rm CondaPkg environment

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ton
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"""Image restoration module.
"""
from .deconvolution import wiener, unsupervised_wiener, richardson_lucy
from .unwrap import unwrap_phase
from ._denoise import (denoise_tv_chambolle, denoise_tv_bregman,
denoise_bilateral, denoise_wavelet, estimate_sigma)
from ._cycle_spin import cycle_spin
from .non_local_means import denoise_nl_means
from .inpaint import inpaint_biharmonic
from .j_invariant import calibrate_denoiser
from .rolling_ball import rolling_ball, ball_kernel, ellipsoid_kernel
__all__ = ['wiener',
'unsupervised_wiener',
'richardson_lucy',
'unwrap_phase',
'denoise_tv_bregman',
'denoise_tv_chambolle',
'denoise_bilateral',
'denoise_wavelet',
'denoise_nl_means',
'estimate_sigma',
'inpaint_biharmonic',
'cycle_spin',
'calibrate_denoiser',
'rolling_ball',
'ellipsoid_kernel',
'ball_kernel',
]

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from itertools import product
import numpy as np
from .._shared import utils
from .._shared.utils import warn
try:
import dask
dask_available = True
except ImportError:
dask_available = False
def _generate_shifts(ndim, multichannel, max_shifts, shift_steps=1):
"""Returns all combinations of shifts in n dimensions over the specified
max_shifts and step sizes.
Examples
--------
>>> s = list(_generate_shifts(2, False, max_shifts=(1, 2), shift_steps=1))
>>> print(s)
[(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2)]
"""
mc = int(multichannel)
if np.isscalar(max_shifts):
max_shifts = (max_shifts, ) * (ndim - mc) + (0, ) * mc
elif multichannel and len(max_shifts) == ndim - 1:
max_shifts = tuple(max_shifts) + (0, )
elif len(max_shifts) != ndim:
raise ValueError("max_shifts should have length ndim")
if np.isscalar(shift_steps):
shift_steps = (shift_steps, ) * (ndim - mc) + (1, ) * mc
elif multichannel and len(shift_steps) == ndim - 1:
shift_steps = tuple(shift_steps) + (1, )
elif len(shift_steps) != ndim:
raise ValueError("max_shifts should have length ndim")
if any(s < 1 for s in shift_steps):
raise ValueError("shift_steps must all be >= 1")
if multichannel and max_shifts[-1] != 0:
raise ValueError(
"Multichannel cycle spinning should not have shifts along the "
"last axis.")
return product(*[range(0, s + 1, t) for
s, t in zip(max_shifts, shift_steps)])
@utils.channel_as_last_axis()
def cycle_spin(x, func, max_shifts, shift_steps=1, num_workers=None,
func_kw={}, *, channel_axis=None):
"""Cycle spinning (repeatedly apply func to shifted versions of x).
Parameters
----------
x : array-like
Data for input to ``func``.
func : function
A function to apply to circularly shifted versions of ``x``. Should
take ``x`` as its first argument. Any additional arguments can be
supplied via ``func_kw``.
max_shifts : int or tuple
If an integer, shifts in ``range(0, max_shifts+1)`` will be used along
each axis of ``x``. If a tuple, ``range(0, max_shifts[i]+1)`` will be
along axis i.
shift_steps : int or tuple, optional
The step size for the shifts applied along axis, i, are::
``range((0, max_shifts[i]+1, shift_steps[i]))``. If an integer is
provided, the same step size is used for all axes.
num_workers : int or None, optional
The number of parallel threads to use during cycle spinning. If set to
``None``, the full set of available cores are used.
func_kw : dict, optional
Additional keyword arguments to supply to ``func``.
channel_axis : int or None, optional
If None, the image is assumed to be a grayscale (single channel) image.
Otherwise, this parameter indicates which axis of the array corresponds
to channels.
.. versionadded:: 0.19
``channel_axis`` was added in 0.19.
Returns
-------
avg_y : np.ndarray
The output of ``func(x, **func_kw)`` averaged over all combinations of
the specified axis shifts.
Notes
-----
Cycle spinning was proposed as a way to approach shift-invariance via
performing several circular shifts of a shift-variant transform [1]_.
For a n-level discrete wavelet transforms, one may wish to perform all
shifts up to ``max_shifts = 2**n - 1``. In practice, much of the benefit
can often be realized with only a small number of shifts per axis.
For transforms such as the blockwise discrete cosine transform, one may
wish to evaluate shifts up to the block size used by the transform.
References
----------
.. [1] R.R. Coifman and D.L. Donoho. "Translation-Invariant De-Noising".
Wavelets and Statistics, Lecture Notes in Statistics, vol.103.
Springer, New York, 1995, pp.125-150.
:DOI:`10.1007/978-1-4612-2544-7_9`
Examples
--------
>>> import skimage.data
>>> from skimage import img_as_float
>>> from skimage.restoration import denoise_wavelet, cycle_spin
>>> img = img_as_float(skimage.data.camera())
>>> sigma = 0.1
>>> img = img + sigma * np.random.standard_normal(img.shape)
>>> denoised = cycle_spin(img, func=denoise_wavelet,
... max_shifts=3)
"""
x = np.asanyarray(x)
multichannel = channel_axis is not None
all_shifts = _generate_shifts(x.ndim, multichannel, max_shifts,
shift_steps)
all_shifts = list(all_shifts)
roll_axes = tuple(range(x.ndim))
def _run_one_shift(shift):
# shift, apply function, inverse shift
xs = np.roll(x, shift, axis=roll_axes)
tmp = func(xs, **func_kw)
return np.roll(tmp, tuple(-s for s in shift), axis=roll_axes)
if not dask_available and (num_workers is None or num_workers > 1):
num_workers = 1
warn('The optional dask dependency is not installed. '
'The number of workers is set to 1. To silence '
'this warning, install dask or explicitly set `num_workers=1` '
'when calling the `cycle_spin` function')
# compute a running average across the cycle shifts
if num_workers == 1:
# serial processing
mean = _run_one_shift(all_shifts[0])
for shift in all_shifts[1:]:
mean += _run_one_shift(shift)
mean /= len(all_shifts)
else:
# multithreaded via dask
futures = [dask.delayed(_run_one_shift)(s) for s in all_shifts]
mean = sum(futures) / len(futures)
mean = mean.compute(num_workers=num_workers)
return mean

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"""Implementations restoration functions"""
import numpy as np
from scipy.signal import convolve
from .._shared.utils import _supported_float_type
from . import uft
def wiener(image, psf, balance, reg=None, is_real=True, clip=True):
r"""Wiener-Hunt deconvolution
Return the deconvolution with a Wiener-Hunt approach (i.e. with
Fourier diagonalisation).
Parameters
----------
image : ndarray
Input degraded image (can be n-dimensional).
psf : ndarray
Point Spread Function. This is assumed to be the impulse
response (input image space) if the data-type is real, or the
transfer function (Fourier space) if the data-type is
complex. There is no constraints on the shape of the impulse
response. The transfer function must be of shape
`(N1, N2, ..., ND)` if `is_real is True`,
`(N1, N2, ..., ND // 2 + 1)` otherwise (see `np.fft.rfftn`).
balance : float
The regularisation parameter value that tunes the balance
between the data adequacy that improve frequency restoration
and the prior adequacy that reduce frequency restoration (to
avoid noise artifacts).
reg : ndarray, optional
The regularisation operator. The Laplacian by default. It can
be an impulse response or a transfer function, as for the
psf. Shape constraint is the same as for the `psf` parameter.
is_real : boolean, optional
True by default. Specify if ``psf`` and ``reg`` are provided
with hermitian hypothesis, that is only half of the frequency
plane is provided (due to the redundancy of Fourier transform
of real signal). It's apply only if ``psf`` and/or ``reg`` are
provided as transfer function. For the hermitian property see
``uft`` module or ``np.fft.rfftn``.
clip : boolean, optional
True by default. If True, pixel values of the result above 1 or
under -1 are thresholded for skimage pipeline compatibility.
Returns
-------
im_deconv : (M, N) ndarray
The deconvolved image.
Examples
--------
>>> from skimage import color, data, restoration
>>> img = color.rgb2gray(data.astronaut())
>>> from scipy.signal import convolve2d
>>> psf = np.ones((5, 5)) / 25
>>> img = convolve2d(img, psf, 'same')
>>> rng = np.random.default_rng()
>>> img += 0.1 * img.std() * rng.standard_normal(img.shape)
>>> deconvolved_img = restoration.wiener(img, psf, 0.1)
Notes
-----
This function applies the Wiener filter to a noisy and degraded
image by an impulse response (or PSF). If the data model is
.. math:: y = Hx + n
where :math:`n` is noise, :math:`H` the PSF and :math:`x` the
unknown original image, the Wiener filter is
.. math::
\hat x = F^\dagger (|\Lambda_H|^2 + \lambda |\Lambda_D|^2)
\Lambda_H^\dagger F y
where :math:`F` and :math:`F^\dagger` are the Fourier and inverse
Fourier transforms respectively, :math:`\Lambda_H` the transfer
function (or the Fourier transform of the PSF, see [Hunt] below)
and :math:`\Lambda_D` the filter to penalize the restored image
frequencies (Laplacian by default, that is penalization of high
frequency). The parameter :math:`\lambda` tunes the balance
between the data (that tends to increase high frequency, even
those coming from noise), and the regularization.
These methods are then specific to a prior model. Consequently,
the application or the true image nature must correspond to the
prior model. By default, the prior model (Laplacian) introduce
image smoothness or pixel correlation. It can also be interpreted
as high-frequency penalization to compensate the instability of
the solution with respect to the data (sometimes called noise
amplification or "explosive" solution).
Finally, the use of Fourier space implies a circulant property of
:math:`H`, see [2]_.
