1011 lines
36 KiB
Python
1011 lines
36 KiB
Python
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# Copyright (C) 2003-2005 Peter J. Verveer
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#
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# Redistribution and use in source and binary forms, with or without
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# modification, are permitted provided that the following conditions
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# are met:
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#
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# 1. Redistributions of source code must retain the above copyright
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# notice, this list of conditions and the following disclaimer.
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#
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# 2. Redistributions in binary form must reproduce the above
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# copyright notice, this list of conditions and the following
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# disclaimer in the documentation and/or other materials provided
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# with the distribution.
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#
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# 3. The name of the author may not be used to endorse or promote
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# products derived from this software without specific prior
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# written permission.
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#
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# THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
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# OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
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# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
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# GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
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# WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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import itertools
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import warnings
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import numpy
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from scipy._lib._util import normalize_axis_index
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from scipy import special
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from . import _ni_support
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from . import _nd_image
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from ._ni_docstrings import docfiller
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__all__ = ['spline_filter1d', 'spline_filter', 'geometric_transform',
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'map_coordinates', 'affine_transform', 'shift', 'zoom', 'rotate']
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@docfiller
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def spline_filter1d(input, order=3, axis=-1, output=numpy.float64,
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mode='mirror'):
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"""
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Calculate a 1-D spline filter along the given axis.
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The lines of the array along the given axis are filtered by a
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spline filter. The order of the spline must be >= 2 and <= 5.
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Parameters
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----------
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%(input)s
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order : int, optional
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The order of the spline, default is 3.
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axis : int, optional
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The axis along which the spline filter is applied. Default is the last
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axis.
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output : ndarray or dtype, optional
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The array in which to place the output, or the dtype of the returned
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array. Default is ``numpy.float64``.
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%(mode_interp_mirror)s
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Returns
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-------
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spline_filter1d : ndarray
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The filtered input.
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See Also
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--------
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spline_filter : Multidimensional spline filter.
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Notes
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-----
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All of the interpolation functions in `ndimage` do spline interpolation of
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the input image. If using B-splines of `order > 1`, the input image
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values have to be converted to B-spline coefficients first, which is
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done by applying this 1-D filter sequentially along all
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axes of the input. All functions that require B-spline coefficients
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will automatically filter their inputs, a behavior controllable with
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the `prefilter` keyword argument. For functions that accept a `mode`
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parameter, the result will only be correct if it matches the `mode`
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used when filtering.
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For complex-valued `input`, this function processes the real and imaginary
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components independently.
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.. versionadded:: 1.6.0
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Complex-valued support added.
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Examples
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--------
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We can filter an image using 1-D spline along the given axis:
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>>> from scipy.ndimage import spline_filter1d
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>>> import numpy as np
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>>> import matplotlib.pyplot as plt
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>>> orig_img = np.eye(20) # create an image
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>>> orig_img[10, :] = 1.0
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>>> sp_filter_axis_0 = spline_filter1d(orig_img, axis=0)
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>>> sp_filter_axis_1 = spline_filter1d(orig_img, axis=1)
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>>> f, ax = plt.subplots(1, 3, sharex=True)
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>>> for ind, data in enumerate([[orig_img, "original image"],
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... [sp_filter_axis_0, "spline filter (axis=0)"],
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... [sp_filter_axis_1, "spline filter (axis=1)"]]):
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... ax[ind].imshow(data[0], cmap='gray_r')
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... ax[ind].set_title(data[1])
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>>> plt.tight_layout()
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>>> plt.show()
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"""
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if order < 0 or order > 5:
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raise RuntimeError('spline order not supported')
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input = numpy.asarray(input)
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complex_output = numpy.iscomplexobj(input)
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output = _ni_support._get_output(output, input,
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complex_output=complex_output)
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if complex_output:
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spline_filter1d(input.real, order, axis, output.real, mode)
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spline_filter1d(input.imag, order, axis, output.imag, mode)
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return output
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if order in [0, 1]:
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output[...] = numpy.array(input)
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else:
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mode = _ni_support._extend_mode_to_code(mode)
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axis = normalize_axis_index(axis, input.ndim)
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_nd_image.spline_filter1d(input, order, axis, output, mode)
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return output
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@docfiller
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def spline_filter(input, order=3, output=numpy.float64, mode='mirror'):
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"""
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Multidimensional spline filter.
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Parameters
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----------
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%(input)s
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order : int, optional
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The order of the spline, default is 3.
