# Copyright (C) 2003-2005 Peter J. Verveer
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# 1. Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
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# 2. Redistributions in binary form must reproduce the above
# copyright notice, this list of conditions and the following
# disclaimer in the documentation and/or other materials provided
# with the distribution.
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# 3. The name of the author may not be used to endorse or promote
# products derived from this software without specific prior
# written permission.
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# THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
# OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
# GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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# WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
from __future__ import division, print_function, absolute_import
import math
import numpy
import warnings
from . import _ni_support
from . import _nd_image
from ._ni_docstrings import docdict
from scipy.misc import doccer
# Change the default 'reflect' to 'constant' via modifying a copy of docdict
docdict_copy = docdict.copy()
del docdict
docdict_copy['mode'] = docdict_copy['mode'].replace("Default is 'reflect'",
"Default is 'constant'")
docfiller = doccer.filldoc(docdict_copy)
__all__ = ['spline_filter1d', 'spline_filter', 'geometric_transform',
'map_coordinates', 'affine_transform', 'shift', 'zoom', 'rotate']
@docfiller
def spline_filter1d(input, order=3, axis=-1, output=numpy.float64,
mode='mirror'):
"""
Calculate a one-dimensional spline filter along the given axis.
The lines of the array along the given axis are filtered by a
spline filter. The order of the spline must be >= 2 and <= 5.
Parameters
----------
%(input)s
order : int, optional
The order of the spline, default is 3.
axis : int, optional
The axis along which the spline filter is applied. Default is the last
axis.
output : ndarray or dtype, optional
The array in which to place the output, or the dtype of the returned
array. Default is `numpy.float64`.
%(mode)s
Returns
-------
spline_filter1d : ndarray
The filtered input.
Notes
-----
All functions in `ndimage.interpolation` do spline interpolation of
the input image. If using b-splines of `order > 1`, the input image
values have to be converted to b-spline coefficients first, which is
done by applying this one-dimensional filter sequentially along all
axes of the input. All functions that require b-spline coefficients
will automatically filter their inputs, a behavior controllable with
the `prefilter` keyword argument. For functions that accept a `mode`
parameter, the result will only be correct if it matches the `mode`
used when filtering.
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if numpy.iscomplexobj(input):
raise TypeError('Complex type not supported')
output = _ni_support._get_output(output, input)
if order in [0, 1]:
output[...] = numpy.array(input)
else:
mode = _ni_support._extend_mode_to_code(mode)
axis = _ni_support._check_axis(axis, input.ndim)
_nd_image.spline_filter1d(input, order, axis, output, mode)
return output
def spline_filter(input, order=3, output=numpy.float64, mode='mirror'):
"""
Multi-dimensional spline filter.
For more details, see `spline_filter1d`.
See Also
--------
spline_filter1d
Notes
-----
The multi-dimensional filter is implemented as a sequence of
one-dimensional spline filters. The intermediate arrays are stored
in the same data type as the output. Therefore, for output types
with a limited precision, the results may be imprecise because
intermediate results may be stored with insufficient precision.
"""
if order < 2 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if numpy.iscomplexobj(input):
raise TypeError('Complex type not supported')
output = _ni_support._get_output(output, input)
if order not in [0, 1] and input.ndim > 0:
for axis in range(input.ndim):
spline_filter1d(input, order, axis, output=output, mode=mode)
input = output
else:
output[...] = input[...]
return output
@docfiller
def geometric_transform(input, mapping, output_shape=None,
output=None, order=3,
mode='constant', cval=0.0, prefilter=True,
extra_arguments=(), extra_keywords={}):
"""
Apply an arbitrary geometric transform.
The given mapping function is used to find, for each point in the
output, the corresponding coordinates in the input. The value of the
input at those coordinates is determined by spline interpolation of
the requested order.
Parameters
----------
%(input)s
mapping : {callable, scipy.LowLevelCallable}
A callable object that accepts a tuple of length equal to the output
array rank, and returns the corresponding input coordinates as a tuple
of length equal to the input array rank.
output_shape : tuple of ints, optional
Shape tuple.