References
----------
.. [1] François Orieux, Jean-François Giovannelli, and Thomas
Rodet, "Bayesian estimation of regularization and point
spread function parameters for Wiener-Hunt deconvolution",
J. Opt. Soc. Am. A 27, 1593-1607 (2010)
https://www.osapublishing.org/josaa/abstract.cfm?URI=josaa-27-7-1593
https://hal.archives-ouvertes.fr/hal-00674508
.. [2] B. R. Hunt "A matrix theory proof of the discrete
convolution theorem", IEEE Trans. on Audio and
Electroacoustics, vol. au-19, no. 4, pp. 285-288, dec. 1971
"""
if reg is None:
reg, _ = uft.laplacian(image.ndim, image.shape, is_real=is_real)
if not np.iscomplexobj(reg):
reg = uft.ir2tf(reg, image.shape, is_real=is_real)
float_type = _supported_float_type(image.dtype)
image = image.astype(float_type, copy=False)
psf = psf.real.astype(float_type, copy=False)
reg = reg.real.astype(float_type, copy=False)
if psf.shape != reg.shape:
trans_func = uft.ir2tf(psf, image.shape, is_real=is_real)
else:
trans_func = psf
wiener_filter = np.conj(trans_func) / (np.abs(trans_func) ** 2 +
balance * np.abs(reg) ** 2)
if is_real:
deconv = uft.uirfftn(wiener_filter * uft.urfftn(image),
shape=image.shape)
else:
deconv = uft.uifftn(wiener_filter * uft.ufftn(image))
if clip:
deconv[deconv > 1] = 1
deconv[deconv < -1] = -1
return deconv
def unsupervised_wiener(image, psf, reg=None, user_params=None, is_real=True,
clip=True, *, random_state=None):
"""Unsupervised Wiener-Hunt deconvolution.
Return the deconvolution with a Wiener-Hunt approach, where the
hyperparameters are automatically estimated. The algorithm is a
stochastic iterative process (Gibbs sampler) described in the
reference below. See also ``wiener`` function.
Parameters
----------
image : (M, N) ndarray
The input degraded image.
psf : ndarray
The impulse response (input image's space) or the transfer
function (Fourier space). Both are accepted. The transfer
function is automatically recognized as being complex
(``np.iscomplexobj(psf)``).
reg : ndarray, optional
The regularisation operator. The Laplacian by default. It can
be an impulse response or a transfer function, as for the psf.
user_params : dict, optional
Dictionary of parameters for the Gibbs sampler. See below.
clip : boolean, optional
True by default. If true, pixel values of the result above 1 or
under -1 are thresholded for skimage pipeline compatibility.
random_state : {None, int, `numpy.random.Generator`}, optional
If `random_state` is None the `numpy.random.Generator` singleton is
used.
If `random_state` is an int, a new ``Generator`` instance is used,
seeded with `random_state`.
If `random_state` is already a ``Generator`` instance then that
instance is used.
.. versionadded:: 0.19
Returns
-------
x_postmean : (M, N) ndarray
The deconvolved image (the posterior mean).
chains : dict
The keys ``noise`` and ``prior`` contain the chain list of
noise and prior precision respectively.
Other parameters
----------------
The keys of ``user_params`` are:
threshold : float
The stopping criterion: the norm of the difference between to
successive approximated solution (empirical mean of object
samples, see Notes section). 1e-4 by default.
burnin : int
The number of sample to ignore to start computation of the
mean. 15 by default.
min_num_iter : int
The minimum number of iterations. 30 by default.
max_num_iter : int
The maximum number of iterations if ``threshold`` is not
satisfied. 200 by default.
callback : callable (None by default)
A user provided callable to which is passed, if the function
exists, the current image sample for whatever purpose. The user
can store the sample, or compute other moments than the
mean. It has no influence on the algorithm execution and is
only for inspection.
Examples
--------
>>> from skimage import color, data, restoration
>>> img = color.rgb2gray(data.astronaut())
>>> from scipy.signal import convolve2d
>>> psf = np.ones((5, 5)) / 25
>>> img = convolve2d(img, psf, 'same')
>>> rng = np.random.default_rng()
>>> img += 0.1 * img.std() * rng.standard_normal(img.shape)
>>> deconvolved_img = restoration.unsupervised_wiener(img, psf)
Notes
-----
The estimated image is design as the posterior mean of a
probability law (from a Bayesian analysis). The mean is defined as
a sum over all the possible images weighted by their respective
probability. Given the size of the problem, the exact sum is not
tractable. This algorithm use of MCMC to draw image under the
posterior law. The practical idea is to only draw highly probable
images since they have the biggest contribution to the mean. At the
opposite, the less probable images are drawn less often since
their contribution is low. Finally, the empirical mean of these
samples give us an estimation of the mean, and an exact
computation with an infinite sample set.
References
----------
.. [1] François Orieux, Jean-François Giovannelli, and Thomas
Rodet, "Bayesian estimation of regularization and point
spread function parameters for Wiener-Hunt deconvolution",
J. Opt. Soc. Am. A 27, 1593-1607 (2010)
https://www.osapublishing.org/josaa/abstract.cfm?URI=josaa-27-7-1593
https://hal.archives-ouvertes.fr/hal-00674508
"""
params = {'threshold': 1e-4, 'max_num_iter': 200,
'min_num_iter': 30, 'burnin': 15, 'callback': None}
params.update(user_params or {})
if reg is None:
reg, _ = uft.laplacian(image.ndim, image.shape, is_real=is_real)
if not np.iscomplexobj(reg):
reg = uft.ir2tf(reg, image.shape, is_real=is_real)
float_type = _supported_float_type(image.dtype)
image = image.astype(float_type, copy=False)
psf = psf.real.astype(float_type, copy=False)
reg = reg.real.astype(float_type, copy=False)
if psf.shape != reg.shape:
trans_fct = uft.ir2tf(psf, image.shape, is_real=is_real)
else:
trans_fct = psf
# The mean of the object
x_postmean = np.zeros(trans_fct.shape, dtype=float_type)
# The previous computed mean in the iterative loop
prev_x_postmean = np.zeros(trans_fct.shape, dtype=float_type)
# Difference between two successive mean
delta = np.NAN
# Initial state of the chain
gn_chain, gx_chain = [1], [1]
# The correlation of the object in Fourier space (if size is big,
# this can reduce computation time in the loop)
areg2 = np.abs(reg) ** 2
atf2 = np.abs(trans_fct) ** 2
# The Fourier transform may change the image.size attribute, so we
# store it.
if is_real:
data_spectrum = uft.urfft2(image)
else:
data_spectrum = uft.ufft2(image)
rng = np.random.default_rng(random_state)
# Gibbs sampling
for iteration in range(params['max_num_iter']):
# Sample of Eq. 27 p(circX^k | gn^k-1, gx^k-1, y).
# weighting (correlation in direct space)
precision = gn_chain[-1] * atf2 + gx_chain[-1] * areg2 # Eq. 29
# Note: Use astype instead of dtype argument to standard_normal to get
# similar random values across precisions, as needed for
# reference data used by test_unsupervised_wiener.
_rand1 = rng.standard_normal(data_spectrum.shape)
_rand1 = _rand1.astype(float_type, copy=False)
_rand2 = rng.standard_normal(data_spectrum.shape)
_rand2 = _rand2.astype(float_type, copy=False)
excursion = np.sqrt(0.5 / precision) * (_rand1 + 1j * _rand2)
# mean Eq. 30 (RLS for fixed gn, gamma0 and gamma1 ...)
wiener_filter = gn_chain[-1] * np.conj(trans_fct) / precision
# sample of X in Fourier space
x_sample = wiener_filter * data_spectrum + excursion
if params['callback']:
params['callback'](x_sample)
# sample of Eq. 31 p(gn | x^k, gx^k, y)
gn_chain.append(rng.gamma(image.size / 2,
2 / uft.image_quad_norm(data_spectrum
- x_sample
* trans_fct)))
# sample of Eq. 31 p(gx | x^k, gn^k-1, y)
gx_chain.append(rng.gamma((image.size - 1) / 2,
2 / uft.image_quad_norm(x_sample * reg)))
# current empirical average
if iteration > params['burnin']:
x_postmean = prev_x_postmean + x_sample
if iteration > (params['burnin'] + 1):
current = x_postmean / (iteration - params['burnin'])
previous = prev_x_postmean / (iteration - params['burnin'] - 1)
delta = (np.sum(np.abs(current - previous))
/ np.sum(np.abs(x_postmean))
/ (iteration - params['burnin']))
prev_x_postmean = x_postmean
# stop of the algorithm
if (
(iteration > params['min_num_iter'])
and (delta < params['threshold'])
):
break
# Empirical average \approx POSTMEAN Eq. 44
x_postmean = x_postmean / (iteration - params['burnin'])
if is_real:
x_postmean = uft.uirfft2(x_postmean, shape=image.shape)
else:
x_postmean = uft.uifft2(x_postmean)
if clip:
x_postmean[x_postmean > 1] = 1
x_postmean[x_postmean < -1] = -1
return (x_postmean, {'noise': gn_chain, 'prior': gx_chain})
def richardson_lucy(image, psf, num_iter=50, clip=True, filter_epsilon=None):
"""Richardson-Lucy deconvolution.
Parameters
----------
image : ndarray
Input degraded image (can be n-dimensional).
psf : ndarray
The point spread function.
num_iter : int, optional
Number of iterations. This parameter plays the role of
regularisation.
clip : boolean, optional
True by default. If true, pixel value of the result above 1 or
under -1 are thresholded for skimage pipeline compatibility.
filter_epsilon: float, optional
Value below which intermediate results become 0 to avoid division
by small numbers.
Returns
-------
im_deconv : ndarray
The deconvolved image.
