Rigid alignment in 2D

This is an example of rigid alignment in 2D for meshes with points in dense correspondence.

import pyvista as pv
import torch
from pyvista import examples

import skshapes as sks

We load two toy shapes in 2D: wireframe meshes representing circles. To be able to see orientations, we remove one edge from each circle. The points of both circles are in dense correspondence.

source = sks.PolyData(examples.download_human())
target = sks.PolyData(examples.download_doorman())

# Load the circles
source = sks.Circle()
target = sks.Circle()

# Remove one edge from each circle
source.edges = source.edges[:-1]
target.edges = target.edges[:-1]

/opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/skshapes/input_validation/converters.py:102: UserWarning: Mesh has been cleaned and points were removed. point_data is ignored.
  return func(*new_args, **kwargs)

Rigid motion are parametrized by a rotation and a translation. We apply a rigid motion to one of the circles.

theta = 0.75 * torch.pi  # angle in radians
translation = torch.tensor([1.0, 0.8])  # translation in the plane

# In 2D, the parameter is a 3D vector: [theta, tx, ty]
parameter = torch.cat([torch.tensor([theta]), translation])

# Apply the rigid motion to the circle
rigid_motion = sks.RigidMotion()
source = rigid_motion.morph(
    shape=source,
    parameter=torch.cat([torch.tensor([theta]), translation]),
).morphed_shape

plotter = pv.Plotter()
plotter.add_mesh(
    source.to_pyvista(),
    color="blue",
    show_edges=True,
    line_width=5,
    label="Source",
)
plotter.add_mesh(
    target.to_pyvista(),
    color="red",
    show_edges=True,
    line_width=5,
    label="Target",
)
plotter.add_legend()
plotter.show()

Static Scene

Interactive Scene

Registration

from skshapes.loss import L2Loss
from skshapes.morphing import RigidMotion
from skshapes.tasks import Registration

loss = L2Loss()
model = RigidMotion(n_steps=5)

registration = Registration(
    model=model,
    loss=loss,
    n_iter=5,
    verbose=True,
)


registration.fit(source=source, target=target)

Initial loss : 4.99e+01
  = 4.99e+01 + 1 * 0.00e+00 (fidelity + regularization_weight * regularization)
Loss after 1 iteration(s) : 4.30e-13
  = 4.30e-13 + 1 * 0.00e+00 (fidelity + regularization_weight * regularization)
Loss after 2 iteration(s) : 4.30e-13
  = 4.30e-13 + 1 * 0.00e+00 (fidelity + regularization_weight * regularization)
Loss after 3 iteration(s) : 4.30e-13
  = 4.30e-13 + 1 * 0.00e+00 (fidelity + regularization_weight * regularization)
Loss after 4 iteration(s) : 4.30e-13
  = 4.30e-13 + 1 * 0.00e+00 (fidelity + regularization_weight * regularization)
Loss after 5 iteration(s) : 4.30e-13
  = 4.30e-13 + 1 * 0.00e+00 (fidelity + regularization_weight * regularization)

<skshapes.tasks.registration.Registration object at 0x7ff40d655050>

Animation

path = registration.path_
plotter = pv.Plotter()
actor = plotter.add_mesh(
    source.to_pyvista(), color="blue", show_edges=True, line_width=5
)
plotter.add_mesh(
    target.to_pyvista(), color="red", show_edges=True, line_width=5
)
plotter.open_gif("rigid_registration.gif", fps=3)
for _i, shape in enumerate(path):
    plotter.remove_actor(actor)
    actor = plotter.add_mesh(
        shape.to_pyvista(), color="blue", show_edges=True, line_width=5
    )
    plotter.write_frame()

plotter.close()