DifferentiableR2LogR2RBF

class menpofit.transform.DifferentiableR2LogR2RBF(c)

Bases: R2LogR2RBF, DL

The \(r^2 \log{r^2}\) basis function.

The derivative of this function is \(2 r (\log{r^2} + 1)\), where \(r = \lVert x - c \rVert\).

It can compute its own derivative with respect to landmark changes.

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)

Apply the derivative of the basis function wrt the centres and the points given by points. Let points be \(x\), then \(2(x - c)^T (\log{r^2_{x, l}}+1) = 2(x - c)^T (2\log{r_{x, l}}+1)\) where \(r_{x, l} = \| x - c \|\).

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 tensor representing the first order derivative of the radius from each centre wrt the centre’s position, evaluated at each point.

property n_centres

The number of centres.

Type

int

property n_dims

The RBF can only be applied on points with the same dimensionality as the centres.

Type

int

property n_dims_output

The result of the transform has a dimension (weight) for every centre.

Type

int