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Module « scipy.ndimage »

Fonction affine_transform - 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

help(scipy.ndimage.affine_transform)

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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