DifferentiablePiecewiseAffine

class menpofit.transform.DifferentiablePiecewiseAffine(source, target)

Bases: CachedPWA, DL, DX

A differentiable Piecewise Affine Transformation.

This is composed of a number of triangles defined be a set of source and target vertices. These vertices are related by a common triangle list. No limitations on the nature of the triangle list are imposed. Points can then be mapped via barycentric coordinates from the source to the target space. Trying to map points that are not contained by any source triangle throws a TriangleContainmentError, which contains diagnostic information.

The transform can compute its own derivative with respect to spatial changes, as well as anchor landmark changes.

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

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().

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_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_dl(points)

The derivative of the warp with respect to spatial changes in anchor landmark points or centres, evaluated at points.

Parameters:points ((n_points, n_dims) ndarray) – The spatial points at which the derivative should be evaluated. Returns:d_dl ((n_points, n_centres, n_dims) ndarray) – The Jacobian wrt landmark changes.

d_dl[i, k, m] is the scalar differential change that the any dimension of the i‘th point experiences due to a first order change in the m‘th dimension of the k‘th landmark point.

Note that at present this assumes that the change in every dimension is equal.

d_dx(points)

The first order derivative of the warp with respect to spatial changes evaluated at points.

Parameters:points ((n_points, n_dims) ndarray) – The spatial points at which the derivative should be evaluated. Returns:d_dx ((n_points, n_dims, n_dims) ndarray) – The Jacobian wrt spatial changes.

d_dx[i, 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.

It may be the case that the Jacobian is constant across space - in this case axis zero may have length 1 to allow for broadcasting.

Raises:TriangleContainmentError: – If any point is outside any triangle of this PWA.

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)

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.

has_true_inverse

The inverse is true.

Type:True

n_dims

The number of dimensions of the target.

Type:int

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

n_points

The number of points on the target.

Type:int

n_tris

The number of triangles in the triangle list.

Type:int

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

trilist

The triangle list.

Type:(n_tris, 3) ndarray