.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "_auto_examples/leaf_growth/plot_leaf_acropetal_imodal.py"
.. LINE NUMBERS ARE GIVEN BELOW.
.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here <sphx_glr_download__auto_examples_leaf_growth_plot_leaf_acropetal_imodal.py>`
to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr__auto_examples_leaf_growth_plot_leaf_acropetal_imodal.py:
Acropetal Leaf Growth Model Using Implicit Modules
==================================================
1. Curve and dots registration using implicit modules of order 1, learning the growth model tensor.
2. Curve registration using implicit modules of order with learned growth model tensor.
.. GENERATED FROM PYTHON SOURCE LINES 10-12
Import relevant Python modules.
.. GENERATED FROM PYTHON SOURCE LINES 12-27
.. code-block:: default
import sys
sys.path.append("../../")
import math
import copy
import pickle
import torch
import matplotlib.pyplot as plt
import imodal
torch.set_default_dtype(torch.float32)
imodal.Utilities.set_compute_backend('torch')
.. GENERATED FROM PYTHON SOURCE LINES 28-33
Learning the growth model tensor
--------------------------------
We load the data (shape and dots of the source and target leaves).
.. GENERATED FROM PYTHON SOURCE LINES 33-47
.. code-block:: default
with open("../../data/acropetal.pickle", 'rb') as f:
data = pickle.load(f)
dots_source = torch.tensor(data['dots_source'], dtype=torch.get_default_dtype())
dots_target = torch.tensor(data['dots_target'], dtype=torch.get_default_dtype())
shape_source = imodal.Utilities.close_shape(torch.tensor(data['shape_source']).type(torch.get_default_dtype()))
shape_target = imodal.Utilities.close_shape(torch.tensor(data['shape_target']).type(torch.get_default_dtype()))
aabb_source = imodal.Utilities.AABB.build_from_points(shape_source)
aabb_target = imodal.Utilities.AABB.build_from_points(shape_target)
.. GENERATED FROM PYTHON SOURCE LINES 48-50
Plot source and target.
.. GENERATED FROM PYTHON SOURCE LINES 50-61
.. code-block:: default
plt.title("Source and target")
plt.plot(shape_source[:, 0].numpy(), shape_source[:, 1].numpy(), color='black')
plt.plot(dots_source[:, 0].numpy(), dots_source[:, 1].numpy(), '.', color='black')
plt.plot(shape_target[:, 0].numpy(), shape_target[:, 1].numpy(), color='red')
plt.plot(dots_target[:, 0].numpy(), dots_target[:, 1].numpy(), '.', color='red')
plt.axis('equal')
plt.show()
.. image:: /_auto_examples/leaf_growth/images/sphx_glr_plot_leaf_acropetal_imodal_001.png
:alt: Source and target
:class: sphx-glr-single-img
.. GENERATED FROM PYTHON SOURCE LINES 62-65
We now sample the points that will be used by the implicit deformation
module of order 1 (growth module).
.. GENERATED FROM PYTHON SOURCE LINES 65-80
.. code-block:: default
# Build AABB (Axis Aligned Bounding Box) around the source shape and uniformly
# sample points for the growth module.
points_density = 0.05
aabb_source = imodal.Utilities.AABB.build_from_points(shape_source)
points_growth = imodal.Utilities.fill_area_uniform_density(imodal.Utilities.area_shape, aabb_source, points_density, shape=1.5*shape_source)
points_growth_mask = imodal.Utilities.area_shape(points_growth, shape=1.*shape_source)
points_growth = points_growth[points_growth_mask]
# Initial normal frames for the growth module.
rot_growth = torch.stack([imodal.Utilities.rot2d(0.)]*points_growth.shape[0], axis=0)
.. GENERATED FROM PYTHON SOURCE LINES 81-83
Plot points of the growth module.