%(output)s
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
%(mode)s
%(cval)s
%(prefilter)s
extra_arguments : tuple, optional
Extra arguments passed to `mapping`.
extra_keywords : dict, optional
Extra keywords passed to `mapping`.
Returns
-------
output : ndarray
The filtered input.
See Also
--------
map_coordinates, affine_transform, spline_filter1d
Notes
-----
This function also accepts low-level callback functions with one
the following signatures and wrapped in `scipy.LowLevelCallable`:
.. code:: c
int mapping(npy_intp *output_coordinates, double *input_coordinates,
int output_rank, int input_rank, void *user_data)
int mapping(intptr_t *output_coordinates, double *input_coordinates,
int output_rank, int input_rank, void *user_data)
The calling function iterates over the elements of the output array,
calling the callback function at each element. The coordinates of the
current output element are passed through ``output_coordinates``. The
callback function must return the coordinates at which the input must
be interpolated in ``input_coordinates``. The rank of the input and
output arrays are given by ``input_rank`` and ``output_rank``
respectively. ``user_data`` is the data pointer provided
to `scipy.LowLevelCallable` as-is.
The callback function must return an integer error status that is zero
if something went wrong and one otherwise. If an error occurs, you should
normally set the python error status with an informative message
before returning, otherwise a default error message is set by the
calling function.
In addition, some other low-level function pointer specifications
are accepted, but these are for backward compatibility only and should
not be used in new code.
Examples
--------
>>> import numpy as np
>>> from scipy.ndimage import geometric_transform
>>> a = np.arange(12.).reshape((4, 3))
>>> def shift_func(output_coords):
... return (output_coords[0] - 0.5, output_coords[1] - 0.5)
...
>>> geometric_transform(a, shift_func)
array([[ 0. , 0. , 0. ],
[ 0. , 1.362, 2.738],
[ 0. , 4.812, 6.187],
[ 0. , 8.263, 9.637]])
>>> b = [1, 2, 3, 4, 5]
>>> def shift_func(output_coords):
... return (output_coords[0] - 3,)
...
>>> geometric_transform(b, shift_func, mode='constant')
array([0, 0, 0, 1, 2])
>>> geometric_transform(b, shift_func, mode='nearest')
array([1, 1, 1, 1, 2])
>>> geometric_transform(b, shift_func, mode='reflect')
array([3, 2, 1, 1, 2])
>>> geometric_transform(b, shift_func, mode='wrap')
array([2, 3, 4, 1, 2])
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if numpy.iscomplexobj(input):
raise TypeError('Complex type not supported')
if output_shape is None:
output_shape = input.shape
if input.ndim < 1 or len(output_shape) < 1:
raise RuntimeError('input and output rank must be > 0')
mode = _ni_support._extend_mode_to_code(mode)
if prefilter and order > 1:
filtered = spline_filter(input, order, output=numpy.float64)
else:
filtered = input
output = _ni_support._get_output(output, input, shape=output_shape)
_nd_image.geometric_transform(filtered, mapping, None, None, None, output,
order, mode, cval, extra_arguments,
extra_keywords)
return output
[docs]@docfiller
def map_coordinates(input, coordinates, output=None, order=3,
mode='constant', cval=0.0, prefilter=True):
"""
Map the input array to new coordinates by interpolation.
The array of coordinates is used to find, for each point in the output,
the corresponding coordinates in the input. The value of the input at
those coordinates is determined by spline interpolation of the
requested order.
The shape of the output is derived from that of the coordinate
array by dropping the first axis. The values of the array along
the first axis are the coordinates in the input array at which the
output value is found.
Parameters
----------
%(input)s
coordinates : array_like
The coordinates at which `input` is evaluated.
%(output)s
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
%(mode)s
%(cval)s
%(prefilter)s
Returns
-------
map_coordinates : ndarray
The result of transforming the input. The shape of the output is
derived from that of `coordinates` by dropping the first axis.
See Also
--------
spline_filter, geometric_transform, scipy.interpolate
Examples
--------
>>> from scipy import ndimage
>>> a = np.arange(12.).reshape((4, 3))
>>> a
array([[ 0., 1., 2.],
[ 3., 4., 5.],
[ 6., 7., 8.],
[ 9., 10., 11.]])
