422233882411, 1.3012755902068773),
        (1.191160019984921, 0.01901107976782581, -0.0052552929581526076),
        (0.006053690112347382, 0.13347614338229413, 0.9910335372649167),
    ]

    source = sks.Sphere()
    target = sks.Sphere()

    decimation = sks.Decimation(n_points=200)
    source = decimation.fit_transform(source)
    target = decimation.transform(target)

    target.points = target.points + torch.tensor([2, 0.0, 0.0])

    plotter = pv.Plotter()
    plotter.add_mesh(source.to_pyvista(), color="teal", opacity=0.8, **plot_kwargs)
    plotter.add_mesh(target.to_pyvista(), color="red", opacity=0.8, **plot_kwargs)
    plotter.camera_position = cpos
    plotter.show()









.. tab-set::



   .. tab-item:: Static Scene



            
     .. image-sg:: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_001.png
        :alt: plot lddmm 1 normalization
        :srcset: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_001.png
        :class: sphx-glr-single-img
     


   .. tab-item:: Interactive Scene



       .. offlineviewer:: /home/runner/work/scikit-shapes/scikit-shapes/doc/source/auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_001.vtksz






.. GENERATED FROM PYTHON SOURCE LINES 69-71

LDDM without normalization
--------------------------

.. GENERATED FROM PYTHON SOURCE LINES 71-105

.. code-block:: Python


    model = sks.ExtrinsicDeformation(
        n_steps=4,
        kernel="gaussian",
        scale=0.3,
    )

    loss = sks.L2Loss()

    task = sks.Registration(
        model=model,
        loss=loss,
        optimizer=sks.LBFGS(),
        n_iter=3,
        regularization_weight=1e-1,
        verbose=True,
    )

    start = time()
    task.fit(source=source, target=target)
    print("Elapsed time: ", time() - start)
    path = task.path_

    plotter = pv.Plotter()
    plotter.add_mesh(source.to_pyvista(), color="teal", opacity=0.2, **plot_kwargs)
    plotter.add_mesh(target.to_pyvista(), color="red", opacity=0.2, **plot_kwargs)
    for i in range(len(path)):
        plotter.add_mesh(
            path[i].to_pyvista(), color="tan", opacity=0.8, **plot_kwargs
        )
    plotter.camera_position = cpos
    plotter.show()









.. tab-set::



   .. tab-item:: Static Scene



            
     .. image-sg:: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_002.png
        :alt: plot lddmm 1 normalization
        :srcset: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_002.png
        :class: sphx-glr-single-img
     


   .. tab-item:: Interactive Scene



       .. offlineviewer:: /home/runner/work/scikit-shapes/scikit-shapes/doc/source/auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_002.vtksz



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

 .. code-block:: none

    Initial loss : 8.04e+02
      = 8.04e+02 + 0.1 * 0.00e+00 (fidelity + regularization_weight * regularization)
    Loss after 1 iteration(s) : 1.84e+00
      = 1.42e+00 + 0.1 * 4.16e+00 (fidelity + regularization_weight * regularization)
    Loss after 2 iteration(s) : 5.25e-01
      = 1.21e-01 + 0.1 * 4.04e+00 (fidelity + regularization_weight * regularization)
    Loss after 3 iteration(s) : 4.40e-01
      = 3.99e-02 + 0.1 * 4.00e+00 (fidelity + regularization_weight * regularization)
    Elapsed time:  69.92670607566833




.. GENERATED FROM PYTHON SOURCE LINES 106-107

Extrapolation

.. GENERATED FROM PYTHON SOURCE LINES 107-142

.. code-block:: Python


    back = model.morph(
        shape=source,
        parameter=task.parameter_,
        final_time=-1.0,
        return_path=True,
    ).path

    model.n_steps = 8
    forward = model.morph(
        shape=source,
        parameter=task.parameter_,
        final_time=2.0,
        return_path=True,
    ).path

    path = back[::-1] + forward[1:]

    plotter = pv.Plotter()
    plotter.open_gif("lddmm_no_normalization.gif", fps=4)
    for i in range(len(path)):
        plotter.clear_actors()
        plotter.add_mesh(
            source.to_pyvista(), color="teal", opacity=0.2, **plot_kwargs
        )
        plotter.add_mesh(
            target.to_pyvista(), color="red", opacity=0.2, **plot_kwargs
        )
        plotter.add_mesh(
            path[i].to_pyvista(), color="tan", opacity=0.8, **plot_kwargs
        )
        plotter.camera_position = cpos
        plotter.write_frame()
    plotter.close()