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output : ndarray or dtype, optional
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The array in which to place the output, or the dtype of the returned
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array. Default is ``numpy.float64``.
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%(mode_interp_mirror)s
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Returns
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-------
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spline_filter : ndarray
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Filtered array. Has the same shape as `input`.
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See Also
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--------
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spline_filter1d : Calculate a 1-D spline filter along the given axis.
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Notes
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-----
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The multidimensional filter is implemented as a sequence of
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1-D spline filters. The intermediate arrays are stored
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in the same data type as the output. Therefore, for output types
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with a limited precision, the results may be imprecise because
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intermediate results may be stored with insufficient precision.
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For complex-valued `input`, this function processes the real and imaginary
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components independently.
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.. versionadded:: 1.6.0
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Complex-valued support added.
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Examples
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--------
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We can filter an image using multidimentional splines:
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>>> from scipy.ndimage import spline_filter
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>>> import numpy as np
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>>> import matplotlib.pyplot as plt
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>>> orig_img = np.eye(20) # create an image
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>>> orig_img[10, :] = 1.0
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>>> sp_filter = spline_filter(orig_img, order=3)
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>>> f, ax = plt.subplots(1, 2, sharex=True)
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>>> for ind, data in enumerate([[orig_img, "original image"],
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... [sp_filter, "spline filter"]]):
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... ax[ind].imshow(data[0], cmap='gray_r')
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... ax[ind].set_title(data[1])
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>>> plt.tight_layout()
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>>> plt.show()
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"""
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if order < 2 or order > 5:
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raise RuntimeError('spline order not supported')
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input = numpy.asarray(input)
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complex_output = numpy.iscomplexobj(input)
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output = _ni_support._get_output(output, input,
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complex_output=complex_output)
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if complex_output:
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spline_filter(input.real, order, output.real, mode)
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spline_filter(input.imag, order, output.imag, mode)
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return output
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if order not in [0, 1] and input.ndim > 0:
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for axis in range(input.ndim):
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spline_filter1d(input, order, axis, output=output, mode=mode)
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input = output
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else:
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output[...] = input[...]
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return output
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def _prepad_for_spline_filter(input, mode, cval):
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if mode in ['nearest', 'grid-constant']:
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npad = 12
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if mode == 'grid-constant':
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padded = numpy.pad(input, npad, mode='constant',
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constant_values=cval)
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elif mode == 'nearest':
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padded = numpy.pad(input, npad, mode='edge')
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else:
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# other modes have exact boundary conditions implemented so
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# no prepadding is needed
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npad = 0
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padded = input
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return padded, npad
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@docfiller
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def geometric_transform(input, mapping, output_shape=None,
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output=None, order=3,
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mode='constant', cval=0.0, prefilter=True,
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extra_arguments=(), extra_keywords={}):
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"""
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Apply an arbitrary geometric transform.
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The given mapping function is used to find, for each point in the
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output, the corresponding coordinates in the input. The value of the
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input at those coordinates is determined by spline interpolation of
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the requested order.
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Parameters
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----------
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%(input)s
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mapping : {callable, scipy.LowLevelCallable}
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A callable object that accepts a tuple of length equal to the output
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array rank, and returns the corresponding input coordinates as a tuple
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of length equal to the input array rank.
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output_shape : tuple of ints, optional
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Shape tuple.
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%(output)s
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order : int, optional
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The order of the spline interpolation, default is 3.
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The order has to be in the range 0-5.
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%(mode_interp_constant)s
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%(cval)s
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%(prefilter)s
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extra_arguments : tuple, optional
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Extra arguments passed to `mapping`.
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extra_keywords : dict, optional
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Extra keywords passed to `mapping`.
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Returns
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-------
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output : ndarray
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The filtered input.
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See Also
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--------
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map_coordinates, affine_transform, spline_filter1d
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Notes
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-----
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This function also accepts low-level callback functions with one
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the following signatures and wrapped in `scipy.LowLevelCallable`:
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.. code:: c
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int mapping(npy_intp *output_coordinates, double *input_coordinates,
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int output_rank, int input_rank, void *user_data)
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int mapping(intptr_t *output_coordinates, double *input_coordinates,
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int output_rank, int input_rank, void *user_data)
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The calling function iterates over the elements of the output array,
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calling the callback function at each element. The coordinates of the
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current output element are passed through ``output_coordinates``. The
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callback function must return the coordinates at which the input must
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be interpolated in ``input_coordinates``. The rank of the input and
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output arrays are given by ``input_rank`` and ``output_rank``
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respectively. ``user_data`` is the data pointer provided
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to `scipy.LowLevelCallable` as-is.