.. GENERATED FROM PYTHON SOURCE LINES 83-90
.. code-block:: default
plt.plot(shape_source[:, 0].numpy(), shape_source[:, 1].numpy(), color='black')
plt.plot(points_growth[:, 0].numpy(), points_growth[:, 1].numpy(), 'o', color='blue')
plt.axis('equal')
plt.show()
.. image:: /_auto_examples/leaf_growth/images/sphx_glr_plot_leaf_acropetal_imodal_002.png
:alt: plot leaf acropetal imodal
:class: sphx-glr-single-img
.. GENERATED FROM PYTHON SOURCE LINES 91-95
Create the deformation model with a combination of 3 modules : implicit module
of order 1 (growth model), implicit module of order 0 (small corrections) and
a global translation.
.. GENERATED FROM PYTHON SOURCE LINES 98-100
Create and initialize the global translation module.
.. GENERATED FROM PYTHON SOURCE LINES 100-106
.. code-block:: default
coeff_global = 15.
global_translation = imodal.DeformationModules.GlobalTranslation(2, coeff=coeff_global)
.. GENERATED FROM PYTHON SOURCE LINES 107-109
Create and initialize the growth module.
.. GENERATED FROM PYTHON SOURCE LINES 109-119
.. code-block:: default
nu = 0.1
coeff_growth = 0.01
scale_growth = 100.
C = torch.empty(points_growth.shape[0], 2, 1)
growth = imodal.DeformationModules.ImplicitModule1(2, points_growth.shape[0], scale_growth, C, coeff=coeff_growth, nu=nu, gd=(points_growth, rot_growth))
.. GENERATED FROM PYTHON SOURCE LINES 120-122
Create and initialize local translations module.
.. GENERATED FROM PYTHON SOURCE LINES 122-130
.. code-block:: default
coeff_small = 100.
nu = 0.1
scale_small = 10.
points_small = shape_source.clone()
small_scale_translations = imodal.DeformationModules.ImplicitModule0(2, points_small.shape[0], scale_small, coeff=coeff_small, nu=nu, gd=points_small)
.. GENERATED FROM PYTHON SOURCE LINES 131-133
Define our growth model tensor.
.. GENERATED FROM PYTHON SOURCE LINES 133-155
.. code-block:: default
# The polynomial model for our growth model tensor.
def pol(pos, a, b, c, d):
return a + b*pos[:, 1] + c*pos[:, 1]**2 + d*pos[:, 1]**3
# Callback called when evaluating the model to compute the growth model tensor from parameters.
def callback_compute_c(init_manifold, modules, parameters, deformables):
abcd = parameters['abcd']['params'][0]
a = abcd[0].unsqueeze(1)
b = abcd[1].unsqueeze(1)
c = abcd[2].unsqueeze(1)
d = abcd[3].unsqueeze(1)
modules[3].C = pol(init_manifold[3].gd[0], a, b, c, d).transpose(0, 1).unsqueeze(2)
# Initial parameters of our growth model tensor.
abcd = torch.zeros(4, 2)
abcd[0] = 0.1 * torch.ones(2)
abcd.requires_grad_()
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
tensor([[0.1000, 0.1000],
[0.0000, 0.0000],
[0.0000, 0.0000],
[0.0000, 0.0000]], requires_grad=True)
.. GENERATED FROM PYTHON SOURCE LINES 156-158
Define deformables used by the registration model.
.. GENERATED FROM PYTHON SOURCE LINES 158-165
.. code-block:: default
deformable_shape_source = imodal.Models.DeformablePoints(shape_source)
deformable_shape_target = imodal.Models.DeformablePoints(shape_target)
deformable_dots_source = imodal.Models.DeformablePoints(dots_source)
deformable_dots_target = imodal.Models.DeformablePoints(dots_target)
.. GENERATED FROM PYTHON SOURCE LINES 166-168
Define the registration model.
.. GENERATED FROM PYTHON SOURCE LINES 168-177
.. code-block:: default
model = imodal.Models.RegistrationModel(
[deformable_shape_source, deformable_dots_source],
[global_translation, growth, small_scale_translations],
[imodal.Attachment.VarifoldAttachment(2, [50., 300.]),
imodal.Attachment.EuclideanPointwiseDistanceAttachment(100.)],
lam=200., other_parameters={'abcd': {'params': [abcd]}},
precompute_callback=callback_compute_c)
.. GENERATED FROM PYTHON SOURCE LINES 178-180
Fitting using Torch LBFGS optimizer.
