algorithms.registration.affine¶

Module: `algorithms.registration.affine`¶

Inheritance diagram for `nipy.algorithms.registration.affine`:

Classes¶

`Affine`¶

Bases: `Transform`

apply(xyz)
as_affine(dtype='double')
compose(other)

Compose this transform onto another

Parameters:
otherTransform

transform that we compose onto

Returns:
composed_transformTransform

a transform implementing the composition of self on other

copy()
from_matrix44(aff)

Convert a 4x4 matrix describing an affine transform into a 12-sized vector of natural affine parameters: translation, rotation, log-scale, pre-rotation (to allow for shearing when combined with non-unitary scales). In case the transform has a negative determinant, set the _direct attribute to False.

inv()

Return the inverse affine transform.

property is_direct
property param
param_inds = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
property pre_rotation
property precond
property rotation
property scaling
property translation

`Affine2D`¶

Bases: `Affine`

apply(xyz)
as_affine(dtype='double')
compose(other)

Compose this transform onto another

Parameters:
otherTransform

transform that we compose onto

Returns:
composed_transformTransform

a transform implementing the composition of self on other

copy()
from_matrix44(aff)

Convert a 4x4 matrix describing an affine transform into a 12-sized vector of natural affine parameters: translation, rotation, log-scale, pre-rotation (to allow for shearing when combined with non-unitary scales). In case the transform has a negative determinant, set the _direct attribute to False.

inv()

Return the inverse affine transform.

property is_direct
property param
param_inds = [0, 1, 5, 6, 7, 11]
property pre_rotation
property precond
property rotation
property scaling
property translation

`Rigid`¶

Bases: `Affine`

apply(xyz)
as_affine(dtype='double')
compose(other)

Compose this transform onto another

Parameters:
otherTransform

transform that we compose onto

Returns:
composed_transformTransform

a transform implementing the composition of self on other

copy()
from_matrix44(aff)

Convert a 4x4 matrix describing a rigid transform into a 12-sized vector of natural affine parameters: translation, rotation, log-scale, pre-rotation (to allow for pre-rotation when combined with non-unitary scales). In case the transform has a negative determinant, set the _direct attribute to False.

inv()

Return the inverse affine transform.

property is_direct
property param
param_inds = [0, 1, 2, 3, 4, 5]
property pre_rotation
property precond
property rotation
property scaling
property translation

`Rigid2D`¶

Bases: `Rigid`

apply(xyz)
as_affine(dtype='double')
compose(other)

Compose this transform onto another

Parameters:
otherTransform

transform that we compose onto

Returns:
composed_transformTransform

a transform implementing the composition of self on other

copy()
from_matrix44(aff)

Convert a 4x4 matrix describing a rigid transform into a 12-sized vector of natural affine parameters: translation, rotation, log-scale, pre-rotation (to allow for pre-rotation when combined with non-unitary scales). In case the transform has a negative determinant, set the _direct attribute to False.

inv()

Return the inverse affine transform.

property is_direct
property param
param_inds = [0, 1, 5]
property pre_rotation
property precond
property rotation
property scaling
property translation

`Similarity`¶

Bases: `Affine`

apply(xyz)
as_affine(dtype='double')
compose(other)

Compose this transform onto another

Parameters:
otherTransform

transform that we compose onto

Returns:
composed_transformTransform

a transform implementing the composition of self on other

copy()
from_matrix44(aff)

Convert a 4x4 matrix describing a similarity transform into a 12-sized vector of natural affine parameters: translation, rotation, log-scale, pre-rotation (to allow for pre-rotation when combined with non-unitary scales). In case the transform has a negative determinant, set the _direct attribute to False.

inv()

Return the inverse affine transform.

property is_direct
property param
param_inds = [0, 1, 2, 3, 4, 5, 6]
property pre_rotation
property precond
property rotation
property scaling
property translation

`Similarity2D`¶

Bases: `Similarity`

apply(xyz)
as_affine(dtype='double')
compose(other)

Compose this transform onto another

Parameters:
otherTransform

transform that we compose onto

Returns:
composed_transformTransform

a transform implementing the composition of self on other

copy()
from_matrix44(aff)