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The callback function must return an integer error status that is zero
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if something went wrong and one otherwise. If an error occurs, you should
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normally set the Python error status with an informative message
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before returning, otherwise a default error message is set by the
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calling function.
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In addition, some other low-level function pointer specifications
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are accepted, but these are for backward compatibility only and should
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not be used in new code.
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For complex-valued `input`, this function transforms the real and imaginary
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components independently.
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.. versionadded:: 1.6.0
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Complex-valued support added.
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Examples
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--------
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>>> import numpy as np
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>>> from scipy.ndimage import geometric_transform
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>>> a = np.arange(12.).reshape((4, 3))
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>>> def shift_func(output_coords):
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... return (output_coords[0] - 0.5, output_coords[1] - 0.5)
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...
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>>> geometric_transform(a, shift_func)
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array([[ 0. , 0. , 0. ],
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[ 0. , 1.362, 2.738],
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[ 0. , 4.812, 6.187],
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[ 0. , 8.263, 9.637]])
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>>> b = [1, 2, 3, 4, 5]
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>>> def shift_func(output_coords):
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... return (output_coords[0] - 3,)
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...
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>>> geometric_transform(b, shift_func, mode='constant')
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array([0, 0, 0, 1, 2])
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>>> geometric_transform(b, shift_func, mode='nearest')
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array([1, 1, 1, 1, 2])
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>>> geometric_transform(b, shift_func, mode='reflect')
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array([3, 2, 1, 1, 2])
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>>> geometric_transform(b, shift_func, mode='wrap')
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array([2, 3, 4, 1, 2])
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"""
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if order < 0 or order > 5:
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raise RuntimeError('spline order not supported')
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input = numpy.asarray(input)
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if output_shape is None:
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output_shape = input.shape
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if input.ndim < 1 or len(output_shape) < 1:
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raise RuntimeError('input and output rank must be > 0')
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complex_output = numpy.iscomplexobj(input)
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output = _ni_support._get_output(output, input, shape=output_shape,
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complex_output=complex_output)
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if complex_output:
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kwargs = dict(order=order, mode=mode, prefilter=prefilter,
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output_shape=output_shape,
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extra_arguments=extra_arguments,
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extra_keywords=extra_keywords)
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geometric_transform(input.real, mapping, output=output.real,
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cval=numpy.real(cval), **kwargs)
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geometric_transform(input.imag, mapping, output=output.imag,
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cval=numpy.imag(cval), **kwargs)
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return output
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if prefilter and order > 1:
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padded, npad = _prepad_for_spline_filter(input, mode, cval)
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filtered = spline_filter(padded, order, output=numpy.float64,
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mode=mode)
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else:
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npad = 0
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filtered = input
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mode = _ni_support._extend_mode_to_code(mode)
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_nd_image.geometric_transform(filtered, mapping, None, None, None, output,
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order, mode, cval, npad, extra_arguments,
|
||
|
|
extra_keywords)
|
||
|
|
return output
|
||
|
|
|
||
|
|
|
||
|
|
@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_interp_constant)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
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
For complex-valued `input`, this function maps the real and imaginary
|
||
|
|
components independently.
|
||
|
|
|
||
|
|
.. versionadded:: 1.6.0
|
||
|
|
Complex-valued support added.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from scipy import ndimage
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> 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)
|
||
|
|
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')
|
||
|
|
complex_output = numpy.iscomplexobj(input)
|
||
|
|
output = _ni_support._get_output(output, input, shape=output_shape,
|
||
|
|
complex_output=complex_output)
|
||
|
|
if complex_output:
|
||
|
|
kwargs = dict(order=order, mode=mode, prefilter=prefilter)
|
||
|
|
map_coordinates(input.real, coordinates, output=output.real,
|
||
|
|
cval=numpy.real(cval), **kwargs)
|
||
|
|
map_coordinates(input.imag, coordinates, output=output.imag,
|
||
|
|
cval=numpy.imag(cval), **kwargs)
|
||
|
|
return output
|
||
|
|
if prefilter and order > 1:
|
||
|
|
padded, npad = _prepad_for_spline_filter(input, mode, cval)
|
||
|
|
filtered = spline_filter(padded, order, output=numpy.float64,
|
||
|
|
mode=mode)
|
||
|
|
else:
|
||
|
|
npad = 0
|
||
|
|
filtered = input
|
||
|
|
mode = _ni_support._extend_mode_to_code(mode)
|
||
|
|
_nd_image.geometric_transform(filtered, None, coordinates, None, None,
|
||
|
|
output, order, mode, cval, npad, 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``.
