AlignmentTranslation

class menpo.transform.homogeneous.translation.AlignmentTranslation(source, target)

Bases: HomogFamilyAlignment, Translation

apply(x, **kwargs)

Applies this transform to x.

If x is Transformable, x will be handed this transform object to transform itself non-destructively (a transformed copy of the object will be returned).

If not, x is assumed to be an ndarray. The transformation will be non-destructive, 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.

kwargs : dict

Passed through to _apply().

Returns:

transformed : type(x)

The transformed object or array

apply_inplace(x, **kwargs)

Applies this transform to a Transformable x destructively.

Any kwargs will be passed to the specific transform _apply() method.

Parameters:

x : Transformable

The Transformable object to be transformed.

kwargs : dict

Passed through to _apply().

Returns:

transformed : type(x)

The transformed object

as_non_alignment()

Returns a copy of this translation without it’s alignment nature.

Returns:

transform : Translation

A version of this transform 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 and b 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. See composes_with for a description of how the mode of composition is decided.

Parameters:

transform : Transform

Transform to be applied before self

Returns:

transform : Transform or TransformChain

If the composition was native, a single new Transform will be returned. If not, a TransformChain is returned instead.

compose_after_inplace(transform)

Update self so that it represents this transform composed after the given transform:

a_orig = deepcopy(a)
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 before self

Raises:

ValueError :

If transform isn’t an instance of composes_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 and b are left unchanged.

An attempt is made to perform native composition, but will fall back to a TransformChain as a last resort. See composes_with for a description of how the mode of composition is decided.

Parameters:

transform : Transform

Transform to be applied after self

Returns:

transform : Transform or TransformChain

If the composition was native, a single new Transform will be returned. If not, a TransformChain is returned instead.

compose_before_inplace(transform)

Update self so that it represents this transform composed before the given transform:

a_orig = deepcopy(a)
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 after self

Raises:

ValueError :

If transform isn’t an instance of composes_inplace_with

copy()

Returns an efficient copy of this Homogeneous family transform (i.e. one with the same homogeneous matrix). If you need all state to be perfectly replicated, consider deepcopy() instead.

Returns:

h_transform: :map:`Homogeneous` or :map:`Homogeneous` subclass :

A copy fo the transform with the same h_matrix.

d_dx(points)

The first order derivative of this Affine transform wrt spatial changes evaluated at points.

The Jacobian for a given point (for 2D) is of the form:

Jx = [(1 + a),     -b  ]
Jy = [   b,     (1 + a)]
J =  [Jx, Jy] = [[(1 + a), -b], [b, (1 + a)]]

where a and b come from:

W(x;p) = [1 + a -b tx] [x]

[b 1 + a ty] [y]

[1]

Hence it is simply the linear component of the transform.

Parameters:

points: ndarray shape (n_points, n_dims) :

The spatial points at which the derivative should be evaluated.

Returns:

d_dx: (1, n_dims, n_dims) ndarray :

The jacobian wrt spatial changes.

d_dx[0, j, k] is the scalar differential change that the j’th dimension of the i’th point experiences due to a first order change in the k’th dimension.

Note that because the jacobian is constant across space the first axis is length 1 to allow for broadcasting.

decompose()

A DiscreteAffine is already maximally decomposed - return a copy of self in a list.

Returns:

transform : DiscreteAffine

Deep copy of self.

from_vector(vector)

Build a new instance of the object from it’s 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 which is a deepcopy of the object followed by a call to from_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 : type(self)

An new instance of this class.

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 of self

Returns:

pseudoinverse_vector : (n_parameters,) ndarray

The pseudoinverse of the vector provided

set_h_matrix(value, copy=True, skip_checks=False)

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 the h_matrix could change the nature of the transform. See h_matrix_is_mutable for how you can discover if the h_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 :

If h_matrix_is_mutable returns False.

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.

view(**kwargs)

View the object using the default rendering engine figure handling. For example, the default behaviour for Matplotlib is that all draw commands are applied to the same figure object.

Parameters:

kwargs : dict

Passed through to specific rendering engine.

Returns:

viewer : Renderer

The renderer instantiated.

view_new(**kwargs)

View the object on a new figure.

Parameters:

kwargs : dict

Passed through to specific rendering engine.

Returns:

viewer : Renderer

The renderer instantiated.

view_on(figure_id, **kwargs)

View the object on a a specific figure specified by the given id.

Parameters:

figure_id : object

A unique identifier for a figure.

kwargs : dict

Passed through to specific rendering engine.

Returns:

viewer : Renderer

The renderer instantiated.

aligned_source

The result of applying self to source

Type:PointCloud

alignment_error

The Frobenius Norm of the difference between the target and the aligned source.

Type:float

composes_with

Any Homogeneous can compose with any other Homogeneous.

linear_component

The linear component of this affine transform.

Type:(n_dims, n_dims) ndarray

n_dims

The number of dimensions of the target.

Type:int

n_parameters

The number of parameters: n_dims

Type:int

n_points

The number of points on the target.

Type:int

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.

Type:type(self)

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