AlignmentSimilarity¶

class
menpo.transform.
AlignmentSimilarity
(source, target, rotation=True, allow_mirror=False)[source]¶ Bases:
HomogFamilyAlignment
,Similarity
Infers the similarity transform relating two vectors with the same dimensionality. This is simply the procrustes alignment of the source to the target.
Parameters:  source (
PointCloud
) – The source pointcloud instance used in the alignment  target (
PointCloud
) – The target pointcloud instance used in the alignment  rotation (bool, optional) – If
False
, the rotation component of the similarity transform is not inferred.  allow_mirror (bool, optional) – If
True
, the Kabsch algorithm check is not performed, and mirroring of the Rotation matrix is permitted.

aligned_source
()¶ The result of applying
self
tosource
Type: PointCloud

alignment_error
()¶ The Frobenius Norm of the difference between the target and the aligned source.
Type: float

apply
(x, batch_size=None, **kwargs)¶ Applies this transform to
x
.If
x
isTransformable
,x
will be handed this transform object to transform itself nondestructively (a transformed copy of the object will be returned).If not,
x
is assumed to be an ndarray. The transformation will be nondestructive, returning the transformed version.Any
kwargs
will be passed to the specific transform_apply()
method.Parameters:  x (
Transformable
or(n_points, n_dims)
ndarray) – The array or object to be transformed.  batch_size (int, optional) – If not
None
, this determines how many items from the numpy array will be passed through the transform at a time. This is useful for operations that require large intermediate matrices to be computed.  kwargs (dict) – Passed through to
_apply()
.
Returns: transformed (
type(x)
) – The transformed object or array x (

apply_inplace
(*args, **kwargs)¶ Deprecated as public supported API, use the nonmutating apply() instead.
For internal performancespecific uses, see _apply_inplace().

as_non_alignment
()[source]¶ Returns a copy of this similarity without it’s alignment nature.
Returns: transform ( Similarity
) – A version of this similarity with the same transform behavior but without the alignment logic.

as_vector
(**kwargs)¶ Returns a flattened representation of the object as a single vector.
Returns: vector ((N,) ndarray) – The core representation of the object, flattened into a single vector. Note that this is always a view back on to the original object, but is not writable.

compose_after
(transform)¶ A
Transform
that represents this transform composed after the given transform:c = a.compose_after(b) c.apply(p) == a.apply(b.apply(p))
a
andb
are left unchanged.This corresponds to the usual mathematical formalism for the compose operator,
o
.An attempt is made to perform native composition, but will fall back to a
TransformChain
as a last resort. Seecomposes_with
for a description of how the mode of composition is decided.Parameters: transform ( Transform
) – Transform to be applied beforeself
Returns: transform ( Transform
orTransformChain
) – If the composition was native, a single newTransform
will be returned. If not, aTransformChain
is returned instead.

compose_after_inplace
(transform)¶ Update
self
so that it represents this transform composed after the given transform:a_orig = a.copy() a.compose_after_inplace(b) a.apply(p) == a_orig.apply(b.apply(p))
a
is permanently altered to be the result of the composition.b
is left unchanged.Parameters: transform ( composes_inplace_with
) – Transform to be applied beforeself
Raises: ValueError
– Iftransform
isn’t an instance ofcomposes_inplace_with

compose_before
(transform)¶ A
Transform
that represents this transform composed before the given transform:c = a.compose_before(b) c.apply(p) == b.apply(a.apply(p))
a
andb
are left unchanged.An attempt is made to perform native composition, but will fall back to a
TransformChain
as a last resort. Seecomposes_with
for a description of how the mode of composition is decided.Parameters: transform ( Transform
) – Transform to be applied afterself
Returns: transform ( Transform
orTransformChain
) – If the composition was native, a single newTransform
will be returned. If not, aTransformChain
is returned instead.

