R2LogRRBF¶
- class menpo.transform.rbf.R2LogRRBF(c)[source]¶
Bases: RadialBasisFunction
Calculates the \(r^2 \log{r}\) basis function.
The derivative of this function is \(r (1 + 2 \log{r})\).
Note
\(r = \lVert x - c \rVert\)
Parameters: c : (n_centres, n_dims) ndarray
The set of centers that make the basis. Usually represents a set of source landmarks.
- 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
- 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.
- d_dl(points)[source]¶
The derivative of the basis function wrt the coordinate system evaluated at points.
\((x - c)^T (1 + 2 \log{r_{x, l}})\).
Note
:math:`r_{x, l} = lVert x - c
Vert`
Parameters: points : (n_points, n_dims) ndarray
Set of points to apply the basis to.
Returns: d_dl : (n_points, n_centres, n_dims) ndarray
The jacobian tensor representing the first order partial derivative of each points wrt the centres
- n_dims¶
The RBF can only be applied on points with the same dimensionality as the centres.
- n_dims_output¶
The result of the transform has a dimension (weight) for every centre