>>> ndimage.map_coordinates(a, [[0.5, 2], [0.5, 1]], order=1)
array([ 2., 7.])
Above, the interpolated value of a[0.5, 0.5] gives output[0], while
a[2, 1] is output[1].
>>> inds = np.array([[0.5, 2], [0.5, 4]])
>>> ndimage.map_coordinates(a, inds, order=1, cval=-33.3)
array([ 2. , -33.3])
>>> ndimage.map_coordinates(a, inds, order=1, mode='nearest')
array([ 2., 8.])
>>> ndimage.map_coordinates(a, inds, order=1, cval=0, output=bool)
array([ True, False], dtype=bool)
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if numpy.iscomplexobj(input):
raise TypeError('Complex type not supported')
coordinates = numpy.asarray(coordinates)
if numpy.iscomplexobj(coordinates):
raise TypeError('Complex type not supported')
output_shape = coordinates.shape[1:]
if input.ndim < 1 or len(output_shape) < 1:
raise RuntimeError('input and output rank must be > 0')
if coordinates.shape[0] != input.ndim:
raise RuntimeError('invalid shape for coordinate array')
mode = _ni_support._extend_mode_to_code(mode)
if prefilter and order > 1:
filtered = spline_filter(input, order, output=numpy.float64)
else:
filtered = input
output = _ni_support._get_output(output, input,
shape=output_shape)
_nd_image.geometric_transform(filtered, None, coordinates, None, None,
output, order, mode, cval, None, None)
return output
@docfiller
def affine_transform(input, matrix, offset=0.0, output_shape=None,
output=None, order=3,
mode='constant', cval=0.0, prefilter=True):
"""
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``.
Parameters
----------
%(input)s
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 2D 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)s
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
%(mode)s
%(cval)s
%(prefilter)s
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 one-dimensional or
two-dimensional array. If a one-dimensional 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)``.
References
----------
.. [1] https://en.wikipedia.org/wiki/Homogeneous_coordinates
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if numpy.iscomplexobj(input):
raise TypeError('Complex type not supported')
if output_shape is None:
output_shape = input.shape
if input.ndim < 1 or len(output_shape) < 1:
raise RuntimeError('input and output rank must be > 0')
mode = _ni_support._extend_mode_to_code(mode)
if prefilter and order > 1:
filtered = spline_filter(input, order, output=numpy.float64)
else:
filtered = input
output = _ni_support._get_output(output, input,
shape=output_shape)
matrix = numpy.asarray(matrix, dtype=numpy.float64)
if matrix.ndim not in [1, 2] or matrix.shape[0] < 1:
raise RuntimeError('no proper affine matrix provided')
if (matrix.ndim == 2 and matrix.shape[1] == input.ndim + 1 and
(matrix.shape[0] in [input.ndim, input.ndim + 1])):
if matrix.shape[0] == input.ndim + 1:
exptd = [0] * input.ndim + [1]
if not numpy.all(matrix[input.ndim] == exptd):
msg = ('Expected homogeneous transformation matrix with '
'shape %s for image shape %s, but bottom row was '
'not equal to %s' % (matrix.shape, input.shape, exptd))
raise ValueError(msg)
# assume input is homogeneous coordinate transformation matrix
offset = matrix[:input.ndim, input.ndim]
matrix = matrix[:input.ndim, :input.ndim]
if matrix.shape[0] != input.ndim:
raise RuntimeError('affine matrix has wrong number of rows')
if matrix.ndim == 2 and matrix.shape[1] != output.ndim:
raise RuntimeError('affine matrix has wrong number of columns')
if not matrix.flags.contiguous:
matrix = matrix.copy()
offset = _ni_support._normalize_sequence(offset, input.ndim)
offset = numpy.asarray(offset, dtype=numpy.float64)
if offset.ndim != 1 or offset.shape[0] < 1:
raise RuntimeError('no proper offset provided')
if not offset.flags.contiguous:
offset = offset.copy()
if matrix.ndim == 1:
warnings.warn(
"The behaviour of affine_transform with a one-dimensional "
"array supplied for the matrix parameter has changed in "
"scipy 0.18.0."