Examples
--------
>>> from skimage import img_as_float, data, restoration
>>> camera = img_as_float(data.camera())
>>> from scipy.signal import convolve2d
>>> psf = np.ones((5, 5)) / 25
>>> camera = convolve2d(camera, psf, 'same')
>>> rng = np.random.default_rng()
>>> camera += 0.1 * camera.std() * rng.standard_normal(camera.shape)
>>> deconvolved = restoration.richardson_lucy(camera, psf, 5)
References
----------
.. [1] https://en.wikipedia.org/wiki/Richardson%E2%80%93Lucy_deconvolution
"""
float_type = _supported_float_type(image.dtype)
image = image.astype(float_type, copy=False)
psf = psf.astype(float_type, copy=False)
im_deconv = np.full(image.shape, 0.5, dtype=float_type)
psf_mirror = np.flip(psf)
# Small regularization parameter used to avoid 0 divisions
eps = 1e-12
for _ in range(num_iter):
conv = convolve(im_deconv, psf, mode='same') + eps
if filter_epsilon:
relative_blur = np.where(conv < filter_epsilon, 0, image / conv)
else:
relative_blur = image / conv
im_deconv *= convolve(relative_blur, psf_mirror, mode='same')
if clip:
im_deconv[im_deconv > 1] = 1
im_deconv[im_deconv < -1] = -1
return im_deconv

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import numpy as np
from scipy import sparse
from scipy.sparse.linalg import spsolve
import scipy.ndimage as ndi
from scipy.ndimage import laplace
import skimage
from .._shared import utils
from ..measure import label
from ._inpaint import _build_matrix_inner
def _get_neighborhood(nd_idx, radius, nd_shape):
bounds_lo = np.maximum(nd_idx - radius, 0)
bounds_hi = np.minimum(nd_idx + radius + 1, nd_shape)
return bounds_lo, bounds_hi
def _get_neigh_coef(shape, center, dtype=float):
# Create biharmonic coefficients ndarray
neigh_coef = np.zeros(shape, dtype=dtype)
neigh_coef[center] = 1
neigh_coef = laplace(laplace(neigh_coef))
# extract non-zero locations and values
coef_idx = np.where(neigh_coef)
coef_vals = neigh_coef[coef_idx]
coef_idx = np.stack(coef_idx, axis=0)
return neigh_coef, coef_idx, coef_vals
def _inpaint_biharmonic_single_region(image, mask, out, neigh_coef_full,
coef_vals, raveled_offsets):
"""Solve a (sparse) linear system corresponding to biharmonic inpainting.
This function creates a linear system of the form:
``A @ u = b``
where ``A`` is a sparse matrix, ``b`` is a vector enforcing smoothness and
boundary constraints and ``u`` is the vector of inpainted values to be
(uniquely) determined by solving the linear system.
``A`` is a sparse matrix of shape (n_mask, n_mask) where `n_mask``
corresponds to the number of non-zero values in ``mask`` (i.e. the number
of pixels to be inpainted). Each row in A will have a number of non-zero
values equal to the number of non-zero values in the biharmonic kernel,
``neigh_coef_full``. In practice, biharmonic kernels with reduced extent
are used at the image borders. This matrix, ``A`` is the same for all
image channels (since the same inpainting mask is currently used for all
channels).
``u`` is a dense matrix of shape ``(n_mask, n_channels)`` and represents
the vector of unknown values for each channel.
``b`` is a dense matrix of shape ``(n_mask, n_channels)`` and represents
the desired output of convolving the solution with the biharmonic kernel.
At mask locations where there is no overlap with known values, ``b`` will
have a value of 0. This enforces the biharmonic smoothness constraint in
the interior of inpainting regions. For regions near the boundary that
overlap with known values, the entries in ``b`` enforce boundary conditions
designed to avoid discontinuity with the known values.
"""
n_channels = out.shape[-1]
radius = neigh_coef_full.shape[0] // 2
edge_mask = np.ones(mask.shape, dtype=bool)
edge_mask[(slice(radius, -radius),) * mask.ndim] = 0
boundary_mask = edge_mask * mask
center_mask = ~edge_mask * mask
boundary_pts = np.where(boundary_mask)
boundary_i = np.flatnonzero(boundary_mask)
center_i = np.flatnonzero(center_mask)
mask_i = np.concatenate((boundary_i, center_i))
center_pts = np.where(center_mask)
mask_pts = tuple(
[np.concatenate((b, c)) for b, c in zip(boundary_pts, center_pts)]
)
# Use convolution to predetermine the number of non-zero entries in the
# sparse system matrix.
structure = neigh_coef_full != 0
tmp = ndi.convolve(mask, structure, output=np.uint8, mode='constant')
nnz_matrix = tmp[mask].sum()
# Need to estimate the number of zeros for the right hand side vector.
# The computation below will slightly overestimate the true number of zeros
# due to edge effects (the kernel itself gets shrunk in size near the
# edges, but that isn't accounted for here). We can trim any excess entries
# later.
n_mask = np.count_nonzero(mask)
n_struct = np.count_nonzero(structure)
nnz_rhs_vector_max = n_mask - np.count_nonzero(tmp == n_struct)
# pre-allocate arrays storing sparse matrix indices and values
row_idx_known = np.empty(nnz_rhs_vector_max, dtype=np.intp)
data_known = np.zeros((nnz_rhs_vector_max, n_channels), dtype=out.dtype)
row_idx_unknown = np.empty(nnz_matrix, dtype=np.intp)
col_idx_unknown = np.empty(nnz_matrix, dtype=np.intp)
data_unknown = np.empty(nnz_matrix, dtype=out.dtype)
# cache the various small, non-square Laplacians used near the boundary
coef_cache = {}
# Iterate over masked points near the boundary
mask_flat = mask.reshape(-1)
out_flat = np.ascontiguousarray(out.reshape((-1, n_channels)))
idx_known = 0
idx_unknown = 0
mask_pt_n = -1
boundary_pts = np.stack(boundary_pts, axis=1)
for mask_pt_n, nd_idx in enumerate(boundary_pts):
# Get bounded neighborhood of selected radius
b_lo, b_hi = _get_neighborhood(nd_idx, radius, mask.shape)
# Create (truncated) biharmonic coefficients ndarray
coef_shape = tuple(b_hi - b_lo)
coef_center = tuple(nd_idx - b_lo)
coef_idx, coefs = coef_cache.get((coef_shape, coef_center),
(None, None))
if coef_idx is None:
_ , coef_idx, coefs = _get_neigh_coef(coef_shape,
coef_center,
dtype=out.dtype)
coef_cache[(coef_shape, coef_center)] = (coef_idx, coefs)
# compute corresponding 1d indices into the mask
coef_idx = coef_idx + b_lo[:, np.newaxis]
index1d = np.ravel_multi_index(coef_idx, mask.shape)
# Iterate over masked point's neighborhood
nvals = 0
for coef, i in zip(coefs, index1d):
if mask_flat[i]:
row_idx_unknown[idx_unknown] = mask_pt_n
col_idx_unknown[idx_unknown] = i
data_unknown[idx_unknown] = coef
idx_unknown += 1
else:
data_known[idx_known, :] -= coef * out_flat[i, :]
nvals += 1
if nvals:
row_idx_known[idx_known] = mask_pt_n
idx_known += 1
# Call an efficient Cython-based implementation for all interior points
row_start = mask_pt_n + 1
known_start_idx = idx_known
unknown_start_idx = idx_unknown
nnz_rhs = _build_matrix_inner(
# starting indices
row_start, known_start_idx, unknown_start_idx,
# input arrays
center_i, raveled_offsets, coef_vals, mask_flat,
out_flat,
# output arrays
row_idx_known, data_known, row_idx_unknown, col_idx_unknown,
data_unknown
)
# trim RHS vector values and indices to the exact length
row_idx_known = row_idx_known[:nnz_rhs]
data_known = data_known[:nnz_rhs, :]
# Form sparse matrix of unknown values
sp_shape = (n_mask, out.size)
matrix_unknown = sparse.coo_matrix(
(data_unknown, (row_idx_unknown, col_idx_unknown)), shape=sp_shape
).tocsr()
# Solve linear system for masked points
matrix_unknown = matrix_unknown[:, mask_i]
# dense vectors representing the right hand side for each channel
rhs = np.zeros((n_mask, n_channels), dtype=out.dtype)
rhs[row_idx_known, :] = data_known
# set use_umfpack to False so float32 data is supported
result = spsolve(matrix_unknown, rhs, use_umfpack=False,
permc_spec='MMD_ATA')
if result.ndim == 1:
result = result[:, np.newaxis]
out[mask_pts] = result
return out
@utils.channel_as_last_axis()
def inpaint_biharmonic(image, mask, *,
split_into_regions=False, channel_axis=None):
"""Inpaint masked points in image with biharmonic equations.
Parameters
----------
image : (M[, N[, ..., P]][, C]) ndarray
Input image.
mask : (M[, N[, ..., P]]) ndarray
Array of pixels to be inpainted. Have to be the same shape as one
of the 'image' channels. Unknown pixels have to be represented with 1,
known pixels - with 0.
split_into_regions : boolean, optional
If True, inpainting is performed on a region-by-region basis. This is
likely to be slower, but will have reduced memory requirements.
channel_axis : int or None, optional
If None, the image is assumed to be a grayscale (single channel) image.
Otherwise, this parameter indicates which axis of the array corresponds
to channels.
.. versionadded:: 0.19
``channel_axis`` was added in 0.19.
Returns
-------
out : (M[, N[, ..., P]][, C]) ndarray
Input image with masked pixels inpainted.