.. image-sg:: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_003.gif
   :alt: plot lddmm 1 normalization
   :srcset: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_003.gif
   :class: sphx-glr-single-img







.. GENERATED FROM PYTHON SOURCE LINES 143-145

Normalizing the rows of the kernel
----------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 145-177

.. code-block:: Python


    model_norm = sks.ExtrinsicDeformation(
        n_steps=4,
        kernel="gaussian",
        scale=0.3,
        normalization="rows",
    )

    task_norm = sks.Registration(
        model=model_norm,
        loss=loss,
        optimizer=sks.LBFGS(),
        n_iter=1,
        regularization_weight=0.0,
        verbose=True,
    )

    start = time()
    task_norm.fit(source=source, target=target)
    print("Elapsed time: ", time() - start)
    path = task_norm.path_

    plotter = pv.Plotter()
    plotter.add_mesh(source.to_pyvista(), color="teal", opacity=0.2, **plot_kwargs)
    plotter.add_mesh(target.to_pyvista(), color="red", opacity=0.2, **plot_kwargs)
    for i in range(len(path)):
        plotter.add_mesh(
            path[i].to_pyvista(), color="tan", opacity=0.8, **plot_kwargs
        )
    plotter.camera_position = cpos
    plotter.show()








.. tab-set::



   .. tab-item:: Static Scene



            
     .. image-sg:: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_004.png
        :alt: plot lddmm 1 normalization
        :srcset: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_004.png
        :class: sphx-glr-single-img
     


   .. tab-item:: Interactive Scene



       .. offlineviewer:: /home/runner/work/scikit-shapes/scikit-shapes/doc/source/auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_004.vtksz



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

 .. code-block:: none

    Initial loss : 8.04e+02
      = 8.04e+02 + 0 (fidelity + regularization_weight * regularization)
    Loss after 1 iteration(s) : 1.67e-03
      = 1.67e-03 + 0 (fidelity + regularization_weight * regularization)
    Elapsed time:  41.609856843948364




.. GENERATED FROM PYTHON SOURCE LINES 178-179

Extrapolation

.. GENERATED FROM PYTHON SOURCE LINES 179-214

.. code-block:: Python


    back = model_norm.morph(
        shape=source,
        parameter=task_norm.parameter_,
        final_time=-1.0,
        return_path=True,
    ).path

    model_norm.n_steps = 8
    forward = model_norm.morph(
        shape=source,
        parameter=task_norm.parameter_,
        final_time=2.0,
        return_path=True,
    ).path

    path = back[::-1] + forward[1:]

    plotter = pv.Plotter()
    plotter.open_gif("lddmm_normalization.gif", fps=4)
    for i in range(len(path)):
        plotter.clear_actors()
        plotter.add_mesh(
            source.to_pyvista(), color="teal", opacity=0.2, **plot_kwargs
        )
        plotter.add_mesh(
            target.to_pyvista(), color="red", opacity=0.2, **plot_kwargs
        )
        plotter.add_mesh(
            path[i].to_pyvista(), color="tan", opacity=0.8, **plot_kwargs
        )
        plotter.camera_position = cpos
        plotter.write_frame()
    plotter.close()





.. image-sg:: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_005.gif
   :alt: plot lddmm 1 normalization
   :srcset: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_005.gif
   :class: sphx-glr-single-img







.. GENERATED FROM PYTHON SOURCE LINES 215-217

Normalizing both rows and columns of the kernel
-----------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 217-249

