Registration

Presentation

Registration is the task of finding a suitable transformation from a source to a target shape.

A registration task must be at least parametrized with a deformation model and a loss function

The deformation model specifies constrains about the way source can be transformed to match target.
The loss function measure the discrepancy between the morphed source and the target

import skshapes as sks

# Source and target are circles, the difference between these is a translation
source = sks.Circle()
target = sks.Circle()
target.points += torch.tensor([1.0, 2.0], dtype=sks.float_dtype)
# Define loss and deformation model
loss = sks.L2Loss()
model = sks.RigidMotion()
# Initialize the registration object
r = sks.Registration(
    model=model,
    loss=loss,
)
# Fit the registration
r.fit(
    source=source,
    target=target,
)
# Print the translation parameter
print(r.translation_)

tensor([1., 2.])

Choosing a Loss function

A loss function is a way to quantify the difference between two shapes. In scikit-shapes a loss function is represented by a class that can be initialized with some hyperparameters

import skshapes as sks

l1_loss = sks.LpLoss(p=1)

Linear combination of loss function are valid loss functions:

import skshapes as sks

custom_loss = 2 * sks.LandmarkLoss() + sks.NearestNeighborsLoss()

Some losses requires that source and target fulfill certains conditions:

for polydatas

Loss function	Description	Restrictions
`LpLoss`	Lp loss for vertices	`source` and `target` must be in correspondence
`L2Loss`	L2 loss for vertices	`source` and `target` must be in correspondence
`LandmarkLoss`	Lp loss for landmarks	`source` and `target` must have corresponding landmarks
`NearestNeighborsLoss`	Nearest neighbors distance	NA

for images

Loss function	Description	Restrictions

Choosing a Registration model

Deformation model	Description
`RigidMotion`	Rotation + translation
`AffineDeformation`	Affine transformation
`IntrinsicDeformation`	Sequence of
`ExtrinsicDeformation`	Distord the ambiant space to make the shape move