.. GENERATED FROM PYTHON SOURCE LINES 180-189
.. code-block:: default
shoot_solver = 'euler'
shoot_it = 10
costs = {}
fitter = imodal.Models.Fitter(model, optimizer='torch_lbfgs')
fitter.fit([deformable_shape_target, deformable_dots_target], 200, costs=costs, options={'shoot_solver': shoot_solver, 'shoot_it': shoot_it, 'line_search_fn': 'strong_wolfe'})
.. 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': 389514912.0}
1e-10
Evaluated model with costs=389514912.0
Evaluated model with costs=389017248.0784309
Evaluated model with costs=386759138.37632895
Evaluated model with costs=360678089.23446655
Evaluated model with costs=262140285.0810547
Evaluated model with costs=121890011.91992188
Evaluated model with costs=93003823.87695312
Evaluated model with costs=92206315.44921875
Evaluated model with costs=90143611.37304688
Evaluated model with costs=81597550.7890625
Evaluated model with costs=72592011.3046875
Evaluated model with costs=68825231.87109375
Evaluated model with costs=67356862.42578125
Evaluated model with costs=66452007.34765625
Evaluated model with costs=66087941.10546875
Evaluated model with costs=63723252.7265625
Evaluated model with costs=58526261.38671875
Evaluated model with costs=53242483.0859375
Evaluated model with costs=42919517.75
Evaluated model with costs=39089258.54296875
Evaluated model with costs=36472452.53515625
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Evaluated model with costs=35618638.89453125
Evaluated model with costs=33920214.6015625
Evaluated model with costs=33916584.4765625
Evaluated model with costs=33873124.41015625
================================================================================
Time: 43.663380257003155
Iteration: 0
Costs
deformation=52000.41015625
attach=33821124.0
Total cost=33873124.41015625
1e-10
Evaluated model with costs=33873124.41015625
Evaluated model with costs=73905388.76953125
Evaluated model with costs=33842895.48828125
Evaluated model with costs=32958255.27734375
Evaluated model with costs=32759891.1796875
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Evaluated model with costs=28420440.59375
Evaluated model with costs=28417674.5546875
Evaluated model with costs=28414425.12890625
Evaluated model with costs=28414247.765625
================================================================================
Time: 82.46674059799989
Iteration: 1
Costs
deformation=61635.765625
attach=28352612.0
Total cost=28414247.765625
1e-10
Evaluated model with costs=28414247.765625
Evaluated model with costs=28414309.77734375
Evaluated model with costs=28414281.92578125
Evaluated model with costs=28414311.796875
Evaluated model with costs=28414247.765625
================================================================================
Time: 91.62942164700144
Iteration: 2
Costs
deformation=61635.765625
attach=28352612.0
Total cost=28414247.765625
================================================================================
Optimisation process exited with message: Convergence achieved.
Final cost=28414247.765625
Model evaluation count=55
Time elapsed = 91.6297703900018
.. GENERATED FROM PYTHON SOURCE LINES 190-192
Compute optimized deformation trajectory.
.. GENERATED FROM PYTHON SOURCE LINES 192-204
.. code-block:: default
intermediates = {}
with torch.autograd.no_grad():
deformed = model.compute_deformed(shoot_solver, shoot_it, intermediates=intermediates)
deformed_shape = deformed[0][0]
deformed_dots = deformed[1][0]
deformed_growth = intermediates['states'][-1][3].gd[0]
deformed_growth_rot = intermediates['states'][-1][3].gd[1]
global_translation_controls = [control[2] for control in intermediates['controls']]
growth_controls = [control[3] for control in intermediates['controls']]
.. GENERATED FROM PYTHON SOURCE LINES 205-207
Plot results.
