deepali.spatial.linear

Linear transformation models.

Module Contents

Classes

HomogeneousTransform	Arbitrary homogeneous coordinate transformation.
Translation	Translation.
EulerRotation	Euler rotation.
QuaternionRotation	Quaternion based rotation in 3D.
IsotropicScaling	Isotropic scaling.
AnisotropicScaling	Anisotropic scaling.
Shearing	Shear transformation.
RigidTransform	Rigid transformation.
RigidQuaternionTransform	Rigid transformation parameterized by rotation quaternion.
SimilarityTransform	Similarity transformation with isotropic scaling.
AffineTransform	Affine transformation without shearing.
FullAffineTransform	Affine transformation including shearing.

class HomogeneousTransform(grid: deepali.core.grid.Grid, groups: Optional[int] = None, params: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True)

Arbitrary homogeneous coordinate transformation.

Initialize transformation parameters.

Parameters

• grid – Grid domain on which transformation is defined.

• groups – Number of transformations. Must be either 1 or equal to batch size.

• params – Homogeneous transform as tensor of shape (N, D, D + 1).

property data_shape: torch.Size

Get shape of transformation parameters tensor.

matrix_(arg: torch.Tensor) → HomogeneousTransform

Set transformation matrix.

tensor() → torch.Tensor

Get tensor representation of this transformation

Returns

Batch of homogeneous transformation matrices as tensor of shape (N, D, D + 1).

extra_repr() → str

Print current transformation.

class Translation(grid: deepali.core.grid.Grid, groups: Optional[int] = None, params: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True)

Translation.

Initialize transformation parameters.

Parameters

• grid – Grid domain on which transformation is defined.

• groups – Number of transformations. Must be either 1 or equal to batch size.

• params – Translation offsets as tensor of shape (N, D) or (N, D, 1).

property data_shape: torch.Size

Get shape of transformation parameters tensor.

offset() → torch.Tensor

Get current translation offset in cube units.

offset_(arg: torch.Tensor) → Translation

Reset parameters to given translation in cube units.

tensor() → torch.Tensor

Get tensor representation of this transformation

Returns

Batch of homogeneous transformation matrices as tensor of shape (N, D, 1).

extra_repr() → str

Print current transformation.

class EulerRotation(grid: deepali.core.grid.Grid, groups: Optional[int] = None, params: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True, order: Optional[str] = None)

Euler rotation.

Initialize transformation parameters.

Parameters

• grid – Grid domain on which transformation is defined.

• groups – Number of transformations. Must be 1 or equal to batch size.

• params – Rotation angles in degrees. This parameterization is adopted from MIRTK and ensures that rotation angles and scaling factors (percentage) are within a similar range of magnitude which is useful for direct optimization of these parameters. If parameters are predicted by a callable torch.nn.Module, different output activations may be chosen before converting these to degrees.

• order – Order in which to compose elementary rotations. For example in 3D, “zxz” means that the first rotation occurs about z, the second about x, and the third rotation about z again. In 2D, this argument is ignored and a single rotation about z (plane normal) is applied.

property data_shape: torch.Size

Get shape of transformation parameters tensor.

property nangles: int

Number of Euler angles.

angles() → torch.Tensor

Get Euler angles in radians.

angles_(arg: torch.Tensor) → EulerRotation

Reset parameters to given Euler angles in radians.

matrix_(arg: torch.Tensor) → EulerRotation

Set rotation angles from rotation matrix.

tensor() → torch.Tensor

Get tensor representation of this transformation

Returns

Batch of homogeneous transformation matrices as tensor of shape (N, D, D).

extra_repr() → str

Print current transformation.

class QuaternionRotation(grid: deepali.core.grid.Grid, groups: Optional[int] = None, params: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True)

Quaternion based rotation in 3D.

Initialize transformation parameters.

Parameters

• grid – Grid domain on which transformation is defined.

• groups – Number of transformations. Must be either 1 or equal to batch size.

• params – (normalized quaternion as 2-dimensional tensor of (N, 4).

property data_shape: torch.Size

Get shape of transformation parameters tensor.

reset_parameters() → None

Reset transformation parameters.

quaternion() → torch.Tensor

Get rotation quaternion.

quaternion_(arg: torch.Tensor) → QuaternionRotation

Set rotation quaternion.

matrix_(arg: torch.Tensor) → QuaternionRotation

Set rotation quaternion from rotation matrix.

tensor() → torch.Tensor

Get tensor representation of this transformation

Returns

Batch of homogeneous transformation matrices as tensor of shape (N, D, D).

extra_repr() → str

Print current transformation.

class IsotropicScaling(grid: deepali.core.grid.Grid, groups: Optional[int] = None, params: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True)

Isotropic scaling.

Initialize transformation parameters.

Parameters

• grid – Grid domain on which transformation is defined.

• groups – Number of transformations. Must be either 1 or equal to batch size.