|
||
|
|
|
||
|
|
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)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 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)s
|
||
|
|
order : int, optional
|
||
|
|
The order of the spline interpolation, default is 3.
|
||
|
|
The order has to be in the range 0-5.
|
||
|
|
%(mode_interp_constant)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 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
|
||
|
|
"""
|
||
|
|
if order < 0 or order > 5:
|
||
|
|
raise RuntimeError('spline order not supported')
|
||
|
|
input = numpy.asarray(input)
|
||
|
|
if output_shape is None:
|
||
|
|
if isinstance(output, numpy.ndarray):
|
||
|
|
output_shape = output.shape
|
||
|
|
else:
|
||
|
|
output_shape = input.shape
|
||
|
|
if input.ndim < 1 or len(output_shape) < 1:
|
||
|
|
raise RuntimeError('input and output rank must be > 0')
|
||
|
|
complex_output = numpy.iscomplexobj(input)
|
||
|
|
output = _ni_support._get_output(output, input, shape=output_shape,
|
||
|
|
complex_output=complex_output)
|
||
|
|
if complex_output:
|
||
|
|
kwargs = dict(offset=offset, output_shape=output_shape, order=order,
|
||
|
|
mode=mode, prefilter=prefilter)
|
||
|
|
affine_transform(input.real, matrix, output=output.real,
|
||
|
|
cval=numpy.real(cval), **kwargs)
|
||
|
|
affine_transform(input.imag, matrix, output=output.imag,
|
||
|
|
cval=numpy.imag(cval), **kwargs)
|
||
|
|
return output
|
||
|
|
if prefilter and order > 1:
|
||
|
|
padded, npad = _prepad_for_spline_filter(input, mode, cval)
|
||
|
|
filtered = spline_filter(padded, order, output=numpy.float64,
|
||
|
|
mode=mode)
|
||
|
|
else:
|
||
|
|
npad = 0
|
||
|
|
filtered = input
|
||
|
|
mode = _ni_support._extend_mode_to_code(mode)
|
||
|
|
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 {} for image shape {}, but bottom row was '
|
||
|
|
'not equal to {}'.format(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 behavior of affine_transform with a 1-D "
|
||
|
|
"array supplied for the matrix parameter has changed in "
|
||
|
|
"SciPy 0.18.0.",
|
||
|
|
stacklevel=2
|
||
|
|
)
|
||
|
|
_nd_image.zoom_shift(filtered, matrix, offset/matrix, output, order,
|
||
|
|
mode, cval, npad, False)
|
||
|
|
else:
|
||
|
|
_nd_image.geometric_transform(filtered, None, None, matrix, offset,
|
||
|
|
output, order, mode, cval, npad, 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_interp_constant)s
|
||
|
|
%(cval)s
|
||
|
|
%(prefilter)s
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
shift : ndarray
|
||
|
|
The shifted input.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
affine_transform : Affine transformations
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
For complex-valued `input`, this function shifts the real and imaginary
|
||
|
|
components independently.
|
||
|
|
|
||
|
|
.. versionadded:: 1.6.0
|
||
|
|
Complex-valued support added.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
Import the necessary modules and an exemplary image.
|
||
|
|
|
||
|
|
>>> from scipy.ndimage import shift
|
||
|
|
>>> import matplotlib.pyplot as plt
|
||
|
|
>>> from scipy import datasets
|
||
|
|
>>> image = datasets.ascent()
|
||
|
|
|
||
|
|
Shift the image vertically by 20 pixels.
|
||
|
|
|
||
|
|
>>> image_shifted_vertically = shift(image, (20, 0))
|
||
|
|
|
||
|
|
Shift the image vertically by -200 pixels and horizontally by 100 pixels.
|
||
|
|
|
||
|
|
>>> image_shifted_both_directions = shift(image, (-200, 100))
|
||
|
|
|
||
|
|
Plot the original and the shifted images.
