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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "_auto_tutorials/plot_matching.py"
.. LINE NUMBERS ARE GIVEN BELOW.
.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here <sphx_glr_download__auto_tutorials_plot_matching.py>`
to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr__auto_tutorials_plot_matching.py:
Unstructured Shape Matching
===========================
In this tutorial, we register two curves with IMODAL without deformation prior.
To achieve this, a local translation deformation module is used.
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Initialization
--------------
Import relevant Python modules.
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.. code-block:: default
import sys
sys.path.append("../")
import math
import copy
import torch
import matplotlib.pyplot as plt
import imodal
imodal.Utilities.set_compute_backend('torch')
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First, we generate the **source** (circle) and the **target** (square) and plot them.
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.. code-block:: default
# nb_points_source = 50
# radius = 1.
# source = radius*imodal.Utilities.generate_unit_circle(nb_points_source)
nb_points_square_side = 12
source = imodal.Utilities.generate_unit_square(nb_points_square_side)
source = imodal.Utilities.linear_transform(source, imodal.Utilities.rot2d(-math.pi/14.))
nb_points_square_side = 4
target = 0.7*imodal.Utilities.generate_unit_square(nb_points_square_side)
target = imodal.Utilities.linear_transform(target, imodal.Utilities.rot2d(math.pi/18.))
plt.figure(figsize=[4., 4.])
imodal.Utilities.plot_closed_shape(source, color='black')
imodal.Utilities.plot_closed_shape(target, color='red')
plt.axis('equal')
plt.subplots_adjust(left=0.1, right=0.9, top=0.9, bottom=0.1)
plt.show()
.. image:: /_auto_tutorials/images/sphx_glr_plot_matching_001.png
:alt: plot matching
:class: sphx-glr-single-img
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From these objects, **DeformablePoints** are created to be used for the registration.
This is a sub class of **Deformables** which represents geometrical objects that can be deformed by the framework.
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.. code-block:: default
source_deformable = imodal.Models.DeformablePoints(source)
target_deformable = imodal.Models.DeformablePoints(target)
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We define the local translation module **translation**: we need to specify the gaussian
kernel scale (**sigma_translation**). We initialize its geometrical descriptor (**gd**) with the source points.
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.. code-block:: default
sigma_translation = 1.
# sigma_translation1 = 0.1
# sigma_translation2 = 0.2
translation = imodal.DeformationModules.ImplicitModule0(2, source.shape[0], sigma_translation, nu=1e-4, gd=source)
# translation1 = imodal.DeformationModules.ImplicitModule0(2, source.shape[0], sigma_translation1, gd=source, nu=0.1)
# translation2 = imodal.DeformationModules.ImplicitModule0(2, source.shape[0], sigma_translation2, gd=source, nu=0.1)
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The distance between the deformed source and the target is measured using the
varifold framework, which does not require point correspondance. The spatial
kernel is a scalar gaussian kernel for which we specify the scale **sigma_varifold**.
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.. code-block:: default
sigma_varifold = [0.5]
attachment = imodal.Attachment.VarifoldAttachment(2, sigma_varifold, backend='torch')
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Registration
------------
We create the registration model.
The **lam** parameter is the weight of the attachment term of the total energy to minimize.
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.. code-block:: default
model = imodal.Models.RegistrationModel(source_deformable, [translation], attachment, lam=100.)
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We launch the energy minimization using the **Fitter** class.
We specify the ODE solver algorithm **shoot_solver** and the number of iteration steps **shoot_it** used to integrate the shooting equation.
The optimizer can be manually selected. Here, we select Pytorch's LBFGS algorithm with strong Wolfe termination conditions.
**max_iter** defines the maximum number of iteration for the optimization.
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.. code-block:: default
shoot_solver = 'euler'
shoot_it = 10
fitter = imodal.Models.Fitter(model, optimizer='torch_lbfgs')
max_iter = 10
fitter.fit(target_deformable, max_iter, options={'line_search_fn': 'strong_wolfe', 'shoot_solver': shoot_solver, 'shoot_it': shoot_it})
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
Starting optimization with method torch LBFGS, using solver euler with 10 iterations.
Initial cost={'deformation': 0.0, 'attach': 54.57539367675781}
1e-10
Evaluated model with costs=54.57539367675781
Evaluated model with costs=19.14338093996048
Evaluated model with costs=6.4000039249658585
Evaluated model with costs=3.1447209417819977
Evaluated model with costs=1.5842044353485107
Evaluated model with costs=9.115530669689178
Evaluated model with costs=1.26090669631958
Evaluated model with costs=0.8082702159881592
Evaluated model with costs=0.602929562330246
Evaluated model with costs=0.4900495111942291
Evaluated model with costs=0.479810893535614
Evaluated model with costs=0.48361146450042725
Evaluated model with costs=0.4796399474143982
Evaluated model with costs=0.47953301668167114
Evaluated model with costs=0.47956109046936035
Evaluated model with costs=0.4795800745487213
Evaluated model with costs=0.4795333743095398
Evaluated model with costs=0.4795810580253601
================================================================================
Time: 2.8076504664495587
Iteration: 0
Costs
deformation=0.3482601046562195
attach=0.13132095336914062
Total cost=0.4795810580253601
1e-10
Evaluated model with costs=0.47953301668167114
Evaluated model with costs=0.47956109046936035
Evaluated model with costs=0.4795800745487213
Evaluated model with costs=0.4795333743095398
Evaluated model with costs=0.4795810580253601
================================================================================
Time: 3.6211067866533995
Iteration: 1
Costs
deformation=0.3482601046562195
attach=0.13132095336914062
Total cost=0.4795810580253601
================================================================================
Optimisation process exited with message: Convergence achieved.