compose_before_inplace
(transform)¶ Update
self
so that it represents this transform composed before the given transform:a_orig = a.copy() a.compose_before_inplace(b) a.apply(p) == b.apply(a_orig.apply(p))
a
is permanently altered to be the result of the composition.b
is left unchanged.Parameters: transform ( composes_inplace_with
) – Transform to be applied afterself
Raises: ValueError
– Iftransform
isn’t an instance ofcomposes_inplace_with

copy
()¶ Generate an efficient copy of this
HomogFamilyAlignment
.Returns: new_transform ( type(self)
) – A copy of this object

decompose
()¶ Decompose this transform into discrete Affine Transforms.
Useful for understanding the effect of a complex composite transform.
Returns: transforms (list of DiscreteAffine
) – Equivalent to this affine transform, such thatreduce(lambda x, y: x.chain(y), self.decompose()) == self

from_vector
(vector)¶ Build a new instance of the object from its vectorized state.
self
is used to fill out the missing state required to rebuild a full object from it’s standardized flattened state. This is the default implementation, which is adeepcopy
of the object followed by a call tofrom_vector_inplace()
. This method can be overridden for a performance benefit if desired.Parameters: vector ( (n_parameters,)
ndarray) – Flattened representation of the object.Returns: transform ( Homogeneous
) – An new instance of this class.

from_vector_inplace
(vector)¶ Deprecated. Use the nonmutating API,
from_vector
.For internal usage in performancesensitive spots, see _from_vector_inplace()
Parameters: vector ( (n_parameters,)
ndarray) – Flattened representation of this object

has_nan_values
()¶ Tests if the vectorized form of the object contains
nan
values or not. This is particularly useful for objects with unknown values that have been mapped tonan
values.Returns: has_nan_values (bool) – If the vectorized object contains nan
values.

init_identity
(n_dims)¶ Creates an identity transform.
Parameters: n_dims (int) – The number of dimensions. Returns: identity ( Similarity
) – The identity matrix transform.

pseudoinverse
()¶ The pseudoinverse of the transform  that is, the transform that results from swapping source and target, or more formally, negating the transforms parameters. If the transform has a true inverse this is returned instead.
Returns: transform ( type(self)
) – The inverse of this transform.

pseudoinverse_vector
(vector)¶ The vectorized pseudoinverse of a provided vector instance. Syntactic sugar for:
self.from_vector(vector).pseudoinverse().as_vector()
Can be much faster than the explict call as object creation can be entirely avoided in some cases.
Parameters: vector ( (n_parameters,)
ndarray) – A vectorized version ofself
Returns: pseudoinverse_vector ( (n_parameters,)
ndarray) – The pseudoinverse of the vector provided

set_h_matrix
(value, copy=True, skip_checks=False)¶ Deprecated Deprecated  do not use this method  you are better off just creating a new transform!
Updates
h_matrix
, optionally performing sanity checks.Note that it won’t always be possible to manually specify the
h_matrix
through this method, specifically if changing theh_matrix
could change the nature of the transform. Seeh_matrix_is_mutable
for how you can discover if theh_matrix
is allowed to be set for a given class.Parameters:  value (ndarray) – The new homogeneous matrix to set.
 copy (bool, optional) – If
False
, do not copy the h_matrix. Useful for performance.  skip_checks (bool, optional) – If
True
, skip checking. Useful for performance.
Raises: NotImplementedError
– Ifh_matrix_is_mutable
returnsFalse
.

set_target
(new_target)¶ Update this object so that it attempts to recreate the
new_target
.Parameters: new_target ( PointCloud
) – The new target that this object should try and regenerate.

composes_with
¶ Any Homogeneous can compose with any other Homogeneous.

h_matrix
¶ The homogeneous matrix defining this transform.
Type: (n_dims + 1, n_dims + 1)
ndarray

h_matrix_is_mutable
¶ Deprecated
True
iffset_h_matrix()
is permitted on this type of transform.If this returns
False
calls toset_h_matrix()
will raise aNotImplementedError
.Type: bool

has_true_inverse
¶ The pseudoinverse is an exact inverse.
Type: True

linear_component
¶ The linear component of this affine transform.
Type: (n_dims, n_dims)
ndarray

n_dims_output
¶ The output of the data from the transform.
Type: int

n_parameters
¶ Number of parameters of Similarity
2D Similarity  4 parameters
[(1 + a), b, tx] [b, (1 + a), ty]
3D Similarity: Currently not supported
Returns: n_parameters (int) – The transform parameters Raises: DimensionalityError, NotImplementedError – Only 2D transforms are supported.

source
¶ The source
PointCloud
that is used in the alignment.The source is not mutable.
Type: PointCloud

target
¶ The current
PointCloud
that this object produces.To change the target, use
set_target()
.Type: PointCloud

translation_component
¶ The translation component of this affine transform.
Type: (n_dims,)
ndarray
 source (