|
||
|
|
|
||
|
|
>>> fig, axes = plt.subplots(3, 1, figsize=(4, 12))
|
||
|
|
>>> plt.gray() # show the filtered result in grayscale
|
||
|
|
>>> top, middle, bottom = axes
|
||
|
|
>>> for ax in axes:
|
||
|
|
... ax.set_axis_off() # remove coordinate system
|
||
|
|
>>> top.imshow(image)
|
||
|
|
>>> top.set_title("Original image")
|
||
|
|
>>> middle.imshow(image_shifted_vertically)
|
||
|
|
>>> middle.set_title("Vertically shifted image")
|
||
|
|
>>> bottom.imshow(image_shifted_both_directions)
|
||
|
|
>>> bottom.set_title("Image shifted in both directions")
|
||
|
|
>>> fig.tight_layout()
|
||
|
|
"""
|
||
|
|
if order < 0 or order > 5:
|
||
|
|
raise RuntimeError('spline order not supported')
|
||
|
|
input = numpy.asarray(input)
|
||
|
|
if input.ndim < 1:
|
||
|
|
raise RuntimeError('input and output rank must be > 0')
|
||
|
|
complex_output = numpy.iscomplexobj(input)
|
||
|
|
output = _ni_support._get_output(output, input,
|
||
|
|
complex_output=complex_output)
|
||
|
|
if complex_output:
|
||
|
|
# import under different name to avoid confusion with shift parameter
|
||
|
|
from scipy.ndimage._interpolation import shift as _shift
|
||
|
|
|
||
|
|
kwargs = dict(order=order, mode=mode, prefilter=prefilter)
|
||
|
|
_shift(input.real, shift, output=output.real, cval=numpy.real(cval),
|
||
|
|
**kwargs)
|
||
|
|
_shift(input.imag, shift, output=output.imag, cval=numpy.imag(cval),
|
||
|
|
**kwargs)
|
||
|
|
return output
|
||
|
|
if prefilter and order > 1:
|
||
|
|
padded, npad = _prepad_for_spline_filter(input, mode, cval)
|
||
|
|
filtered = spline_filter(padded, order, output=numpy.float64,
|
||
|
|
mode=mode)
|
||
|
|
else:
|
||
|
|
npad = 0
|
||
|
|
filtered = input
|
||
|
|
mode = _ni_support._extend_mode_to_code(mode)
|
||
|
|
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,
|
||
|
|
npad, False)
|
||
|
|
return output
|
||
|
|
|
||
|
|
|
||
|
|
@docfiller
|
||
|
|
def zoom(input, zoom, output=None, order=3, mode='constant', cval=0.0,
|
||
|
|
prefilter=True, *, grid_mode=False):
|
||
|
|
"""
|
||
|
|
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_interp_constant)s
|
||
|
|
%(cval)s
|
||
|
|
%(prefilter)s
|
||
|
|
grid_mode : bool, optional
|
||
|
|
If False, the distance from the pixel centers is zoomed. Otherwise, the
|
||
|
|
distance including the full pixel extent is used. For example, a 1d
|
||
|
|
signal of length 5 is considered to have length 4 when `grid_mode` is
|
||
|
|
False, but length 5 when `grid_mode` is True. See the following
|
||
|
|
visual illustration:
|
||
|
|
|
||
|
|
.. code-block:: text
|
||
|
|
|
||
|
|
| pixel 1 | pixel 2 | pixel 3 | pixel 4 | pixel 5 |
|
||
|
|
|<-------------------------------------->|
|
||
|
|
vs.
|
||
|
|
|<----------------------------------------------->|
|
||
|
|
|
||
|
|
The starting point of the arrow in the diagram above corresponds to
|
||
|
|
coordinate location 0 in each mode.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
zoom : ndarray
|
||
|
|
The zoomed input.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
For complex-valued `input`, this function zooms the real and imaginary
|
||
|
|
components independently.