.. code-block:: Python


    model_norm = sks.ExtrinsicDeformation(
        n_steps=4,
        kernel="gaussian",
        scale=0.3,
        normalization="both",
    )

    task_norm = sks.Registration(
        model=model_norm,
        loss=loss,
        optimizer=sks.LBFGS(),
        n_iter=1,
        regularization_weight=0.0,
        verbose=True,
    )

    start = time()
    task_norm.fit(source=source, target=target)
    elapsed_time = time() - start
    path = task_norm.path_

    plotter = pv.Plotter()
    plotter.add_mesh(source.to_pyvista(), color="teal", opacity=0.2, **plot_kwargs)
    plotter.add_mesh(target.to_pyvista(), color="red", opacity=0.2, **plot_kwargs)
    for i in range(len(path)):
        plotter.add_mesh(
            path[i].to_pyvista(), color="tan", opacity=0.8, **plot_kwargs
        )
    plotter.camera_position = cpos
    plotter.show()








.. tab-set::



   .. tab-item:: Static Scene



            
     .. image-sg:: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_006.png
        :alt: plot lddmm 1 normalization
        :srcset: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_006.png
        :class: sphx-glr-single-img
     


   .. tab-item:: Interactive Scene



       .. offlineviewer:: /home/runner/work/scikit-shapes/scikit-shapes/doc/source/auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_006.vtksz



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

 .. code-block:: none

    Initial loss : 8.04e+02
      = 8.04e+02 + 0 (fidelity + regularization_weight * regularization)
    Loss after 1 iteration(s) : 4.98e-06
      = 4.98e-06 + 0 (fidelity + regularization_weight * regularization)




.. GENERATED FROM PYTHON SOURCE LINES 250-251

Extrapolation

.. GENERATED FROM PYTHON SOURCE LINES 251-286

.. code-block:: Python


    back = model_norm.morph(
        shape=source,
        parameter=task_norm.parameter_,
        final_time=-1.0,
        return_path=True,
    ).path

    model_norm.n_steps = 8
    forward = model_norm.morph(
        shape=source,
        parameter=task_norm.parameter_,
        final_time=2.0,
        return_path=True,
    ).path

    path = back[::-1] + forward[1:]

    plotter = pv.Plotter()
    plotter.open_gif("lddmm_normalization.gif", fps=4)
    for i in range(len(path)):
        plotter.clear_actors()
        plotter.add_mesh(
            source.to_pyvista(), color="teal", opacity=0.2, **plot_kwargs
        )
        plotter.add_mesh(
            target.to_pyvista(), color="red", opacity=0.2, **plot_kwargs
        )
        plotter.add_mesh(
            path[i].to_pyvista(), color="tan", opacity=0.8, **plot_kwargs
        )
        plotter.camera_position = cpos
        plotter.write_frame()
    plotter.close()





.. image-sg:: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_007.gif
   :alt: plot lddmm 1 normalization
   :srcset: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_007.gif
   :class: sphx-glr-single-img







.. GENERATED FROM PYTHON SOURCE LINES 287-289

Example with a more complex shape
---------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 289-324

.. code-block:: Python


    n_steps = 3

    plot_kwargs = {
        "smooth_shading": True,
        "pbr": True,
        "metallic": 0.7,
        "roughness": 0.6,
    }

    cpos = [
        (3.6401575998373183, -1.183408993703478, 1.0915912440258628),
        (0.7463583722710609, 0.762569822371006, 0.48035204596817493),
        (-0.1745415166347431, 0.04933887578777028, 0.9834129012306287),
    ]

    # 5 - 8
    source = sks.PolyData("../test_data/cactus/cactus3.ply")
    target = sks.PolyData("../test_data/cactus/cactus11.ply")
    target.points += torch.Tensor([0.5, 0.5, 0])

    decimation = sks.Decimation(n_points=500)
    source = decimation.fit_transform(source)
    target = decimation.transform(target)


    model = sks.ExtrinsicDeformation(
        n_steps=n_steps,
        kernel="gaussian",
        scale=0.1,
        normalization="both",
    )

    loss = sks.L2Loss()








