Module « scipy.ndimage »
Signature de la fonction affine_transform
def affine_transform(input, matrix, offset=0.0, output_shape=None, output=None, order=3, mode='constant', cval=0.0, prefilter=True)
Description
affine_transform.__doc__
Apply an affine transformation.
Given an output image pixel index vector ``o``, the pixel value
is determined from the input image at position
``np.dot(matrix, o) + offset``.
This does 'pull' (or 'backward') resampling, transforming the output space
to the input to locate data. Affine transformations are often described in
the 'push' (or 'forward') direction, transforming input to output. If you
have a matrix for the 'push' transformation, use its inverse
(:func:`numpy.linalg.inv`) in this function.
Parameters
----------
input : array_like
The input array.
matrix : ndarray
The inverse coordinate transformation matrix, mapping output
coordinates to input coordinates. If ``ndim`` is the number of
dimensions of ``input``, the given matrix must have one of the
following shapes:
- ``(ndim, ndim)``: the linear transformation matrix for each
output coordinate.
- ``(ndim,)``: assume that the 2-D transformation matrix is
diagonal, with the diagonal specified by the given value. A more
efficient algorithm is then used that exploits the separability
of the problem.
- ``(ndim + 1, ndim + 1)``: assume that the transformation is
specified using homogeneous coordinates [1]_. In this case, any
value passed to ``offset`` is ignored.
- ``(ndim, ndim + 1)``: as above, but the bottom row of a
homogeneous transformation matrix is always ``[0, 0, ..., 1]``,
and may be omitted.
offset : float or sequence, optional
The offset into the array where the transform is applied. If a float,
`offset` is the same for each axis. If a sequence, `offset` should
contain one value for each axis.
output_shape : tuple of ints, optional
Shape tuple.
output : array or dtype, optional
The array in which to place the output, or the dtype of the
returned array. By default an array of the same dtype as input
will be created.
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
mode : {'reflect', 'grid-mirror', 'constant', 'grid-constant', 'nearest', 'mirror', 'grid-wrap', 'wrap'}, optional
The `mode` parameter determines how the input array is extended
beyond its boundaries. Default is 'constant'. Behavior for each valid
value is as follows (see additional plots and details on
:ref:`boundary modes <ndimage-interpolation-modes>`):
'reflect' (`d c b a | a b c d | d c b a`)
The input is extended by reflecting about the edge of the last
pixel. This mode is also sometimes referred to as half-sample
symmetric.
'grid-mirror'
This is a synonym for 'reflect'.
'constant' (`k k k k | a b c d | k k k k`)
The input is extended by filling all values beyond the edge with
the same constant value, defined by the `cval` parameter. No
interpolation is performed beyond the edges of the input.
'grid-constant' (`k k k k | a b c d | k k k k`)
The input is extended by filling all values beyond the edge with
the same constant value, defined by the `cval` parameter. Interpolation
occurs for samples outside the input's extent as well.
'nearest' (`a a a a | a b c d | d d d d`)
The input is extended by replicating the last pixel.
'mirror' (`d c b | a b c d | c b a`)
The input is extended by reflecting about the center of the last
pixel. This mode is also sometimes referred to as whole-sample
symmetric.
'grid-wrap' (`a b c d | a b c d | a b c d`)
The input is extended by wrapping around to the opposite edge.
'wrap' (`d b c d | a b c d | b c a b`)
The input is extended by wrapping around to the opposite edge, but in a
way such that the last point and initial point exactly overlap. In this
case it is not well defined which sample will be chosen at the point of
overlap.
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
prefilter : bool, optional
Determines if the input array is prefiltered with `spline_filter`
before interpolation. The default is True, which will create a
temporary `float64` array of filtered values if `order > 1`. If
setting this to False, the output will be slightly blurred if
`order > 1`, unless the input is prefiltered, i.e. it is the result
of calling `spline_filter` on the original input.
Returns
-------
affine_transform : ndarray
The transformed input.
Notes
-----
The given matrix and offset are used to find for each point in the
output the corresponding coordinates in the input by an affine
transformation. The value of the input at those coordinates is
determined by spline interpolation of the requested order. Points
outside the boundaries of the input are filled according to the given
mode.
.. versionchanged:: 0.18.0
Previously, the exact interpretation of the affine transformation
depended on whether the matrix was supplied as a 1-D or a
2-D array. If a 1-D array was supplied
to the matrix parameter, the output pixel value at index ``o``
was determined from the input image at position
``matrix * (o + offset)``.
For complex-valued `input`, this function transforms the real and imaginary
components independently.
.. versionadded:: 1.6.0
Complex-valued support added.
References
----------
.. [1] https://en.wikipedia.org/wiki/Homogeneous_coordinates
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