Convert a 4x4 matrix describing a similarity transform into a 12-sized vector of natural affine parameters: translation, rotation, log-scale, pre-rotation (to allow for pre-rotation when combined with non-unitary scales). In case the transform has a negative determinant, set the _direct attribute to False.

inv()

Return the inverse affine transform.

property is_direct
property param
param_inds = [0, 1, 5, 6]
property pre_rotation
property precond
property rotation
property scaling
property translation

Functions¶

nipy.algorithms.registration.affine.inverse_affine(affine)

Computes a scaling vector pc such that, if p=(u,r,s,q) represents affine transformation parameters, where u is a translation, r and q are rotation vectors, and s is the vector of log-scales, then all components of (p/pc) are roughly comparable to the translation component.

To that end, we use a radius parameter which represents the ‘typical size’ of the object being registered. This is used to reformat the parameter vector (translation+rotation+scaling+pre-rotation) so that each element roughly represents a variation in mm.

nipy.algorithms.registration.affine.rotation_mat2vec(R)

Rotation vector from rotation matrix R

Parameters:
R(3,3) array-like

Rotation matrix

Returns:
vec(3,) array

Rotation vector, where norm of vec is the angle `theta`, and the axis of rotation is given by `vec / theta`

nipy.algorithms.registration.affine.rotation_vec2mat(r)

The rotation matrix is given by the Rodrigues formula:

R = Id + sin(theta)*Sn + (1-cos(theta))*Sn^2

with:

0 -nz ny

Sn = nz 0 -nx
-ny

nx 0

where n = r / ||r||

In case the angle ||r|| is very small, the above formula may lead to numerical instabilities. We instead use a Taylor expansion around theta=0:

R = I + sin(theta)/tetha Sr + (1-cos(theta))/teta2 Sr^2

R = I + (1-theta2/6)*Sr + (1/2-theta2/24)*Sr^2

To avoid numerical instabilities, an upper threshold is applied to the angle. It is chosen to be a multiple of 2*pi, hence the resulting rotation is then the identity matrix. This strategy warrants that the output matrix is a continuous function of the input vector.

nipy.algorithms.registration.affine.slices2aff(slices)

Return affine from start, step of sequence slices of slice objects

Parameters:
slicessequence of slice objects
Returns:
affndarray

If `N = len(slices)` then affine is shape (N+1, N+1) with diagonal given by the `step` attribute of the slice objects (where None corresponds to 1), and the :N elements in the last column are given by the `start` attribute of the slice objects

Examples

```>>> slices2aff([slice(None), slice(None)])
array([[ 1.,  0.,  0.],
[ 0.,  1.,  0.],
[ 0.,  0.,  1.]])
>>> slices2aff([slice(2, 3, 4), slice(3, 4, 5), slice(4, 5, 6)])
array([[ 4.,  0.,  0.,  2.],
[ 0.,  5.,  0.,  3.],
[ 0.,  0.,  6.,  4.],
[ 0.,  0.,  0.,  1.]])
```
nipy.algorithms.registration.affine.subgrid_affine(affine, slices)

Return dot prodoct of affine and affine resulting from slices

Parameters:
affinearray-like

Affine to apply on right of affine resulting from slices

slicessequence of slice objects

Slices generating (N+1, N+1) affine from `slices2aff`, where ```N = len(slices)```

Returns:
affndarray

result of `np.dot(affine, slice_affine)` where `slice_affine` is affine resulting from `slices2aff(slices)`.

Raises:
ValueErrorif the `slice_affine` contains non-integer values
nipy.algorithms.registration.affine.threshold(x, th)
nipy.algorithms.registration.affine.to_matrix44(t)

t is a vector of affine transformation parameters with size at least 6.

size < 6 ==> error size == 6 ==> t is interpreted as translation + rotation size == 7 ==> t is interpreted as translation + rotation + isotropic scaling 7 < size < 12 ==> error size >= 12 ==> t is interpreted as translation + rotation + scaling + pre-rotation