|
||
|
|
|
||
|
|
.. versionadded:: 1.6.0
|
||
|
|
Complex-valued support added.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from scipy import ndimage, datasets
|
||
|
|
>>> import matplotlib.pyplot as plt
|
||
|
|
|
||
|
|
>>> fig = plt.figure()
|
||
|
|
>>> ax1 = fig.add_subplot(121) # left side
|
||
|
|
>>> ax2 = fig.add_subplot(122) # right side
|
||
|
|
>>> ascent = datasets.ascent()
|
||
|
|
>>> result = ndimage.zoom(ascent, 3.0)
|
||
|
|
>>> ax1.imshow(ascent, vmin=0, vmax=255)
|
||
|
|
>>> ax2.imshow(result, vmin=0, vmax=255)
|
||
|
|
>>> 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 input.ndim < 1:
|
||
|
|
raise RuntimeError('input and output rank must be > 0')
|
||
|
|
zoom = _ni_support._normalize_sequence(zoom, input.ndim)
|
||
|
|
output_shape = tuple(
|
||
|
|
[int(round(ii * jj)) for ii, jj in zip(input.shape, zoom)])
|
||
|
|
complex_output = numpy.iscomplexobj(input)
|
||
|
|
output = _ni_support._get_output(output, input, shape=output_shape,
|
||
|
|
complex_output=complex_output)
|
||
|
|
if complex_output:
|
||
|
|
# import under different name to avoid confusion with zoom parameter
|
||
|
|
from scipy.ndimage._interpolation import zoom as _zoom
|
||
|
|
|
||
|
|
kwargs = dict(order=order, mode=mode, prefilter=prefilter)
|
||
|
|
_zoom(input.real, zoom, output=output.real, cval=numpy.real(cval),
|
||
|
|
**kwargs)
|
||
|
|
_zoom(input.imag, zoom, output=output.imag, cval=numpy.imag(cval),
|
||
|
|
**kwargs)
|
||
|
|
return output
|
||
|
|
if prefilter and order > 1:
|
||
|
|
padded, npad = _prepad_for_spline_filter(input, mode, cval)
|
||
|
|
filtered = spline_filter(padded, order, output=numpy.float64,
|
||
|
|
mode=mode)
|
||
|
|
else:
|
||
|
|
npad = 0
|
||
|
|
filtered = input
|
||
|
|
if grid_mode:
|
||
|
|
# warn about modes that may have surprising behavior
|
||
|
|
suggest_mode = None
|
||
|
|
if mode == 'constant':
|
||
|
|
suggest_mode = 'grid-constant'
|
||
|
|
elif mode == 'wrap':
|
||
|
|
suggest_mode = 'grid-wrap'
|
||
|
|
if suggest_mode is not None:
|
||
|
|
warnings.warn(
|
||
|
|
("It is recommended to use mode = {} instead of {} when "
|
||
|
|
"grid_mode is True.").format(suggest_mode, mode),
|
||
|
|
stacklevel=2
|
||
|
|
)
|
||
|
|
mode = _ni_support._extend_mode_to_code(mode)
|
||
|
|
|
||
|
|
zoom_div = numpy.array(output_shape)
|
||
|
|
zoom_nominator = numpy.array(input.shape)
|
||
|
|
if not grid_mode:
|
||
|
|
zoom_div -= 1
|
||
|
|
zoom_nominator -= 1
|
||
|
|
|
||
|
|
# Zooming to infinite values is unpredictable, so just choose
|
||
|
|
# zoom factor 1 instead
|
||
|
|
zoom = numpy.divide(zoom_nominator, zoom_div,
|
||
|
|
out=numpy.ones_like(input.shape, dtype=numpy.float64),
|
||
|
|
where=zoom_div != 0)
|
||
|
|
zoom = numpy.ascontiguousarray(zoom)
|
||
|
|
_nd_image.zoom_shift(filtered, zoom, None, output, order, mode, cval, npad,
|
||
|
|
grid_mode)
|
||
|
|
return output
|
||
|
|
|
||
|
|
|
||
|
|
@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_interp_constant)s
|
||
|
|
%(cval)s
|
||
|
|
%(prefilter)s
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
rotate : ndarray
|
||
|
|
The rotated input.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
For complex-valued `input`, this function rotates the real and imaginary
|
||
|
|
components independently.