References
----------
.. [1] S.B.Damelin and N.S.Hoang. "On Surface Completion and Image
Inpainting by Biharmonic Functions: Numerical Aspects",
International Journal of Mathematics and Mathematical Sciences,
Vol. 2018, Article ID 3950312
:DOI:`10.1155/2018/3950312`
.. [2] C. K. Chui and H. N. Mhaskar, MRA Contextual-Recovery Extension of
Smooth Functions on Manifolds, Appl. and Comp. Harmonic Anal.,
28 (2010), 104-113,
:DOI:`10.1016/j.acha.2009.04.004`
Examples
--------
>>> img = np.tile(np.square(np.linspace(0, 1, 5)), (5, 1))
>>> mask = np.zeros_like(img)
>>> mask[2, 2:] = 1
>>> mask[1, 3:] = 1
>>> mask[0, 4:] = 1
>>> out = inpaint_biharmonic(img, mask)
"""
if image.ndim < 1:
raise ValueError('Input array has to be at least 1D')
multichannel = channel_axis is not None
img_baseshape = image.shape[:-1] if multichannel else image.shape
if img_baseshape != mask.shape:
raise ValueError('Input arrays have to be the same shape')
if np.ma.isMaskedArray(image):
raise TypeError('Masked arrays are not supported')
image = skimage.img_as_float(image)
# float16->float32 and float128->float64
float_dtype = utils._supported_float_type(image.dtype)
image = image.astype(float_dtype, copy=False)
mask = mask.astype(bool, copy=False)
if not multichannel:
image = image[..., np.newaxis]
out = np.copy(image, order='C')
# Create biharmonic coefficients ndarray
radius = 2
coef_shape = (2 * radius + 1,) * mask.ndim
coef_center = (radius,) * mask.ndim
neigh_coef_full, coef_idx, coef_vals = _get_neigh_coef(coef_shape,
coef_center,
dtype=out.dtype)
# stride for the last spatial dimension
channel_stride_bytes = out.strides[-2]
# offsets to all neighboring non-zero elements in the footprint
offsets = coef_idx - radius
# determine per-channel intensity limits
known_points = image[~mask]
limits = (known_points.min(axis=0), known_points.max(axis=0))
if split_into_regions:
# Split inpainting mask into independent regions
kernel = ndi.generate_binary_structure(mask.ndim, 1)
mask_dilated = ndi.binary_dilation(mask, structure=kernel)
mask_labeled = label(mask_dilated)
mask_labeled *= mask
bbox_slices = ndi.find_objects(mask_labeled)
for idx_region, bb_slice in enumerate(bbox_slices, 1):
# expand object bounding boxes by the biharmonic kernel radius
roi_sl = tuple(slice(max(sl.start - radius, 0),
min(sl.stop + radius, size))
for sl, size in zip(bb_slice, mask_labeled.shape))
# extract only the region surrounding the label of interest
mask_region = mask_labeled[roi_sl] == idx_region
# add slice for axes
roi_sl += (slice(None), )
# copy for contiguity and to account for possible ROI overlap
otmp = out[roi_sl].copy()
# compute raveled offsets for the ROI
ostrides = np.array([s // channel_stride_bytes
for s in otmp[..., 0].strides])
raveled_offsets = np.sum(offsets * ostrides[..., np.newaxis],
axis=0)
_inpaint_biharmonic_single_region(
image[roi_sl], mask_region, otmp,
neigh_coef_full, coef_vals, raveled_offsets
)
# assign output to the
out[roi_sl] = otmp
else:
# compute raveled offsets for output image
ostrides = np.array([s // channel_stride_bytes
for s in out[..., 0].strides])
raveled_offsets = np.sum(offsets * ostrides[..., np.newaxis], axis=0)
_inpaint_biharmonic_single_region(
image, mask, out, neigh_coef_full, coef_vals, raveled_offsets
)
# Handle enormous values on a per-channel basis
np.clip(out, a_min=limits[0], a_max=limits[1], out=out)
if not multichannel:
out = out[..., 0]
return out

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@@ -1,319 +0,0 @@
import itertools
import functools
import numpy as np
from scipy import ndimage as ndi
from .._shared.utils import _supported_float_type
from ..metrics import mean_squared_error
from ..util import img_as_float
def _interpolate_image(image, *, multichannel=False):
"""Replacing each pixel in ``image`` with the average of its neighbors.
Parameters
----------
image : ndarray
Input data to be interpolated.
multichannel : bool, optional
Whether the last axis of the image is to be interpreted as multiple
channels or another spatial dimension.
Returns
-------
interp : ndarray
Interpolated version of `image`.
"""
spatialdims = image.ndim if not multichannel else image.ndim - 1
conv_filter = ndi.generate_binary_structure(spatialdims, 1).astype(image.dtype)
conv_filter.ravel()[conv_filter.size // 2] = 0
conv_filter /= conv_filter.sum()
if multichannel:
interp = np.zeros_like(image)
for i in range(image.shape[-1]):
interp[..., i] = ndi.convolve(image[..., i], conv_filter,
mode='mirror')
else:
interp = ndi.convolve(image, conv_filter, mode='mirror')
return interp
def _generate_grid_slice(shape, *, offset, stride=3):
"""Generate slices of uniformly-spaced points in an array.
Parameters
----------
shape : tuple of int
Shape of the mask.
offset : int
The offset of the grid of ones. Iterating over ``offset`` will cover
the entire array. It should be between 0 and ``stride ** ndim``, not
inclusive, where ``ndim = len(shape)``.
stride : int, optional
The spacing between ones, used in each dimension.
Returns
-------
mask : ndarray
The mask.
Examples
--------
>>> shape = (4, 4)
>>> array = np.zeros(shape, dtype=int)
>>> grid_slice = _generate_grid_slice(shape, offset=0, stride=2)
>>> array[grid_slice] = 1
>>> print(array)
[[1 0 1 0]
[0 0 0 0]
[1 0 1 0]
[0 0 0 0]]
Changing the offset moves the location of the 1s:
>>> array = np.zeros(shape, dtype=int)
>>> grid_slice = _generate_grid_slice(shape, offset=3, stride=2)
>>> array[grid_slice] = 1
>>> print(array)
[[0 0 0 0]
[0 1 0 1]
[0 0 0 0]
[0 1 0 1]]
"""
phases = np.unravel_index(offset, (stride,) * len(shape))
mask = tuple(slice(p, None, stride) for p in phases)
return mask
def _invariant_denoise(image, denoise_function, *, stride=4,
masks=None, denoiser_kwargs=None):
"""Apply a J-invariant version of `denoise_function`.
Parameters
----------
image : ndarray
Input data to be denoised (converted using `img_as_float`).
denoise_function : function
Original denoising function.
stride : int, optional
Stride used in masking procedure that converts `denoise_function`
to J-invariance.
masks : list of ndarray, optional
Set of masks to use for computing J-invariant output. If `None`,
a full set of masks covering the image will be used.
denoiser_kwargs:
Keyword arguments passed to `denoise_function`.
Returns
-------
output : ndarray
Denoised image, of same shape as `image`.
"""
image = img_as_float(image)
# promote float16->float32 if needed
float_dtype = _supported_float_type(image.dtype)
image = image.astype(float_dtype, copy=False)
if denoiser_kwargs is None:
denoiser_kwargs = {}
multichannel = denoiser_kwargs.get('channel_axis', None) is not None
interp = _interpolate_image(image, multichannel=multichannel)
output = np.zeros_like(image)
if masks is None:
spatialdims = image.ndim if not multichannel else image.ndim - 1
n_masks = stride ** spatialdims
masks = (_generate_grid_slice(image.shape[:spatialdims],
offset=idx, stride=stride)
for idx in range(n_masks))
for mask in masks:
input_image = image.copy()
input_image[mask] = interp[mask]
output[mask] = denoise_function(input_image, **denoiser_kwargs)[mask]
return output
def _product_from_dict(dictionary):
"""Utility function to convert parameter ranges to parameter combinations.
Converts a dict of lists into a list of dicts whose values consist of the
cartesian product of the values in the original dict.
Parameters
----------
dictionary : dict of lists
Dictionary of lists to be multiplied.
Yields
------
selections : dicts of values
Dicts containing individual combinations of the values in the input
dict.
"""
keys = dictionary.keys()
for element in itertools.product(*dictionary.values()):
yield dict(zip(keys, element))
def calibrate_denoiser(image, denoise_function, denoise_parameters, *,
stride=4, approximate_loss=True,
extra_output=False):
"""Calibrate a denoising function and return optimal J-invariant version.
The returned function is partially evaluated with optimal parameter values
set for denoising the input image.
Parameters
----------
image : ndarray
Input data to be denoised (converted using `img_as_float`).
denoise_function : function
Denoising function to be calibrated.
denoise_parameters : dict of list
Ranges of parameters for `denoise_function` to be calibrated over.
stride : int, optional
Stride used in masking procedure that converts `denoise_function`
to J-invariance.
approximate_loss : bool, optional
Whether to approximate the self-supervised loss used to evaluate the
denoiser by only computing it on one masked version of the image.
If False, the runtime will be a factor of `stride**image.ndim` longer.
extra_output : bool, optional
If True, return parameters and losses in addition to the calibrated
denoising function
Returns
-------
best_denoise_function : function
The optimal J-invariant version of `denoise_function`.
If `extra_output` is True, the following tuple is also returned:
(parameters_tested, losses) : tuple (list of dict, list of int)
List of parameters tested for `denoise_function`, as a dictionary of
kwargs
Self-supervised loss for each set of parameters in `parameters_tested`.
Notes
-----
The calibration procedure uses a self-supervised mean-square-error loss
to evaluate the performance of J-invariant versions of `denoise_function`.
The minimizer of the self-supervised loss is also the minimizer of the
ground-truth loss (i.e., the true MSE error) [1]. The returned function
can be used on the original noisy image, or other images with similar
characteristics.
Increasing the stride increases the performance of `best_denoise_function`
at the expense of increasing its runtime. It has no effect on the runtime
of the calibration.
References
----------
.. [1] J. Batson & L. Royer. Noise2Self: Blind Denoising by Self-Supervision,
International Conference on Machine Learning, p. 524-533 (2019).
Examples
--------
>>> from skimage import color, data
>>> from skimage.restoration import denoise_wavelet
>>> import numpy as np
>>> img = color.rgb2gray(data.astronaut()[:50, :50])
>>> rng = np.random.default_rng()
>>> noisy = img + 0.5 * img.std() * rng.standard_normal(img.shape)
>>> parameters = {'sigma': np.arange(0.1, 0.4, 0.02)}
>>> denoising_function = calibrate_denoiser(noisy, denoise_wavelet,
... denoise_parameters=parameters)
>>> denoised_img = denoising_function(img)
"""
parameters_tested, losses = _calibrate_denoiser_search(
image, denoise_function,
denoise_parameters=denoise_parameters,
stride=stride,
approximate_loss=approximate_loss
)
idx = np.argmin(losses)
best_parameters = parameters_tested[idx]
best_denoise_function = functools.partial(
_invariant_denoise,
denoise_function=denoise_function,
stride=stride,
denoiser_kwargs=best_parameters,
)
if extra_output:
return best_denoise_function, (parameters_tested, losses)
else:
return best_denoise_function
def _calibrate_denoiser_search(image, denoise_function, denoise_parameters, *,
stride=4, approximate_loss=True):
"""Return a parameter search history with losses for a denoise function.