.. GENERATED FROM PYTHON SOURCE LINES 207-231
.. code-block:: default
plt.subplot(1, 3, 1)
plt.title("Source")
plt.plot(shape_source[:, 0].numpy(), shape_source[:, 1].numpy(), '-', color='black')
plt.plot(dots_source[:, 0].numpy(), dots_source[:, 1].numpy(), '.', color='black')
plt.axis('equal')
plt.subplot(1, 3, 2)
plt.title("Deformed source")
plt.plot(deformed_shape[:, 0], deformed_shape[:, 1], '-', color='blue')
plt.plot(deformed_dots[:, 0], deformed_dots[:, 1], '.', color='blue')
plt.axis('equal')
plt.subplot(1, 3, 3)
plt.title("Deformed source and target")
plt.plot(shape_target[:, 0].numpy(), shape_target[:, 1].numpy(), '-', color='red')
plt.plot(dots_target[:, 0].numpy(), dots_target[:, 1].numpy(), '.', color='red')
plt.plot(deformed_shape[:, 0], deformed_shape[:, 1], '-', color='blue')
plt.plot(deformed_dots[:, 0], deformed_dots[:, 1], '.', color='blue')
# plt.plot(deformed_growth[:, 0], deformed_growth[:, 1], '.', color='blue')
plt.axis('equal')
plt.show()
.. image:: /_auto_examples/leaf_growth/images/sphx_glr_plot_leaf_acropetal_imodal_003.png
:alt: Source, Deformed source, Deformed source and target
:class: sphx-glr-single-img
.. GENERATED FROM PYTHON SOURCE LINES 232-234
Evaluate estimated growth model tensor.
.. GENERATED FROM PYTHON SOURCE LINES 234-244
.. code-block:: default
learned_abcd = abcd.detach()
learned_C = pol(model.init_manifold[3].gd[0].detach(),
learned_abcd[0].unsqueeze(1),
learned_abcd[1].unsqueeze(1),
learned_abcd[2].unsqueeze(1),
learned_abcd[3].unsqueeze(1)).transpose(0, 1).unsqueeze(2).detach()
print("Learned growth model tensor parameters:\n {}".format(learned_abcd))
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
Learned growth model tensor parameters:
tensor([[ 1.0000e-01, 1.0000e-01],
[-1.6238e-07, -5.1295e-06],
[-8.3878e-06, 2.0106e-04],
[ 9.6801e-06, 8.4670e-06]])
.. GENERATED FROM PYTHON SOURCE LINES 245-247
Plot estimated growth factor.
.. GENERATED FROM PYTHON SOURCE LINES 247-256
.. code-block:: default
ax = plt.subplot()
plt.plot(shape_source[:, 0].numpy(), shape_source[:, 1].numpy(), '-')
imodal.Utilities.plot_C_ellipses(ax, points_growth, learned_C, R=deformed_growth_rot, scale=1.)
plt.axis(aabb_source.squared().totuple())
plt.axis('equal')
plt.show()
.. image:: /_auto_examples/leaf_growth/images/sphx_glr_plot_leaf_acropetal_imodal_004.png
:alt: plot leaf acropetal imodal
:class: sphx-glr-single-img
.. GENERATED FROM PYTHON SOURCE LINES 257-260
Recompute the learned deformation trajectory this time with the grid
deformation to visualize growth.
.. GENERATED FROM PYTHON SOURCE LINES 260-289
.. code-block:: default
# We extract the modules of the models and fill the right manifolds.
modules = imodal.DeformationModules.CompoundModule(copy.copy(model.modules))
modules.manifold.fill(model.init_manifold.clone())
silent_shape = copy.copy(modules[0])
silent_dots = copy.copy(modules[1])
global_translation = copy.copy(modules[2])
growth = copy.copy(modules[3])
# Define the deformation grid.
square_size = 1.
growth_grid_resolution = [math.floor(aabb_source.width/square_size),
math.floor(aabb_source.height/square_size)]
deformation_grid = imodal.DeformationModules.DeformationGrid(aabb_source, growth_grid_resolution)
# We construct the controls we will give will shooting.
controls = [[torch.tensor([]), torch.tensor([]), torch.tensor([]), global_translation_control, growth_control] for growth_control, global_translation_control in zip(growth_controls, global_translation_controls)]
# Reshoot.
intermediates_growth = {}
with torch.autograd.no_grad():
imodal.HamiltonianDynamic.shoot(imodal.HamiltonianDynamic.Hamiltonian([silent_shape, silent_dots, deformation_grid, global_translation, growth]), shoot_solver, shoot_it, controls=controls, intermediates=intermediates_growth)
# Store final deformation.
shoot_deformed_shape = silent_shape.manifold.gd.detach()
shoot_deformed_dots = silent_dots.manifold.gd.detach()
shoot_deformed_grid = deformation_grid.togrid()
.. GENERATED FROM PYTHON SOURCE LINES 290-292
Plot the deformation grid.