.. GENERATED FROM PYTHON SOURCE LINES 325-327

Interpolation
-------------

.. GENERATED FROM PYTHON SOURCE LINES 327-353

.. code-block:: Python


    task = sks.Registration(
        model=model,
        loss=loss,
        optimizer=sks.LBFGS(),
        n_iter=1,
        verbose=True,
        regularization_weight=0.001,
    )

    start = time()
    task.fit(source=source, target=target)
    print("Elapsed time: ", time() - start)

    path = task.path_

    plotter = pv.Plotter()
    for frame in path:
        plotter.add_mesh(
            frame.to_pyvista(), color="tan", opacity=0.3, **plot_kwargs
        )
    plotter.add_mesh(source.to_pyvista(), color="teal", opacity=0.5, **plot_kwargs)
    plotter.add_mesh(target.to_pyvista(), color="red", opacity=0.5, **plot_kwargs)
    plotter.camera_position = cpos
    plotter.show()








.. tab-set::



   .. tab-item:: Static Scene



            
     .. image-sg:: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_008.png
        :alt: plot lddmm 1 normalization
        :srcset: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_008.png
        :class: sphx-glr-single-img
     


   .. tab-item:: Interactive Scene



       .. offlineviewer:: /home/runner/work/scikit-shapes/scikit-shapes/doc/source/auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_008.vtksz



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

 .. code-block:: none

    Initial loss : 2.50e+02
      = 2.50e+02 + 0.001 * 0.00e+00 (fidelity + regularization_weight * regularization)
    Loss after 1 iteration(s) : 1.35e-01
      = 9.99e-03 + 0.001 * 1.25e+02 (fidelity + regularization_weight * regularization)
    Elapsed time:  15.22480583190918




.. GENERATED FROM PYTHON SOURCE LINES 354-356

Extrapolation
-------------

.. GENERATED FROM PYTHON SOURCE LINES 356-388

.. code-block:: Python


    back = model.morph(
        shape=source,
        parameter=task.parameter_,
        return_path=True,
        return_regularization=True,
        final_time=-1.0,
    ).path

    model.n_steps = 2 * n_steps

    forward = model.morph(
        shape=source,
        parameter=task.parameter_,
        return_path=True,
        return_regularization=True,
        final_time=2.0,
    ).path

    path = back[::-1] + forward[1:]

    plotter = pv.Plotter()
    for frame in path:
        plotter.add_mesh(
            frame.to_pyvista(), color="tan", opacity=0.3, **plot_kwargs
        )
    plotter.add_mesh(source.to_pyvista(), color="teal", opacity=0.5, **plot_kwargs)
    plotter.add_mesh(target.to_pyvista(), color="red", opacity=0.5, **plot_kwargs)
    plotter.camera_position = cpos
    plotter.show()

    print(plotter.camera_position)







.. tab-set::



   .. tab-item:: Static Scene



            
     .. image-sg:: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_009.png
        :alt: plot lddmm 1 normalization
        :srcset: /auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_009.png
        :class: sphx-glr-single-img
     


   .. tab-item:: Interactive Scene



       .. offlineviewer:: /home/runner/work/scikit-shapes/scikit-shapes/doc/source/auto_examples/registration/images/sphx_glr_plot_lddmm_1_normalization_009.vtksz



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

 .. code-block:: none

    [(3.6401575998373183, -1.183408993703478, 1.0915912440258628),
     (0.7463583722710609, 0.762569822371006, 0.48035204596817493),
     (-0.17454151663474313, 0.049338875787770284, 0.9834129012306289)]





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (3 minutes 27.775 seconds)


.. _sphx_glr_download_auto_examples_registration_plot_lddmm_1_normalization.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_lddmm_1_normalization.ipynb <plot_lddmm_1_normalization.ipynb>`

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

      :download:`Download Python source code: plot_lddmm_1_normalization.py <plot_lddmm_1_normalization.py>`


.. only:: html

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

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