Parameters
----------
image : ndarray
Input data to be denoised (converted using `img_as_float`).
denoise_function : function
Denoising function to be calibrated.
denoise_parameters : dict of list
Ranges of parameters for `denoise_function` to be calibrated over.
stride : int, optional
Stride used in masking procedure that converts `denoise_function`
to J-invariance.
approximate_loss : bool, optional
Whether to approximate the self-supervised loss used to evaluate the
denoiser by only computing it on one masked version of the image.
If False, the runtime will be a factor of `stride**image.ndim` longer.
Returns
-------
parameters_tested : list of dict
List of parameters tested for `denoise_function`, as a dictionary of
kwargs.
losses : list of int
Self-supervised loss for each set of parameters in `parameters_tested`.
"""
image = img_as_float(image)
parameters_tested = list(_product_from_dict(denoise_parameters))
losses = []
for denoiser_kwargs in parameters_tested:
multichannel = denoiser_kwargs.get('channel_axis', None) is not None
if not approximate_loss:
denoised = _invariant_denoise(
image, denoise_function,
stride=stride,
denoiser_kwargs=denoiser_kwargs
)
loss = mean_squared_error(image, denoised)
else:
spatialdims = image.ndim if not multichannel else image.ndim - 1
n_masks = stride ** spatialdims
mask = _generate_grid_slice(image.shape[:spatialdims],
offset=n_masks // 2, stride=stride)
masked_denoised = _invariant_denoise(
image, denoise_function,
masks=[mask],
denoiser_kwargs=denoiser_kwargs
)
loss = mean_squared_error(image[mask], masked_denoised[mask])
losses.append(loss)
return parameters_tested, losses

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@@ -1,178 +0,0 @@
import numpy as np
from .._shared import utils
from .._shared.utils import convert_to_float
from ._nl_means_denoising import (_nl_means_denoising_2d,
_nl_means_denoising_3d,
_fast_nl_means_denoising_2d,
_fast_nl_means_denoising_3d,
_fast_nl_means_denoising_4d)
@utils.channel_as_last_axis()
def denoise_nl_means(image, patch_size=7, patch_distance=11, h=0.1,
fast_mode=True, sigma=0., *,
preserve_range=False, channel_axis=None):
"""Perform non-local means denoising on 2D-4D grayscale or RGB images.
Parameters
----------
image : 2D or 3D ndarray
Input image to be denoised, which can be 2D or 3D, and grayscale
or RGB (for 2D images only, see ``channel_axis`` parameter). There can
be any number of channels (does not strictly have to be RGB).
patch_size : int, optional
Size of patches used for denoising.
patch_distance : int, optional
Maximal distance in pixels where to search patches used for denoising.
h : float, optional
Cut-off distance (in gray levels). The higher h, the more permissive
one is in accepting patches. A higher h results in a smoother image,
at the expense of blurring features. For a Gaussian noise of standard
deviation sigma, a rule of thumb is to choose the value of h to be
sigma of slightly less.
fast_mode : bool, optional
If True (default value), a fast version of the non-local means
algorithm is used. If False, the original version of non-local means is
used. See the Notes section for more details about the algorithms.
sigma : float, optional
The standard deviation of the (Gaussian) noise. If provided, a more
robust computation of patch weights is computed that takes the expected
noise variance into account (see Notes below).
preserve_range : bool, optional
Whether to keep the original range of values. Otherwise, the input
image is converted according to the conventions of `img_as_float`.
Also see https://scikit-image.org/docs/dev/user_guide/data_types.html
channel_axis : int or None, optional
If None, the image is assumed to be a grayscale (single channel) image.
Otherwise, this parameter indicates which axis of the array corresponds
to channels.
.. versionadded:: 0.19
``channel_axis`` was added in 0.19.
Returns
-------
result : ndarray
Denoised image, of same shape as `image`.
Notes
-----
The non-local means algorithm is well suited for denoising images with
specific textures. The principle of the algorithm is to average the value
of a given pixel with values of other pixels in a limited neighborhood,
provided that the *patches* centered on the other pixels are similar enough
to the patch centered on the pixel of interest.
In the original version of the algorithm [1]_, corresponding to
``fast=False``, the computational complexity is::
image.size * patch_size ** image.ndim * patch_distance ** image.ndim
Hence, changing the size of patches or their maximal distance has a
strong effect on computing times, especially for 3-D images.
However, the default behavior corresponds to ``fast_mode=True``, for which
another version of non-local means [2]_ is used, corresponding to a
complexity of::
image.size * patch_distance ** image.ndim
The computing time depends only weakly on the patch size, thanks to
the computation of the integral of patches distances for a given
shift, that reduces the number of operations [1]_. Therefore, this
algorithm executes faster than the classic algorithm
(``fast_mode=False``), at the expense of using twice as much memory.
This implementation has been proven to be more efficient compared to
other alternatives, see e.g. [3]_.
Compared to the classic algorithm, all pixels of a patch contribute
to the distance to another patch with the same weight, no matter
their distance to the center of the patch. This coarser computation
of the distance can result in a slightly poorer denoising
performance. Moreover, for small images (images with a linear size
that is only a few times the patch size), the classic algorithm can
be faster due to boundary effects.
The image is padded using the `reflect` mode of `skimage.util.pad`
before denoising.
If the noise standard deviation, `sigma`, is provided a more robust
computation of patch weights is used. Subtracting the known noise variance
from the computed patch distances improves the estimates of patch
similarity, giving a moderate improvement to denoising performance [4]_.
It was also mentioned as an option for the fast variant of the algorithm in
[3]_.
When `sigma` is provided, a smaller `h` should typically be used to
avoid oversmoothing. The optimal value for `h` depends on the image
content and noise level, but a reasonable starting point is
``h = 0.8 * sigma`` when `fast_mode` is `True`, or ``h = 0.6 * sigma`` when
`fast_mode` is `False`.
References
----------
.. [1] A. Buades, B. Coll, & J-M. Morel. A non-local algorithm for image
denoising. In CVPR 2005, Vol. 2, pp. 60-65, IEEE.
:DOI:`10.1109/CVPR.2005.38`
.. [2] J. Darbon, A. Cunha, T.F. Chan, S. Osher, and G.J. Jensen, Fast
nonlocal filtering applied to electron cryomicroscopy, in 5th IEEE
International Symposium on Biomedical Imaging: From Nano to Macro,
2008, pp. 1331-1334.
:DOI:`10.1109/ISBI.2008.4541250`
.. [3] Jacques Froment. Parameter-Free Fast Pixelwise Non-Local Means
Denoising. Image Processing On Line, 2014, vol. 4, pp. 300-326.
:DOI:`10.5201/ipol.2014.120`
.. [4] A. Buades, B. Coll, & J-M. Morel. Non-Local Means Denoising.
Image Processing On Line, 2011, vol. 1, pp. 208-212.
:DOI:`10.5201/ipol.2011.bcm_nlm`
Examples
--------
>>> a = np.zeros((40, 40))
>>> a[10:-10, 10:-10] = 1.
>>> rng = np.random.default_rng()
>>> a += 0.3 * rng.standard_normal(a.shape)
>>> denoised_a = denoise_nl_means(a, 7, 5, 0.1)
"""
if channel_axis is None:
multichannel = False
image = image[..., np.newaxis]
else:
multichannel = True
ndim_no_channel = image.ndim - 1
if (ndim_no_channel < 2) or (ndim_no_channel > 4):
raise NotImplementedError(
"Non-local means denoising is only implemented for 2D, "
"3D or 4D grayscale or multichannel images.")
image = convert_to_float(image, preserve_range)
if not image.flags.c_contiguous:
image = np.ascontiguousarray(image)
kwargs = dict(s=patch_size, d=patch_distance, h=h, var=sigma * sigma)
if ndim_no_channel == 2:
nlm_func = (_fast_nl_means_denoising_2d if fast_mode else
_nl_means_denoising_2d)
elif ndim_no_channel == 3:
if multichannel and not fast_mode:
raise NotImplementedError(
"Multichannel 3D requires fast_mode to be True.")
if fast_mode:
nlm_func = _fast_nl_means_denoising_3d
else:
# have to drop the size 1 channel axis for slow mode
image = image[..., 0]
nlm_func = _nl_means_denoising_3d
elif ndim_no_channel == 4:
if fast_mode:
nlm_func = _fast_nl_means_denoising_4d
else:
raise NotImplementedError("4D requires fast_mode to be True.")
dn = np.asarray(nlm_func(image, **kwargs))
return dn

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@@ -1,195 +0,0 @@
import numpy as np
from .._shared.utils import _supported_float_type
from ._rolling_ball_cy import apply_kernel, apply_kernel_nan
def rolling_ball(image, *, radius=100, kernel=None,
nansafe=False, num_threads=None):
"""Estimate background intensity by rolling/translating a kernel.
This rolling ball algorithm estimates background intensity for a
ndimage in case of uneven exposure. It is a generalization of the
frequently used rolling ball algorithm [1]_.
Parameters
----------
image : ndarray
The image to be filtered.
radius : int, optional
Radius of a ball shaped kernel to be rolled/translated in the image.
Used if ``kernel = None``.
kernel : ndarray, optional
The kernel to be rolled/translated in the image. It must have the
same number of dimensions as ``image``. Kernel is filled with the
intensity of the kernel at that position.
nansafe: bool, optional
If ``False`` (default) assumes that none of the values in ``image``
are ``np.nan``, and uses a faster implementation.
num_threads: int, optional
The maximum number of threads to use. If ``None`` use the OpenMP
default value; typically equal to the maximum number of virtual cores.