)
_nd_image.zoom_shift(filtered, matrix, offset/matrix, output, order,
mode, cval)
else:
_nd_image.geometric_transform(filtered, None, None, matrix, offset,
output, order, mode, cval, None, None)
return output
@docfiller
def shift(input, shift, output=None, order=3, mode='constant', cval=0.0,
prefilter=True):
"""
Shift an array.
The array is shifted using spline interpolation of the requested order.
Points outside the boundaries of the input are filled according to the
given mode.
Parameters
----------
%(input)s
shift : float or sequence
The shift along the axes. If a float, `shift` is the same for each
axis. If a sequence, `shift` should contain one value for each axis.
%(output)s
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
%(mode)s
%(cval)s
%(prefilter)s
Returns
-------
shift : ndarray
The shifted input.
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if numpy.iscomplexobj(input):
raise TypeError('Complex type not supported')
if input.ndim < 1:
raise RuntimeError('input and output rank must be > 0')
mode = _ni_support._extend_mode_to_code(mode)
if prefilter and order > 1:
filtered = spline_filter(input, order, output=numpy.float64)
else:
filtered = input
output = _ni_support._get_output(output, input)
shift = _ni_support._normalize_sequence(shift, input.ndim)
shift = [-ii for ii in shift]
shift = numpy.asarray(shift, dtype=numpy.float64)
if not shift.flags.contiguous:
shift = shift.copy()
_nd_image.zoom_shift(filtered, None, shift, output, order, mode, cval)
return output
@docfiller
def zoom(input, zoom, output=None, order=3, mode='constant', cval=0.0,
prefilter=True):
"""
Zoom an array.
The array is zoomed using spline interpolation of the requested order.
Parameters
----------
%(input)s
zoom : float or sequence
The zoom factor along the axes. If a float, `zoom` is the same for each
axis. If a sequence, `zoom` should contain one value for each axis.
%(output)s
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
%(mode)s
%(cval)s
%(prefilter)s
Returns
-------
zoom : ndarray
The zoomed input.
Examples
--------
>>> from scipy import ndimage, misc
>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> ax1 = fig.add_subplot(121) # left side
>>> ax2 = fig.add_subplot(122) # right side
>>> ascent = misc.ascent()
>>> result = ndimage.zoom(ascent, 3.0)
>>> ax1.imshow(ascent)
>>> ax2.imshow(result)
>>> plt.show()
>>> print(ascent.shape)
(512, 512)
>>> print(result.shape)
(1536, 1536)
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if numpy.iscomplexobj(input):
raise TypeError('Complex type not supported')
if input.ndim < 1:
raise RuntimeError('input and output rank must be > 0')
mode = _ni_support._extend_mode_to_code(mode)
if prefilter and order > 1:
filtered = spline_filter(input, order, output=numpy.float64)
else:
filtered = input
zoom = _ni_support._normalize_sequence(zoom, input.ndim)
output_shape = tuple(
[int(round(ii * jj)) for ii, jj in zip(input.shape, zoom)])
output_shape_old = tuple(
[int(ii * jj) for ii, jj in zip(input.shape, zoom)])
if output_shape != output_shape_old:
warnings.warn(
"From scipy 0.13.0, the output shape of zoom() is calculated "
"with round() instead of int() - for these inputs the size of "
"the returned array has changed.", UserWarning)
zoom_div = numpy.array(output_shape, float) - 1
# Zooming to infinite values is unpredictable, so just choose
# zoom factor 1 instead
zoom = numpy.divide(numpy.array(input.shape) - 1, zoom_div,
out=numpy.ones_like(input.shape, dtype=numpy.float64),
where=zoom_div != 0)
output = _ni_support._get_output(output, input,
shape=output_shape)
zoom = numpy.ascontiguousarray(zoom)
_nd_image.zoom_shift(filtered, zoom, None, output, order, mode, cval)
return output
def _minmax(coor, minc, maxc):
if coor[0] < minc[0]:
minc[0] = coor[0]
if coor[0] > maxc[0]:
maxc[0] = coor[0]
if coor[1] < minc[1]:
minc[1] = coor[1]
if coor[1] > maxc[1]:
maxc[1] = coor[1]
return minc, maxc
@docfiller
def rotate(input, angle, axes=(1, 0), reshape=True, output=None, order=3,
mode='constant', cval=0.0, prefilter=True):
"""
Rotate an array.