.. GENERATED FROM PYTHON SOURCE LINES 292-306
.. code-block:: default
ax = plt.subplot()
plt.plot(shape_source[:, 0].numpy(), shape_source[:, 1].numpy(), '--', color='black')
plt.plot(dots_source[:, 0].numpy(), dots_source[:, 1].numpy(), '.', color='black')
plt.plot(shape_target[:, 0].numpy(), shape_target[:, 1].numpy(), '.-', color='red')
plt.plot(dots_target[:, 0].numpy(), dots_target[:, 1].numpy(), '.', color='black')
plt.plot(shoot_deformed_shape[:, 0].numpy(), shoot_deformed_shape[:, 1].numpy())
plt.plot(shoot_deformed_dots[:, 0].numpy(), shoot_deformed_dots[:, 1].numpy(), '.')
imodal.Utilities.plot_grid(ax, shoot_deformed_grid[0], shoot_deformed_grid[1], color='xkcd:light blue', lw=0.4)
plt.axis('equal')
plt.show()
.. image:: /_auto_examples/leaf_growth/images/sphx_glr_plot_leaf_acropetal_imodal_005.png
:alt: plot leaf acropetal imodal
:class: sphx-glr-single-img
.. GENERATED FROM PYTHON SOURCE LINES 307-310
Perform curve registration using the previously learned growth factor
--------------------------------------------------------------------
.. GENERATED FROM PYTHON SOURCE LINES 313-315
Redefine deformation modules.
.. GENERATED FROM PYTHON SOURCE LINES 315-323
.. code-block:: default
global_translation = imodal.DeformationModules.GlobalTranslation(2, coeff=coeff_global)
growth = imodal.DeformationModules.ImplicitModule1(2, points_growth.shape[0], scale_growth, learned_C, coeff=coeff_growth, nu=nu, gd=(points_growth, rot_growth))
small_scale_translation = imodal.DeformationModules.ImplicitModule0(2, shape_source.shape[0], scale_small, coeff=coeff_small, nu=nu, gd=shape_source)
.. GENERATED FROM PYTHON SOURCE LINES 324-326
Redefine deformables and registration model.
.. GENERATED FROM PYTHON SOURCE LINES 326-336
.. code-block:: default
deformable_shape_source = imodal.Models.DeformablePoints(shape_source)
deformable_shape_target = imodal.Models.DeformablePoints(shape_target)
refit_model = imodal.Models.RegistrationModel([deformable_shape_source],
[global_translation, growth, small_scale_translation],
[imodal.Attachment.VarifoldAttachment(2, [50., 300.])],
lam=100)
.. GENERATED FROM PYTHON SOURCE LINES 337-339
Fitting using Torch LBFGS optimizer.