Note: This is an upper limit to the number of threads. The exact number
is determined by the system's OpenMP library.
Returns
-------
background : ndarray
The estimated background of the image.
Notes
-----
For the pixel that has its background intensity estimated (without loss
of generality at ``center``) the rolling ball method centers ``kernel``
under it and raises the kernel until the surface touches the image umbra
at some ``pos=(y,x)``. The background intensity is then estimated
using the image intensity at that position (``image[pos]``) plus the
difference of ``kernel[center] - kernel[pos]``.
This algorithm assumes that dark pixels correspond to the background. If
you have a bright background, invert the image before passing it to the
function, e.g., using `utils.invert`. See the gallery example for details.
This algorithm is sensitive to noise (in particular salt-and-pepper
noise). If this is a problem in your image, you can apply mild
gaussian smoothing before passing the image to this function.
References
----------
.. [1] Sternberg, Stanley R. "Biomedical image processing." Computer 1
(1983): 22-34. :DOI:`10.1109/MC.1983.1654163`
Examples
--------
>>> import numpy as np
>>> from skimage import data
>>> from skimage.restoration import rolling_ball
>>> image = data.coins()
>>> background = rolling_ball(data.coins())
>>> filtered_image = image - background
>>> import numpy as np
>>> from skimage import data
>>> from skimage.restoration import rolling_ball, ellipsoid_kernel
>>> image = data.coins()
>>> kernel = ellipsoid_kernel((101, 101), 75)
>>> background = rolling_ball(data.coins(), kernel=kernel)
>>> filtered_image = image - background
"""
image = np.asarray(image)
float_type = _supported_float_type(image.dtype)
img = image.astype(float_type, copy=False)
if num_threads is None:
num_threads = 0
if kernel is None:
kernel = ball_kernel(radius, image.ndim)
kernel = kernel.astype(float_type)
kernel_shape = np.asarray(kernel.shape)
kernel_center = (kernel_shape // 2)
center_intensity = kernel[tuple(kernel_center)]
intensity_difference = center_intensity - kernel
intensity_difference[kernel == np.Inf] = np.Inf
intensity_difference = intensity_difference.astype(img.dtype)
intensity_difference = intensity_difference.reshape(-1)
img = np.pad(img, kernel_center[:, np.newaxis],
constant_values=np.Inf, mode="constant")
func = apply_kernel_nan if nansafe else apply_kernel
background = func(
img.reshape(-1),
intensity_difference,
np.zeros_like(image, dtype=img.dtype).reshape(-1),
np.array(image.shape, dtype=np.intp),
np.array(img.shape, dtype=np.intp),
kernel_shape.astype(np.intp),
num_threads
)
background = background.astype(image.dtype, copy=False)
return background
def ball_kernel(radius, ndim):
"""Create a ball kernel for restoration.rolling_ball.
Parameters
----------
radius : int
Radius of the ball.
ndim : int
Number of dimensions of the ball. ``ndim`` should match the
dimensionality of the image the kernel will be applied to.
Returns
-------
kernel : ndarray
The kernel containing the surface intensity of the top half
of the ellipsoid.
See Also
--------
rolling_ball
"""
kernel_coords = np.stack(
np.meshgrid(
*[np.arange(-x, x + 1) for x in [np.ceil(radius)] * ndim],
indexing='ij'
),
axis=-1
)
sum_of_squares = np.sum(kernel_coords ** 2, axis=-1)
distance_from_center = np.sqrt(sum_of_squares)
kernel = np.sqrt(np.clip(radius ** 2 - sum_of_squares, 0, None))
kernel[distance_from_center > radius] = np.Inf
return kernel
def ellipsoid_kernel(shape, intensity):
"""Create an ellipoid kernel for restoration.rolling_ball.
Parameters
----------
shape : arraylike
Length of the principal axis of the ellipsoid (excluding
the intensity axis). The kernel needs to have the same
dimensionality as the image it will be applied to.
intensity : int
Length of the intensity axis of the ellipsoid.
Returns
-------
kernel : ndarray
The kernel containing the surface intensity of the top half
of the ellipsoid.
See Also
--------
rolling_ball
"""
shape = np.asarray(shape)
semi_axis = np.clip(shape // 2, 1, None)
kernel_coords = np.stack(
np.meshgrid(
*[np.arange(-x, x + 1) for x in semi_axis],
indexing='ij'
),
axis=-1)
intensity_scaling = 1 - np.sum((kernel_coords / semi_axis) ** 2, axis=-1)
kernel = intensity * np.sqrt(np.clip(intensity_scaling, 0, None))
kernel[intensity_scaling < 0] = np.Inf
return kernel

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import numpy as np
from skimage import data, img_as_float
from skimage._shared import testing
from skimage._shared.testing import assert_allclose
from skimage._shared.utils import _supported_float_type
from skimage.color import rgb2gray
from skimage.metrics import mean_squared_error, normalized_root_mse
from skimage.morphology import binary_dilation, disk
from skimage.restoration import inpaint
@testing.parametrize('dtype', [np.float16, np.float32, np.float64])
@testing.parametrize('split_into_regions', [False, True])
def test_inpaint_biharmonic_2d(dtype, split_into_regions):
img = np.tile(np.square(np.linspace(0, 1, 5, dtype=dtype)), (5, 1))
mask = np.zeros_like(img)
mask[2, 2:] = 1
mask[1, 3:] = 1
mask[0, 4:] = 1
img[np.where(mask)] = 0
out = inpaint.inpaint_biharmonic(img, mask,
split_into_regions=split_into_regions)
assert out.dtype == _supported_float_type(img)
ref = np.array(
[[0., 0.0625, 0.25000000, 0.5625000, 0.73925058],
[0., 0.0625, 0.25000000, 0.5478048, 0.76557821],
[0., 0.0625, 0.25842878, 0.5623079, 0.85927796],
[0., 0.0625, 0.25000000, 0.5625000, 1.00000000],
[0., 0.0625, 0.25000000, 0.5625000, 1.00000000]]
)
rtol = 1e-7 if dtype == np.float64 else 1e-6
assert_allclose(ref, out, rtol=rtol)
@testing.parametrize('channel_axis', [0, 1, -1])
def test_inpaint_biharmonic_2d_color(channel_axis):
img = img_as_float(data.astronaut()[:64, :64])
mask = np.zeros(img.shape[:2], dtype=bool)
mask[8:16, :16] = 1
img_defect = img * ~mask[..., np.newaxis]
mse_defect = mean_squared_error(img, img_defect)
img_defect = np.moveaxis(img_defect, -1, channel_axis)
img_restored = inpaint.inpaint_biharmonic(img_defect, mask,
channel_axis=channel_axis)
img_restored = np.moveaxis(img_restored, channel_axis, -1)
mse_restored = mean_squared_error(img, img_restored)
assert mse_restored < 0.01 * mse_defect
@testing.parametrize('dtype', [np.float32, np.float64])
def test_inpaint_biharmonic_2d_float_dtypes(dtype):
img = np.tile(np.square(np.linspace(0, 1, 5)), (5, 1))
mask = np.zeros_like(img)
mask[2, 2:] = 1
mask[1, 3:] = 1
mask[0, 4:] = 1
img[np.where(mask)] = 0
img = img.astype(dtype, copy=False)
out = inpaint.inpaint_biharmonic(img, mask)
assert out.dtype == img.dtype
ref = np.array(
[[0., 0.0625, 0.25000000, 0.5625000, 0.73925058],
[0., 0.0625, 0.25000000, 0.5478048, 0.76557821],
[0., 0.0625, 0.25842878, 0.5623079, 0.85927796],
[0., 0.0625, 0.25000000, 0.5625000, 1.00000000],
[0., 0.0625, 0.25000000, 0.5625000, 1.00000000]]
)
assert_allclose(ref, out, rtol=1e-5)
@testing.parametrize('split_into_regions', [False, True])
def test_inpaint_biharmonic_3d(split_into_regions):
img = np.tile(np.square(np.linspace(0, 1, 5)), (5, 1))
img = np.dstack((img, img.T))
mask = np.zeros_like(img)
mask[2, 2:, :] = 1
mask[1, 3:, :] = 1
mask[0, 4:, :] = 1
img[np.where(mask)] = 0
out = inpaint.inpaint_biharmonic(img, mask,
split_into_regions=split_into_regions)
ref = np.dstack((
np.array(
[[0.0000, 0.0625, 0.25000000, 0.56250000, 0.53752796],
[0.0000, 0.0625, 0.25000000, 0.44443780, 0.53762210],
[0.0000, 0.0625, 0.23693666, 0.46621112, 0.68615592],
[0.0000, 0.0625, 0.25000000, 0.56250000, 1.00000000],
[0.0000, 0.0625, 0.25000000, 0.56250000, 1.00000000]]),
np.array(
[[0.0000, 0.0000, 0.00000000, 0.00000000, 0.19621902],
[0.0625, 0.0625, 0.06250000, 0.17470756, 0.30140091],
[0.2500, 0.2500, 0.27241289, 0.35155440, 0.43068654],
[0.5625, 0.5625, 0.56250000, 0.56250000, 0.56250000],
[1.0000, 1.0000, 1.00000000, 1.00000000, 1.00000000]])
))
assert_allclose(ref, out)
def test_invalid_input():
img, mask = np.zeros([]), np.zeros([])
with testing.raises(ValueError):
inpaint.inpaint_biharmonic(img, mask)
img, mask = np.zeros((2, 2)), np.zeros((4, 1))
with testing.raises(ValueError):
inpaint.inpaint_biharmonic(img, mask)
img = np.ma.array(np.zeros((2, 2)), mask=[[0, 0], [0, 0]])
mask = np.zeros((2, 2))
with testing.raises(TypeError):
inpaint.inpaint_biharmonic(img, mask)
@testing.parametrize('dtype', [np.uint8, np.float32, np.float64])
@testing.parametrize('order', ['C', 'F'])
@testing.parametrize('channel_axis', [None, -1])
