OrthoMDTransform

class menpofit.transform.OrthoMDTransform(model, transform_cls, source=None)

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. If None, 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 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.

• 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 non-mutating apply() instead.

For internal performance-specific 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 and b 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 and b 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 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

object (type(self)) – An new instance of this class.

from_vector_inplace(vector)

Deprecated. Use the non-mutating API, from_vector.

For internal usage in performance-sensitive 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 to nan values.

Returns

has_nan_values (bool) – If the vectorized object contains nan values.

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)

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 n_points

The number of points on the target.

Type

int

property target

The current menpo.shape.PointCloud that this object produces.

Type

menpo.shape.PointCloud