.. GENERATED FROM PYTHON SOURCE LINES 339-347
.. code-block:: default
shoot_solver = 'euler'
shoot_it = 10
costs = {}
fitter = imodal.Models.Fitter(refit_model, optimizer='torch_lbfgs')
fitter.fit([deformable_shape_target], 200, costs=costs, options={'shoot_solver': shoot_solver, 'shoot_it': shoot_it, 'line_search_fn': 'strong_wolfe'})
.. 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': 57479712.0}
1e-10
Evaluated model with costs=57479712.0
Evaluated model with costs=57384212.08517962
Evaluated model with costs=56520040.51559448
Evaluated model with costs=47695985.265625
Evaluated model with costs=26498847.1484375
Evaluated model with costs=9639712.80859375
Evaluated model with costs=5433212.6015625
Evaluated model with costs=3449238.1640625
Evaluated model with costs=2436832.2890625
Evaluated model with costs=1252332.609375
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Evaluated model with costs=976751.8046875
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Evaluated model with costs=690100.7421875
Evaluated model with costs=590372.2578125
Evaluated model with costs=544375.3515625
Evaluated model with costs=538265.0078125
================================================================================
Time: 41.00408576600239
Iteration: 0
Costs
deformation=70210.3203125
attach=468054.6875
Total cost=538265.0078125
1e-10
Evaluated model with costs=538265.0078125
Evaluated model with costs=531507.5234375
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Evaluated model with costs=461350.015625
Evaluated model with costs=458412.609375
================================================================================
Time: 81.97763606700028
Iteration: 1
Costs
deformation=96601.671875
attach=361810.9375
Total cost=458412.609375
1e-10
Evaluated model with costs=458412.609375
Evaluated model with costs=455251.7578125
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Evaluated model with costs=387350.2109375
Evaluated model with costs=385137.890625
Evaluated model with costs=384301.0078125
Evaluated model with costs=384227.71875
================================================================================
Time: 118.38591409199944
Iteration: 2
Costs
deformation=96871.46875
attach=287356.25
Total cost=384227.71875
1e-10
Evaluated model with costs=384227.71875
Evaluated model with costs=384101.3828125
Evaluated model with costs=383643.6015625
Evaluated model with costs=382828.890625
Evaluated model with costs=442592.2421875
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Evaluated model with costs=361365.2734375
Evaluated model with costs=361215.8046875
Evaluated model with costs=360878.9609375
Evaluated model with costs=360127.8828125
================================================================================
Time: 157.24498883400156
Iteration: 3
Costs
deformation=101274.7578125
attach=258853.125
Total cost=360127.8828125
1e-10
Evaluated model with costs=360127.8828125
Evaluated model with costs=358982.2734375
Evaluated model with costs=357429.8046875
Evaluated model with costs=354586.671875
Evaluated model with costs=352394.5546875
Evaluated model with costs=351348.3828125
Evaluated model with costs=349321.25
Evaluated model with costs=347591.015625
Evaluated model with costs=345267.484375
Evaluated model with costs=345146.90625
Evaluated model with costs=344610.046875
Evaluated model with costs=343939.28125
Evaluated model with costs=343318.9765625
Evaluated model with costs=342172.0234375
Evaluated model with costs=336057.828125
Evaluated model with costs=330556.96875
Evaluated model with costs=329407.953125
Evaluated model with costs=328609.71875
Evaluated model with costs=328430.359375
Evaluated model with costs=328132.6875
Evaluated model with costs=327968.0703125
Evaluated model with costs=327889.9609375
================================================================================
Time: 191.51706939500218
Iteration: 4
Costs
deformation=92889.9609375
attach=235000.0
Total cost=327889.9609375
1e-10
Evaluated model with costs=327889.9609375
Evaluated model with costs=327868.875
Evaluated model with costs=327809.5
Evaluated model with costs=327817.8984375
Evaluated model with costs=327819.234375
Evaluated model with costs=327831.3671875
Evaluated model with costs=327823.4921875
Evaluated model with costs=327809.5
Evaluated model with costs=327809.5
Evaluated model with costs=327809.5
================================================================================
Time: 207.0719389320002
Iteration: 5
Costs
deformation=92962.625
attach=234846.875
Total cost=327809.5
1e-10
Evaluated model with costs=327809.5
Evaluated model with costs=327817.8984375
Evaluated model with costs=327819.234375
Evaluated model with costs=327831.3671875
Evaluated model with costs=327823.4921875
Evaluated model with costs=327809.5
Evaluated model with costs=327809.5
Evaluated model with costs=327809.5
================================================================================
Time: 219.47133496899914
Iteration: 6
Costs
deformation=92962.625
attach=234846.875
Total cost=327809.5
================================================================================
Optimisation process exited with message: Convergence achieved.
Final cost=327809.5
Model evaluation count=137
Time elapsed = 219.4716922459993
.. GENERATED FROM PYTHON SOURCE LINES 348-350
Compute optimized deformation trajectory.
.. GENERATED FROM PYTHON SOURCE LINES 350-362
.. code-block:: default
intermediates = {}
with torch.autograd.no_grad():
deformed = refit_model.compute_deformed(shoot_solver, shoot_it, intermediates=intermediates)
deformed_shape = deformed[0][0]
deformed_growth = intermediates['states'][-1][2].gd[0]
deformed_growth_rot = intermediates['states'][-1][2].gd[1]
global_translation_controls = [control[1] for control in intermediates['controls']]
growth_controls = [control[2] for control in intermediates['controls']]
translation_controls = [control[3] for control in intermediates['controls']]
.. GENERATED FROM PYTHON SOURCE LINES 363-365
Plot results.