|
||
|
|
|
||
|
|
.. versionadded:: 1.6.0
|
||
|
|
Complex-valued support added.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from scipy import ndimage, datasets
|
||
|
|
>>> import matplotlib.pyplot as plt
|
||
|
|
>>> fig = plt.figure(figsize=(10, 3))
|
||
|
|
>>> ax1, ax2, ax3 = fig.subplots(1, 3)
|
||
|
|
>>> img = datasets.ascent()
|
||
|
|
>>> img_45 = ndimage.rotate(img, 45, reshape=False)
|
||
|
|
>>> full_img_45 = ndimage.rotate(img, 45, reshape=True)
|
||
|
|
>>> ax1.imshow(img, cmap='gray')
|
||
|
|
>>> ax1.set_axis_off()
|
||
|
|
>>> ax2.imshow(img_45, cmap='gray')
|
||
|
|
>>> ax2.set_axis_off()
|
||
|
|
>>> ax3.imshow(full_img_45, cmap='gray')
|
||
|
|
>>> ax3.set_axis_off()
|
||
|
|
>>> fig.set_layout_engine('tight')
|
||
|
|
>>> plt.show()
|
||
|
|
>>> print(img.shape)
|
||
|
|
(512, 512)
|
||
|
|
>>> print(img_45.shape)
|
||
|
|
(512, 512)
|
||
|
|
>>> print(full_img_45.shape)
|
||
|
|
(724, 724)
|
||
|
|
|
||
|
|
"""
|
||
|
|
input_arr = numpy.asarray(input)
|
||
|
|
ndim = input_arr.ndim
|
||
|
|
|
||
|
|
if ndim < 2:
|
||
|
|
raise ValueError('input array should be at least 2D')
|
||
|
|
|
||
|
|
axes = list(axes)
|
||
|
|
|
||
|
|
if len(axes) != 2:
|
||
|
|
raise ValueError('axes should contain exactly two values')
|
||
|
|
|
||
|
|
if not all([float(ax).is_integer() for ax in axes]):
|
||
|
|
raise ValueError('axes should contain only integer values')
|
||
|
|
|
||
|
|
if axes[0] < 0:
|
||
|
|
axes[0] += ndim
|
||
|
|
if axes[1] < 0:
|
||
|
|
axes[1] += ndim
|
||
|
|
if axes[0] < 0 or axes[1] < 0 or axes[0] >= ndim or axes[1] >= ndim:
|
||
|
|
raise ValueError('invalid rotation plane specified')
|
||
|
|
|
||
|
|
axes.sort()
|
||
|
|
|
||
|
|
c, s = special.cosdg(angle), special.sindg(angle)
|
||
|
|
|
||
|
|
rot_matrix = numpy.array([[c, s],
|
||
|
|
[-s, c]])
|
||
|
|
|
||
|
|
img_shape = numpy.asarray(input_arr.shape)
|
||
|
|
in_plane_shape = img_shape[axes]
|
||
|
|
if reshape:
|
||
|
|
# Compute transformed input bounds
|
||
|
|
iy, ix = in_plane_shape
|
||
|
|
out_bounds = rot_matrix @ [[0, 0, iy, iy],
|
||
|
|
[0, ix, 0, ix]]
|
||
|
|
# Compute the shape of the transformed input plane
|
||
|
|
out_plane_shape = (numpy.ptp(out_bounds, axis=1) + 0.5).astype(int)
|
||
|
|
else:
|
||
|
|
out_plane_shape = img_shape[axes]
|
||
|
|
|
||
|
|
out_center = rot_matrix @ ((out_plane_shape - 1) / 2)
|
||
|
|
in_center = (in_plane_shape - 1) / 2
|
||
|
|
offset = in_center - out_center
|
||
|
|
|
||
|
|
output_shape = img_shape
|
||
|
|
output_shape[axes] = out_plane_shape
|
||
|
|
output_shape = tuple(output_shape)
|
||
|
|
|
||
|
|
complex_output = numpy.iscomplexobj(input_arr)
|
||
|
|
output = _ni_support._get_output(output, input_arr, shape=output_shape,
|
||
|
|
complex_output=complex_output)
|
||
|
|
|
||
|
|
if ndim <= 2:
|
||
|
|
affine_transform(input_arr, rot_matrix, offset, output_shape, output,
|
||
|
|
order, mode, cval, prefilter)
|
||
|
|
else:
|
||
|
|
# If ndim > 2, the rotation is applied over all the planes
|
||
|
|
# parallel to axes
|
||
|
|
planes_coord = itertools.product(
|
||
|
|
*[[slice(None)] if ax in axes else range(img_shape[ax])
|
||
|
|
for ax in range(ndim)])
|
||
|
|
|
||
|
|
out_plane_shape = tuple(out_plane_shape)
|
||
|
|
|
||
|
|
for coordinates in planes_coord:
|
||
|
|
ia = input_arr[coordinates]
|
||
|
|
oa = output[coordinates]
|
||
|
|
affine_transform(ia, rot_matrix, offset, out_plane_shape,
|
||
|
|
oa, order, mode, cval, prefilter)
|
||
|
|
|
||
|
|
return output
|