• params – Isotropic scaling factor as a percentage. This parameterization is adopted from MIRTK and ensures that rotation angles in degrees and scaling factors are within a similar range of magnitude which is useful for direct optimization of these parameters. If parameters are predicted by a callable torch.nn.Module, different output activations may be chosen before converting these to percentages (i.e., multiplied by 100).

property data_shape: torch.Size

Get shape of transformation parameters tensor.

reset_parameters() → None

Reset transformation parameters.

scales() → torch.Tensor

Get scaling factors.

scales_(arg: torch.Tensor) → IsotropicScaling

Set transformation parameters from scaling factors.

tensor() → torch.Tensor

Get tensor representation of this transformation

Returns

Batch of homogeneous transformation matrices as tensor of shape (N, D, D).

extra_repr() → str

Print current transformation.

class AnisotropicScaling(grid: deepali.core.grid.Grid, groups: Optional[int] = None, params: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True)

Anisotropic scaling.

Initialize transformation parameters.

Parameters

• grid – Grid domain on which transformation is defined.

• groups – Number of transformations. Must be either 1 or equal to batch size.

• params – Anisotropic scaling factors as percentages. This parameterization is adopted from MIRTK and ensures that rotation angles in degrees and scaling factors are within a similar range of magnitude which is useful for direct optimization of these parameters. If parameters are predicted by a callable torch.nn.Module, different output activations may be chosen before converting these to percentages (i.e., multiplied by 100).

property data_shape: torch.Size

Get shape of transformation parameters tensor.

reset_parameters() → None

Reset transformation parameters.

scales() → torch.Tensor

Get scaling factors.

scales_(arg: torch.Tensor) → AnisotropicScaling

Set transformation parameters from scaling factors.

tensor() → torch.Tensor

Get tensor representation of this transformation

Returns

Batch of homogeneous transformation matrices as tensor of shape (N, D, D).

extra_repr() → str

Print current transformation.

class Shearing(grid: deepali.core.grid.Grid, groups: Optional[int] = None, params: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True)

Shear transformation.

Initialize transformation parameters.

Parameters

• grid – Grid domain on which transformation is defined.

• groups – Number of transformations. Must be either 1 or equal to batch size.

• params – Shearing angles in degrees. This parameterization is adopted from MIRTK and ensures that rotation angles and scaling factors (percentage) are within a similar range of magnitude which is useful for direct optimization of these parameters. If parameters are predicted by a callable torch.nn.Module, different output activations may be chosen before converting these to degrees.

property data_shape: torch.Size

Get shape of transformation parameters tensor.

property nangles: int

Number of shear angles.

angles() → torch.Tensor

Get shear angles in radians.

angles_(arg: torch.Tensor) → Shearing

Set transformation parameters from shear angles in radians.

tensor() → torch.Tensor

Get tensor representation of this transformation

Returns

Batch of homogeneous transformation matrices as tensor of shape (N, D, D).

extra_repr() → str

Print current transformation.

class RigidTransform(grid: deepali.core.grid.Grid, groups: Optional[int] = None, rotation: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True, translation: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True)

Rigid transformation.

Initialize transformation parameters.

Parameters

• grid – Domain with respect to which transformation is defined.

• groups – Number of transformations N.

• rotation – Parameters of EulerRotation.

• translation – Parameters of Translation.

class RigidQuaternionTransform(grid: deepali.core.grid.Grid, groups: Optional[int] = None, rotation: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True, translation: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True)

Rigid transformation parameterized by rotation quaternion.

Initialize transformation parameters.

Parameters

• grid – Domain with respect to which transformation is defined.

• groups – Number of transformations N.

• rotation – Parameters of QuaternionRotation.

• translation – Parameters of Translation.

class SimilarityTransform(grid: deepali.core.grid.Grid, groups: Optional[int] = None, scaling: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True, rotation: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True, translation: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True)

Similarity transformation with isotropic scaling.

Initialize transformation parameters.

Parameters

• grid – Domain with respect to which transformation is defined.

• groups – Number of transformations N.

• scaling – Parameters of IsotropicScaling.

• rotation – Parameters of EulerRotation.

• translation – Parameters of Translation.

class AffineTransform(grid: deepali.core.grid.Grid, groups: Optional[int] = None, scaling: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True, rotation: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True, translation: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True)

Affine transformation without shearing.

Initialize transformation parameters.

Parameters

• grid – Domain with respect to which transformation is defined.

• groups – Number of transformations N.

• scaling – Parameters of AnisotropicScaling.

• rotation – Parameters of EulerRotation.

• translation – Parameters of Translation.

class FullAffineTransform(grid: deepali.core.grid.Grid, groups: Optional[int] = None, scaling: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True, shearing: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True, rotation: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True, translation: Optional[Union[bool, torch.Tensor, Callable[Ellipsis, torch.Tensor]]] = True)

Affine transformation including shearing.

Initialize transformation parameters.

Parameters

• grid – Domain with respect to which transformation is defined.

• groups – Number of transformations N.

• scaling – Parameters of AnisotropicScaling.

• shearing – Parameters of Shearing.

• rotation – Parameters of EulerRotation.

• translation – Parameters of Translation.