Homogeneous

class menpo.transform.homogeneous.Homogeneous(h_matrix, copy=True, skip_checks=False)

Bases: ComposableTransform, Vectorizable, VComposable, VInvertible

A simple n-dimensional homogeneous transformation.

Adds a unit homogeneous coordinate to points, performs the dot product, re-normalizes by division by the homogeneous coordinate, and returns the result.

Can be composed with another Homogeneous, so long as the dimensionality matches.

Parameters:

h_matrix : (n_dims + 1, n_dims + 1) ndarray

The homogeneous matrix defining this transform.

copy : bool, optional

If False avoid copying h_matrix. Useful for performance.

skip_checks : bool, optional

If True avoid sanity checks on the h_matrix. Useful for performance.

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_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()

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 using deepcopy() instead.

Returns:

transform : type(self)

A copy fo the transform with the same h_matrix.

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.

composes_inplace_with

Homogeneous can swallow composition with any other Homogeneous, subclasses will have to override and be more specific.

composes_with

Any Homogeneous can compose with any other Homogeneous.

h_matrix_is_mutable

True iff set_h_matrix() is permitted on this type of transform. If this returns False calls to :meth:``set_h_matrix` will raise a NonImplimentedError.

Type:bool

n_parameters

The length of the vector that this object produces.

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)