Final cost=0.4795810580253601
Model evaluation count=23
Time elapsed = 3.6212978567928076
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Displaying results
------------------
We compute the optimized deformation.
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.. code-block:: default
intermediates = {}
with torch.autograd.no_grad():
deformed = model.compute_deformed(shoot_solver, shoot_it, intermediates=intermediates)[0][0]
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We display the result.
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.. code-block:: default
display_index = [0, 3, 7, 10]
plt.figure(figsize=[3.*len(display_index), 3.])
for count, i in enumerate(display_index):
plt.subplot(1, len(display_index), 1+count).set_title("t={}".format(i/10.))
deformed_i = intermediates['states'][i][0].gd
imodal.Utilities.plot_closed_shape(source, color='black')
imodal.Utilities.plot_closed_shape(target, color='red')
imodal.Utilities.plot_closed_shape(deformed_i, color='blue')
plt.axis('equal')
plt.axis('off')
plt.subplots_adjust(left=0., right=1., top=1., bottom=0.)
plt.show()
.. image:: /_auto_tutorials/images/sphx_glr_plot_matching_002.png
:alt: t=0.0, t=0.3, t=0.7, t=1.0
:class: sphx-glr-single-img
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In order to visualize the deformation, we will compute the grid deformation.
We first retrieve the modules and initialize their manifolds (with initial values of geometrical descriptor and momentum).
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.. code-block:: default
modules = imodal.DeformationModules.CompoundModule(copy.copy(model.modules))
modules.manifold.fill(model.init_manifold.clone())
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We initialize a grid built from a bounding box and a grid resolution.
We create a bounding box **aabb** around the source, scaled with a 1.3 factor to enhance the visualization of the deformation.
Then, we define the grid resolution **grid_resolution** from the size of each grid gap **square_size**.
Finally, we create a silent deformation module **deformation_grid** whose geometrical descriptor is made of the grid points.
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.. code-block:: default
aabb = imodal.Utilities.AABB.build_from_points(source).scale(1.3)
square_size = 0.05
grid_resolution = [math.floor(aabb.width/square_size),
math.floor(aabb.height/square_size)]
deformation_grid = imodal.DeformationModules.DeformationGrid(aabb, grid_resolution)
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We inject the newly created deformation module **deformation_grid** into the list of deformation modules **modules_grid**.
We create the hamiltonian structure **hamiltonian** allowing us to integrate the shooting equation.
We then recompute the deformation, now tracking the grid deformation.
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.. code-block:: default
modules_grid = [*modules, deformation_grid]
hamiltonian = imodal.HamiltonianDynamic.Hamiltonian(modules_grid)
intermediates_grid = {}
with torch.autograd.no_grad():
imodal.HamiltonianDynamic.shoot(hamiltonian, shoot_solver, shoot_it, intermediates=intermediates_grid)
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We display the result along with the deformation grid.
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.. code-block:: default
display_index = [0, 3, 7, 10]
plt.figure(figsize=[3.*len(display_index), 3.])
for count, i in enumerate(display_index):
ax = plt.subplot(1, len(display_index), 1+count)
# ax.set_title("t={}".format(i/10.))
deformed_i = intermediates_grid['states'][i][0].gd
deformation_grid.manifold.fill_gd(intermediates_grid['states'][i][-1].gd)
grid_x, grid_y = deformation_grid.togrid()
imodal.Utilities.plot_grid(ax, grid_x, grid_y, color='xkcd:light blue')
imodal.Utilities.plot_closed_shape(source, color='black')
imodal.Utilities.plot_closed_shape(target, color='red')
imodal.Utilities.plot_closed_shape(deformed_i, color='blue')
plt.axis('equal')
plt.axis('off')
plt.subplots_adjust(left=0., right=1., top=1., bottom=0.)
plt.show()
.. image:: /_auto_tutorials/images/sphx_glr_plot_matching_003.png
:alt: plot matching
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 5.546 seconds)
.. _sphx_glr_download__auto_tutorials_plot_matching.py:
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:download:`Download Python source code: plot_matching.py <plot_matching.py>`
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:download:`Download Jupyter notebook: plot_matching.ipynb <plot_matching.ipynb>`
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