# -*- coding: utf-8 -*-
import numbers
import dask.array as da
from . import _utils
__all__ = [
"fourier_gaussian",
"fourier_shift",
"fourier_uniform",
]
[docs]def fourier_gaussian(image, sigma, n=-1, axis=-1):
"""
Multi-dimensional Gaussian fourier filter.
The array is multiplied with the fourier transform of a Gaussian
kernel.
Parameters
----------
image : array_like
The input image.
sigma : float or sequence
The sigma of the Gaussian kernel. If a float, `sigma` is the same for
all axes. If a sequence, `sigma` has to contain one value for each
axis.
n : int, optional
If `n` is negative (default), then the image is assumed to be the
result of a complex fft.
If `n` is larger than or equal to zero, the image is assumed to be the
result of a real fft, and `n` gives the length of the array before
transformation along the real transform direction.
axis : int, optional
The axis of the real transform.
Returns
-------
fourier_gaussian : Dask Array
Examples
--------
>>> from scipy import ndimage, misc
>>> import numpy.fft
>>> import matplotlib.pyplot as plt
>>> fig, (ax1, ax2) = plt.subplots(1, 2)
>>> plt.gray() # show the filtered result in grayscale
>>> ascent = misc.ascent()
>>> image = numpy.fft.fft2(ascent)
>>> result = ndimage.fourier_gaussian(image, sigma=4)
>>> result = numpy.fft.ifft2(result)
>>> ax1.imshow(ascent)
"""
# Validate and normalize arguments
image, sigma, n, axis = _utils._norm_args(image, sigma, n=n, axis=axis)
# Compute frequencies
ang_freq_grid = _utils._get_ang_freq_grid(
image.shape,
chunks=image.chunks,
n=n,
axis=axis,
dtype=sigma.dtype
)
# Compute Fourier transformed Gaussian
result = image.copy()
scale = (sigma ** 2) / -2
for ax, f in enumerate(ang_freq_grid):
f *= f
gaussian = da.exp(scale[ax] * f)
gaussian = _utils._reshape_nd(gaussian, ndim=image.ndim, axis=ax)
result *= gaussian
return result
[docs]def fourier_shift(image, shift, n=-1, axis=-1):
"""
Multi-dimensional fourier shift filter.
The array is multiplied with the fourier transform of a shift operation.
Parameters
----------
image : array_like
The input image.
shift : float or sequence
The size of the box used for filtering.
If a float, `shift` is the same for all axes. If a sequence, `shift`
has to contain one value for each axis.
n : int, optional
If `n` is negative (default), then the image is assumed to be the
result of a complex fft.
If `n` is larger than or equal to zero, the image is assumed to be the
result of a real fft, and `n` gives the length of the array before
transformation along the real transform direction.
axis : int, optional
The axis of the real transform.
Returns
-------
fourier_shift : Dask Array
Examples
--------
>>> from scipy import ndimage, misc
>>> import matplotlib.pyplot as plt
>>> import numpy.fft
>>> fig, (ax1, ax2) = plt.subplots(1, 2)
>>> plt.gray() # show the filtered result in grayscale
>>> ascent = misc.ascent()
>>> image = numpy.fft.fft2(ascent)
>>> result = ndimage.fourier_shift(image, shift=200)
>>> result = numpy.fft.ifft2(result)
>>> ax1.imshow(ascent)
>>> ax2.imshow(result.real) # the imaginary part is an artifact
>>> plt.show()
"""
if issubclass(image.dtype.type, numbers.Real):
image = image.astype(complex)
# Validate and normalize arguments
image, shift, n, axis = _utils._norm_args(image, shift, n=n, axis=axis)
# Constants with type converted
J = image.dtype.type(1j)
# Get the grid of frequencies
ang_freq_grid = _utils._get_ang_freq_grid(
image.shape,
chunks=image.chunks,
n=n,
axis=axis,
dtype=shift.dtype
)
# Apply shift
result = image.copy()
for ax, f in enumerate(ang_freq_grid):
phase_shift = da.exp((-J) * shift[ax] * f)
phase_shift = _utils._reshape_nd(phase_shift, ndim=image.ndim, axis=ax)
result *= phase_shift
return result