@testing.parametrize('split_into_regions', [False, True])
def test_inpaint_nrmse(dtype, order, channel_axis, split_into_regions):
image_orig = data.astronaut()[:, :200]
float_dtype = np.float32 if dtype == np.float32 else np.float64
image_orig = image_orig.astype(float_dtype, copy=False)
# Create mask with six block defect regions
mask = np.zeros(image_orig.shape[:-1], dtype=bool)
mask[20:50, 3:20] = 1
mask[165:180, 90:155] = 1
mask[40:60, 170:195] = 1
mask[-60:-40, 170:195] = 1
mask[-180:-165, 90:155] = 1
mask[-50:-20, :20] = 1
# add a few long, narrow defects
mask[200:205, -200:] = 1
mask[150:255, 20:22] = 1
mask[365:368, 60:130] = 1
# add randomly positioned small point-like defects
rstate = np.random.default_rng(0)
for radius in [0, 2, 4]:
# larger defects are less common
thresh = 3.25 + 0.25 * radius # larger defects less common
tmp_mask = rstate.standard_normal(image_orig.shape[:-1]) > thresh
if radius > 0:
tmp_mask = binary_dilation(tmp_mask, disk(radius, dtype=bool))
mask[tmp_mask] = 1
# Defect image over the same region in each color channel
image_defect = image_orig.copy()
for layer in range(image_defect.shape[-1]):
image_defect[np.where(mask)] = 0
if channel_axis is None:
image_orig = rgb2gray(image_orig)
image_defect = rgb2gray(image_defect)
image_orig = image_orig.astype(dtype, copy=False)
image_defect = image_defect.astype(dtype, copy=False)
image_defect = np.asarray(image_defect, order=order)
image_result = inpaint.inpaint_biharmonic(
image_defect, mask, channel_axis=channel_axis,
split_into_regions=split_into_regions
)
assert image_result.dtype == float_dtype
nrmse_defect = normalized_root_mse(image_orig, image_defect)
nrmse_result = normalized_root_mse(img_as_float(image_orig), image_result)
assert nrmse_result < 0.2 * nrmse_defect

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@@ -1,87 +0,0 @@
import functools
import numpy as np
import pytest
from skimage._shared.testing import assert_
from skimage._shared.utils import _supported_float_type
from skimage.data import binary_blobs
from skimage.data import camera, chelsea
from skimage.metrics import mean_squared_error as mse
from skimage.restoration import (calibrate_denoiser,
denoise_wavelet)
from skimage.restoration.j_invariant import _invariant_denoise
from skimage.util import img_as_float, random_noise
test_img = img_as_float(camera())
test_img_color = img_as_float(chelsea())
test_img_3d = img_as_float(binary_blobs(64, n_dim=3)) / 2
noisy_img = random_noise(test_img, mode='gaussian', var=0.01)
noisy_img_color = random_noise(test_img_color, mode='gaussian', var=0.01)
noisy_img_3d = random_noise(test_img_3d, mode='gaussian', var=0.1)
_denoise_wavelet = functools.partial(denoise_wavelet, rescale_sigma=True)
def test_invariant_denoise():
denoised_img = _invariant_denoise(noisy_img, _denoise_wavelet)
denoised_mse = mse(denoised_img, test_img)
original_mse = mse(noisy_img, test_img)
assert_(denoised_mse < original_mse)
@pytest.mark.parametrize('dtype', [np.float16, np.float32, np.float64])
def test_invariant_denoise_color(dtype):
denoised_img_color = _invariant_denoise(
noisy_img_color.astype(dtype), _denoise_wavelet,
denoiser_kwargs=dict(channel_axis=-1))
denoised_mse = mse(denoised_img_color, test_img_color)
original_mse = mse(noisy_img_color, test_img_color)
assert denoised_mse < original_mse
assert denoised_img_color.dtype == _supported_float_type(dtype)
def test_invariant_denoise_3d():
denoised_img_3d = _invariant_denoise(noisy_img_3d, _denoise_wavelet)
denoised_mse = mse(denoised_img_3d, test_img_3d)
original_mse = mse(noisy_img_3d, test_img_3d)
assert_(denoised_mse < original_mse)
def test_calibrate_denoiser_extra_output():
parameter_ranges = {'sigma': np.linspace(0.1, 1, 5) / 2}
_, (parameters_tested, losses) = calibrate_denoiser(
noisy_img,
_denoise_wavelet,
denoise_parameters=parameter_ranges,
extra_output=True
)
all_denoised = [_invariant_denoise(noisy_img, _denoise_wavelet,
denoiser_kwargs=denoiser_kwargs)
for denoiser_kwargs in parameters_tested]
ground_truth_losses = [mse(img, test_img) for img in all_denoised]
assert_(np.argmin(losses) == np.argmin(ground_truth_losses))
def test_calibrate_denoiser():
parameter_ranges = {'sigma': np.linspace(0.1, 1, 5) / 2}
denoiser = calibrate_denoiser(noisy_img, _denoise_wavelet,
denoise_parameters=parameter_ranges)
denoised_mse = mse(denoiser(noisy_img), test_img)
original_mse = mse(noisy_img, test_img)
assert_(denoised_mse < original_mse)
def test_input_image_not_modified():
input_image = noisy_img.copy()
parameter_ranges = {'sigma': np.random.random(5) / 2}
calibrate_denoiser(input_image, _denoise_wavelet,
denoise_parameters=parameter_ranges)
assert_(np.all(noisy_img == input_image))

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@@ -1,177 +0,0 @@
import numpy as np
import pytest
from scipy import ndimage as ndi
from scipy.signal import convolve2d, convolve
from skimage import restoration, util
from skimage._shared import filters
from skimage._shared.testing import fetch
from skimage._shared.utils import _supported_float_type
from skimage.color import rgb2gray
from skimage.data import astronaut, camera
from skimage.restoration import uft
test_img = util.img_as_float(camera())
def _get_rtol_atol(dtype):
rtol = 1e-3
atol = 0
if dtype == np.float16:
rtol = 1e-2
atol = 1e-3
elif dtype == np.float32:
atol = 1e-5
return rtol, atol
@pytest.mark.parametrize('dtype', [np.float16, np.float32, np.float64])
@pytest.mark.parametrize('ndim', [1, 2, 3])
def test_wiener(dtype, ndim):
"""
currently only performs pixelwise comparison to
precomputed result in 2d case.
"""
psf = np.ones([5] * ndim, dtype=dtype) / 5 ** ndim
np.random.seed(0)
# for ndim == 2 use camera (to compare to presaved result)
if ndim != 2:
test_img = np.random.randint(0, 100, [50] * ndim)
else:
test_img = util.img_as_float(camera())
data = convolve(test_img, psf, 'same')
data += 0.1 * data.std() * np.random.standard_normal(data.shape)
data = data.astype(dtype, copy=False)
deconvolved = restoration.wiener(data, psf, 0.05)
assert deconvolved.dtype == _supported_float_type(dtype)
if ndim == 2:
rtol, atol = _get_rtol_atol(dtype)
path = fetch('restoration/tests/camera_wiener.npy')
np.testing.assert_allclose(deconvolved, np.load(path),
rtol=rtol, atol=atol)
_, laplacian = uft.laplacian(ndim, data.shape)
otf = uft.ir2tf(psf, data.shape, is_real=False)
assert otf.real.dtype == _supported_float_type(dtype)
deconvolved = restoration.wiener(data, otf, 0.05,
reg=laplacian,
is_real=False)
assert deconvolved.real.dtype == _supported_float_type(dtype)
if ndim == 2:
np.testing.assert_allclose(np.real(deconvolved),
np.load(path),
rtol=rtol, atol=atol)
@pytest.mark.parametrize('dtype', [np.float16, np.float32, np.float64])
def test_unsupervised_wiener(dtype):
psf = np.ones((5, 5), dtype=dtype) / 25
data = convolve2d(test_img, psf, 'same')
seed = 16829302
# keep old-style RandomState here for compatibility with previously stored
# reference data in camera_unsup.npy and camera_unsup2.npy
rng = np.random.RandomState(seed)
data += 0.1 * data.std() * rng.standard_normal(data.shape)
data = data.astype(dtype, copy=False)
deconvolved, _ = restoration.unsupervised_wiener(data, psf,
random_state=seed)
float_type = _supported_float_type(dtype)
assert deconvolved.dtype == float_type
rtol, atol = _get_rtol_atol(dtype)
path = fetch('restoration/tests/camera_unsup.npy')
np.testing.assert_allclose(deconvolved, np.load(path), rtol=rtol,
atol=atol)
_, laplacian = uft.laplacian(2, data.shape)
otf = uft.ir2tf(psf, data.shape, is_real=False)
assert otf.real.dtype == _supported_float_type(dtype)
deconvolved2 = restoration.unsupervised_wiener(
data, otf, reg=laplacian, is_real=False,
user_params={
"callback": lambda x: None,
"max_num_iter": 200,
"min_num_iter": 30,
},
random_state=seed)[0]
assert deconvolved2.real.dtype == float_type
path = fetch('restoration/tests/camera_unsup2.npy')
np.testing.assert_allclose(np.real(deconvolved2),
np.load(path),
rtol=rtol, atol=atol)
def test_unsupervised_wiener_deprecated_user_param():
psf = np.ones((5, 5), dtype=float) / 25
data = convolve2d(test_img, psf, 'same')
otf = uft.ir2tf(psf, data.shape, is_real=False)
_, laplacian = uft.laplacian(2, data.shape)
restoration.unsupervised_wiener(
data, otf, reg=laplacian, is_real=False,
user_params={"min_num_iter": 30}, random_state=5
)
def test_image_shape():
"""Test that shape of output image in deconvolution is same as input.
This addresses issue #1172.
