OrthoMDTransform¶

class
menpofit.transform.
OrthoMDTransform
(model, transform_cls, source=None)[source]¶ Bases:
GlobalMDTransform
A transform that couples an alignment transform to a statistical model together with a global similarity transform, such that the weights of the transform are fully specified by both the weights of statistical model and the weights of the similarity transform. The model is assumed to generate an instance which is then transformed by the similarity transform; the result defines the target landmarks of the transform. If no source is provided, the mean of the model is defined as the source landmarks of the transform.
This transform (in contrast to the
GlobalMDTransform
) additionally orthonormalises both the global and the model basis against each other, ensuring that orthogonality and normalization is enforced across the unified bases. Parameters
model (
OrthoPDM
or subclass) – A linear statistical shape model (Point Distribution Model) that also has a global similarity transform that is orthonormalised with the shape bases.transform_cls (subclass of menpo.transform.Alignment) – A class of menpo.transform.Alignment. The align constructor will be called on this with the source and target landmarks. The target is set to the points generated from the model using the provide weights  the source is either given or set to the model’s mean.
source (menpo.shape.PointCloud or
None
, optional) – The source landmarks of the transform. IfNone
, the mean of the model is used.

Jp
()¶ Compute the parameters’ Jacobian, as shown in [1].
 Returns
Jp (
(n_params, n_params)
ndarray) – The parameters’ Jacobian.
References
 1
G. Papandreou and P. Maragos, “Adaptive and Constrained Algorithms for Inverse Compositional Active Appearance Model Fitting”, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2008.

apply
(x, batch_size=None, **kwargs)¶ Applies this transform to
x
.If
x
is Transformable,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

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

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)¶ Returns a TransformChain 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.
 Parameters
transform (Transform) – Transform to be applied before self
 Returns
transform (TransformChain) – The resulting transform chain.

compose_after_from_vector_inplace
(delta)¶ Composes two transforms together based on the first order approximation proposed in [1].
 Parameters
delta (
(N,)
ndarray) – Vectorized ModelDrivenTransform to be applied before self. Returns
transform (self) – self, updated to the result of the composition
References
 1
G. Papandreou and P. Maragos, “Adaptive and Constrained Algorithms for Inverse Compositional Active Appearance Model Fitting”, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2008.

compose_before
(transform)¶ Returns a TransformChain 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. Parameters
transform (Transform) – Transform to be applied after self
 Returns
transform (TransformChain) – The resulting transform chain.

copy
()¶ Generate an efficient copy of this object.
Note that Numpy arrays and other Copyable objects on
self
will be deeply copied. Dictionaries and sets will be shallow copied, and everything else will be assigned (no copy will be made).Classes that store state other than numpy arrays and immutable types should overwrite this method to ensure all state is copied.
 Returns
type(self)
– A copy of this object

d_dp
(points)¶ The derivative of this ModelDrivenTransform with respect to the parametrisation changes evaluated at points.
This is done by chaining the derivative of points wrt the source landmarks on the transform (dW/dL) together with the Jacobian of the linear model wrt its weights (dX/dp).
 Parameters
points (
(n_points, n_dims)
ndarray) – The spatial points at which the derivative should be evaluated. Returns
d_dp (
(n_points, n_parameters, n_dims)
ndarray) – The Jacobian with respect to the parametrisation.

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 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
object (
type(self)
) – 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.

pseudoinverse
()[source]¶ 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)

pseudoinverse_vector
(vector)¶ The vectorized pseudoinverse of a provided vector instance. Syntactic sugar for self.from_vector(vector).pseudoinverse.as_vector(). On ModelDrivenTransform this is especially fast  we just negate the vector provided.
 Parameters
vector (
(P,)
ndarray) – A vectorized version of self Returns
pseudoinverse_vector (
(N,)
ndarray) – The pseudoinverse of the vector provided

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.

property
has_true_inverse
¶ Whether the transform has true inverse.
 Type
bool

property
n_dims
¶ The number of dimensions that the transform supports.
 Type
int

property
n_dims_output
¶ The output of the data from the transform.
None
if the output of the transform is not dimension specific. Type
int or
None

property
n_parameters
¶ The total number of parameters.
 Type
int

property
target
¶ The current menpo.shape.PointCloud that this object produces.
 Type
menpo.shape.PointCloud