The array is rotated in the plane defined by the two axes given by the
`axes` parameter using spline interpolation of the requested order.
Parameters
----------
%(input)s
angle : float
The rotation angle in degrees.
axes : tuple of 2 ints, optional
The two axes that define the plane of rotation. Default is the first
two axes.
reshape : bool, optional
If `reshape` is true, the output shape is adapted so that the input
array is contained completely in the output. Default is True.
%(output)s
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
%(mode)s
%(cval)s
%(prefilter)s
Returns
-------
rotate : ndarray
The rotated input.
"""
input = numpy.asarray(input)
axes = list(axes)
rank = input.ndim
if axes[0] < 0:
axes[0] += rank
if axes[1] < 0:
axes[1] += rank
if axes[0] < 0 or axes[1] < 0 or axes[0] > rank or axes[1] > rank:
raise RuntimeError('invalid rotation plane specified')
if axes[0] > axes[1]:
axes = axes[1], axes[0]
angle = numpy.pi / 180 * angle
m11 = math.cos(angle)
m12 = math.sin(angle)
m21 = -math.sin(angle)
m22 = math.cos(angle)
matrix = numpy.array([[m11, m12],
[m21, m22]], dtype=numpy.float64)
iy = input.shape[axes[0]]
ix = input.shape[axes[1]]
if reshape:
mtrx = numpy.array([[m11, -m21],
[-m12, m22]], dtype=numpy.float64)
minc = [0, 0]
maxc = [0, 0]
coor = numpy.dot(mtrx, [0, ix])
minc, maxc = _minmax(coor, minc, maxc)
coor = numpy.dot(mtrx, [iy, 0])
minc, maxc = _minmax(coor, minc, maxc)
coor = numpy.dot(mtrx, [iy, ix])
minc, maxc = _minmax(coor, minc, maxc)
oy = int(maxc[0] - minc[0] + 0.5)
ox = int(maxc[1] - minc[1] + 0.5)
else:
oy = input.shape[axes[0]]
ox = input.shape[axes[1]]
offset = numpy.zeros((2,), dtype=numpy.float64)
offset[0] = float(oy) / 2.0 - 0.5
offset[1] = float(ox) / 2.0 - 0.5
offset = numpy.dot(matrix, offset)
tmp = numpy.zeros((2,), dtype=numpy.float64)
tmp[0] = float(iy) / 2.0 - 0.5
tmp[1] = float(ix) / 2.0 - 0.5
offset = tmp - offset
output_shape = list(input.shape)
output_shape[axes[0]] = oy
output_shape[axes[1]] = ox
output_shape = tuple(output_shape)
output = _ni_support._get_output(output, input,
shape=output_shape)
if input.ndim <= 2:
affine_transform(input, matrix, offset, output_shape, output,
order, mode, cval, prefilter)
else:
coordinates = []
size = numpy.product(input.shape, axis=0)
size //= input.shape[axes[0]]
size //= input.shape[axes[1]]
for ii in range(input.ndim):
if ii not in axes:
coordinates.append(0)
else:
coordinates.append(slice(None, None, None))
iter_axes = list(range(input.ndim))
iter_axes.reverse()
iter_axes.remove(axes[0])
iter_axes.remove(axes[1])
os = (output_shape[axes[0]], output_shape[axes[1]])
for ii in range(size):
ia = input[tuple(coordinates)]
oa = output[tuple(coordinates)]
affine_transform(ia, matrix, offset, os, oa, order, mode,
cval, prefilter)
for jj in iter_axes:
if coordinates[jj] < input.shape[jj] - 1:
coordinates[jj] += 1
break
else:
coordinates[jj] = 0
return output