.. GENERATED FROM PYTHON SOURCE LINES 365-385
.. code-block:: default
plt.subplot(1, 3, 1)
plt.title("Source")
plt.plot(shape_source[:, 0].numpy(), shape_source[:, 1].numpy(), '-', color='black')
plt.axis('equal')
plt.subplot(1, 3, 2)
plt.title("Deformed source")
plt.plot(deformed_shape[:, 0], deformed_shape[:, 1], '-', color='blue')
plt.axis('equal')
plt.subplot(1, 3, 3)
plt.title("Deformed source and target")
plt.plot(shape_target[:, 0].numpy(), shape_target[:, 1].numpy(), '-', color='red')
plt.plot(deformed_shape[:, 0], deformed_shape[:, 1], '-', color='blue')
plt.axis('equal')
plt.show()
.. image:: /_auto_examples/leaf_growth/images/sphx_glr_plot_leaf_acropetal_imodal_006.png
:alt: Source, Deformed source, Deformed source and target
:class: sphx-glr-single-img
.. GENERATED FROM PYTHON SOURCE LINES 386-389
Recompute the learned deformation trajectory this time with the grid
deformation to visualize growth.
.. GENERATED FROM PYTHON SOURCE LINES 389-409
.. code-block:: default
modules = imodal.DeformationModules.CompoundModule(copy.copy(refit_model.modules))
modules.manifold.fill(refit_model.init_manifold)
square_size = 1
grid_resolution = [math.floor(aabb_source.width/square_size),
math.floor(aabb_source.height/square_size)]
deformation_grid = imodal.DeformationModules.DeformationGrid(aabb_source, growth_grid_resolution)
controls = [control[1:] for control in intermediates['controls']]
deformable_shape = imodal.Models.DeformablePoints(shape_source)
deformable_shape.silent_module.manifold.cotan = refit_model.init_manifold[0].cotan
deformable_grid = imodal.Models.DeformableGrid(aabb_source, grid_resolution)
intermediates = {}
with torch.autograd.no_grad():
imodal.Models.deformables_compute_deformed([deformable_shape, deformable_grid], modules[1:], shoot_solver, shoot_it, intermediates=intermediates, controls=controls)
.. GENERATED FROM PYTHON SOURCE LINES 410-412
Plot the growth trajectory.
.. GENERATED FROM PYTHON SOURCE LINES 412-435
.. code-block:: default
indices = [0, 3, 7, 10]
fig = plt.figure(figsize=[5.*len(indices), 5.])
for i, index in enumerate(indices):
state = intermediates['states'][index]
ax = plt.subplot(1, len(indices), i + 1)
deformable_grid.silent_module.manifold.fill_gd(state[1].gd)
grid_x, grid_y = deformable_grid.silent_module.togrid()
imodal.Utilities.plot_grid(ax, grid_x, grid_y, color='xkcd:light blue', lw=0.4)
plt.plot(shape_source[:, 0].numpy(), shape_source[:, 1].numpy(), color='black')
plt.plot(shape_target[:, 0].numpy(), shape_target[:, 1].numpy(), color='red')
plt.plot(state[0].gd[:, 0].numpy(), state[0].gd[:, 1].numpy())
plt.axis('equal')
plt.axis('off')
fig.tight_layout()
plt.show()
.. image:: /_auto_examples/leaf_growth/images/sphx_glr_plot_leaf_acropetal_imodal_007.png
:alt: plot leaf acropetal imodal
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 5 minutes 18.437 seconds)
.. _sphx_glr_download__auto_examples_leaf_growth_plot_leaf_acropetal_imodal.py:
.. only :: html
.. container:: sphx-glr-footer
:class: sphx-glr-footer-example
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_leaf_acropetal_imodal.py <plot_leaf_acropetal_imodal.py>`
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_leaf_acropetal_imodal.ipynb <plot_leaf_acropetal_imodal.ipynb>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_