"""
point = np.zeros((5, 5), float)
point[2, 2] = 1.
psf = filters.gaussian(point, sigma=1., mode='reflect')
# image shape: (45, 45), as reported in #1172
image = util.img_as_float(camera()[65:165, 215:315]) # just the face
image_conv = ndi.convolve(image, psf)
deconv_sup = restoration.wiener(image_conv, psf, 1)
deconv_un = restoration.unsupervised_wiener(image_conv, psf)[0]
# test the shape
np.testing.assert_equal(image.shape, deconv_sup.shape)
np.testing.assert_equal(image.shape, deconv_un.shape)
# test the reconstruction error
sup_relative_error = np.abs(deconv_sup - image) / image
un_relative_error = np.abs(deconv_un - image) / image
np.testing.assert_array_less(np.median(sup_relative_error), 0.1)
np.testing.assert_array_less(np.median(un_relative_error), 0.1)
@pytest.mark.parametrize('ndim', [1, 2, 3])
def test_richardson_lucy(ndim):
psf = np.ones([5] * ndim, dtype=float) / 5 ** ndim
if ndim != 2:
test_img = np.random.randint(0, 100, [30] * ndim)
else:
test_img = util.img_as_float(camera())
data = convolve(test_img, psf, 'same')
np.random.seed(0)
data += 0.1 * data.std() * np.random.standard_normal(data.shape)
deconvolved = restoration.richardson_lucy(data, psf, num_iter=5)
if ndim == 2:
path = fetch('restoration/tests/camera_rl.npy')
np.testing.assert_allclose(deconvolved, np.load(path), rtol=1e-3)
@pytest.mark.parametrize('dtype_image', [np.float16, np.float32, np.float64])
@pytest.mark.parametrize('dtype_psf', [np.float32, np.float64])
def test_richardson_lucy_filtered(dtype_image, dtype_psf):
if dtype_image == np.float64:
atol = 1e-8
else:
atol = 1e-5
test_img_astro = rgb2gray(astronaut())
psf = np.ones((5, 5), dtype=dtype_psf) / 25
data = convolve2d(test_img_astro, psf, 'same')
data = data.astype(dtype_image, copy=False)
deconvolved = restoration.richardson_lucy(data, psf, 5,
filter_epsilon=1e-6)
assert deconvolved.dtype == _supported_float_type(data.dtype)
path = fetch('restoration/tests/astronaut_rl.npy')
np.testing.assert_allclose(deconvolved, np.load(path), rtol=1e-3,
atol=atol)

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@@ -1,103 +0,0 @@
"""
Tests for Rolling Ball Filter
(skimage.restoration.rolling_ball)
"""
import numpy as np
import pytest
from skimage import data
from skimage.restoration import rolling_ball
from skimage.restoration.rolling_ball import ellipsoid_kernel
@pytest.mark.parametrize(
'dtype',
[np.uint8, np.int32, np.float16, np.float32, np.float64]
)
def test_ellipsoid_const(dtype):
img = 155 * np.ones((100, 100), dtype=dtype)
kernel = ellipsoid_kernel((25, 53), 50)
background = rolling_ball(img, kernel=kernel)
assert np.allclose(img - background, np.zeros_like(img))
assert background.dtype == img.dtype
def test_nan_const():
img = 123 * np.ones((100, 100), dtype=float)
img[20, 20] = np.nan
img[50, 53] = np.nan
kernel_shape = (10, 10)
x = np.arange(-kernel_shape[1] // 2,
kernel_shape[1] // 2 + 1)[np.newaxis, :]
y = np.arange(-kernel_shape[0] // 2,
kernel_shape[0] // 2 + 1)[:, np.newaxis]
expected_img = np.zeros_like(img)
expected_img[y + 20, x + 20] = np.nan
expected_img[y + 50, x + 53] = np.nan
kernel = ellipsoid_kernel(kernel_shape, 100)
background = rolling_ball(
img,
kernel=kernel,
nansafe=True
)
assert np.allclose(img - background, expected_img, equal_nan=True)
@pytest.mark.parametrize("radius", [1, 2.5, 10.346, 50])
def test_const_image(radius):
# infinite plane light source at top left corner
img = 23 * np.ones((100, 100), dtype=np.uint8)
background = rolling_ball(img, radius=radius)
assert np.allclose(img - background, np.zeros_like(img))
def test_radial_gradient():
# spot light source at top left corner
spot_radius = 50
x, y = np.meshgrid(range(5), range(5))
img = np.sqrt(np.clip(spot_radius ** 2 - y ** 2 - x ** 2, 0, None))
background = rolling_ball(img, radius=5)
assert np.allclose(img - background, np.zeros_like(img))
def test_linear_gradient():
# linear light source centered at top left corner
x, y = np.meshgrid(range(100), range(100))
img = (y * 20 + x * 20)
expected_img = 19 * np.ones_like(img)
expected_img[0, 0] = 0
background = rolling_ball(img, radius=1)
assert np.allclose(img - background, expected_img)
@pytest.mark.parametrize("radius", [2, 10, 12.5, 50])
def test_preserve_peaks(radius):
x, y = np.meshgrid(range(100), range(100))
img = 0 * x + 0 * y + 10
img[10, 10] = 20
img[20, 20] = 35
img[45, 26] = 156
expected_img = img - 10
background = rolling_ball(img, radius=radius)
assert np.allclose(img - background, expected_img)
@pytest.mark.parametrize("num_threads", [None, 1, 2])
def test_threads(num_threads):
# not testing if we use multiple threads
# just checking if the API throws an exception
img = 23 * np.ones((100, 100), dtype=np.uint8)
rolling_ball(img, radius=10, num_threads=num_threads)
rolling_ball(img, radius=10, nansafe=True, num_threads=num_threads)
def test_ndim():
image = data.cells3d()[:5, 1, ...]
kernel = ellipsoid_kernel((3, 100, 100), 100)
rolling_ball(image, kernel=kernel)

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@@ -1,217 +0,0 @@
import numpy as np
from skimage.restoration import unwrap_phase
import sys
from skimage._shared import testing
from skimage._shared.testing import (assert_array_almost_equal_nulp,
assert_almost_equal, assert_array_equal,
assert_, skipif)
from skimage._shared._warnings import expected_warnings
def assert_phase_almost_equal(a, b, *args, **kwargs):
"""An assert_almost_equal insensitive to phase shifts of n*2*pi."""
shift = 2 * np.pi * np.round((b.mean() - a.mean()) / (2 * np.pi))
with expected_warnings([r'invalid value encountered|\A\Z',
r'divide by zero encountered|\A\Z']):
print('assert_phase_allclose, abs', np.max(np.abs(a - (b - shift))))
print('assert_phase_allclose, rel',
np.max(np.abs((a - (b - shift)) / a)))
if np.ma.isMaskedArray(a):
assert_(np.ma.isMaskedArray(b))
assert_array_equal(a.mask, b.mask)
assert_(a.fill_value == b.fill_value)
au = np.asarray(a)
bu = np.asarray(b)
with expected_warnings([r'invalid value encountered|\A\Z',
r'divide by zero encountered|\A\Z']):
print('assert_phase_allclose, no mask, abs',
np.max(np.abs(au - (bu - shift))))
print('assert_phase_allclose, no mask, rel',
np.max(np.abs((au - (bu - shift)) / au)))
assert_array_almost_equal_nulp(a + shift, b, *args, **kwargs)
def check_unwrap(image, mask=None):
image_wrapped = np.angle(np.exp(1j * image))
if mask is not None:
print('Testing a masked image')
image = np.ma.array(image, mask=mask, fill_value=0.5)
image_wrapped = np.ma.array(image_wrapped, mask=mask, fill_value=0.5)
image_unwrapped = unwrap_phase(image_wrapped, seed=0)
assert_phase_almost_equal(image_unwrapped, image)
def test_unwrap_1d():
image = np.linspace(0, 10 * np.pi, 100)
check_unwrap(image)
# Masked arrays are not allowed in 1D
with testing.raises(ValueError):
check_unwrap(image, True)
# wrap_around is not allowed in 1D
with testing.raises(ValueError):
unwrap_phase(image, True, seed=0)
@testing.parametrize("check_with_mask", (False, True))
def test_unwrap_2d(check_with_mask):
mask = None
x, y = np.ogrid[:8, :16]
image = 2 * np.pi * (x * 0.2 + y * 0.1)
if check_with_mask:
mask = np.zeros(image.shape, dtype=bool)
mask[4:6, 4:8] = True
check_unwrap(image, mask)
@testing.parametrize("check_with_mask", (False, True))
def test_unwrap_3d(check_with_mask):
mask = None
x, y, z = np.ogrid[:8, :12, :16]
image = 2 * np.pi * (x * 0.2 + y * 0.1 + z * 0.05)
if check_with_mask:
mask = np.zeros(image.shape, dtype=bool)
mask[4:6, 4:6, 1:3] = True
check_unwrap(image, mask)
def check_wrap_around(ndim, axis):
# create a ramp, but with the last pixel along axis equalling the first
elements = 100
ramp = np.linspace(0, 12 * np.pi, elements)
ramp[-1] = ramp[0]
image = ramp.reshape(tuple([elements if n == axis else 1
for n in range(ndim)]))
image_wrapped = np.angle(np.exp(1j * image))
index_first = tuple([0] * ndim)
index_last = tuple([-1 if n == axis else 0 for n in range(ndim)])
# unwrap the image without wrap around
# We do not want warnings about length 1 dimensions
with expected_warnings([r'Image has a length 1 dimension|\A\Z']):
image_unwrap_no_wrap_around = unwrap_phase(image_wrapped, seed=0)
print('endpoints without wrap_around:',
image_unwrap_no_wrap_around[index_first],
image_unwrap_no_wrap_around[index_last])
# without wrap around, the endpoints of the image should differ
assert_(abs(image_unwrap_no_wrap_around[index_first] -
image_unwrap_no_wrap_around[index_last]) > np.pi)
# unwrap the image with wrap around
wrap_around = [n == axis for n in range(ndim)]
# We do not want warnings about length 1 dimensions
with expected_warnings([r'Image has a length 1 dimension.|\A\Z']):
image_unwrap_wrap_around = unwrap_phase(image_wrapped, wrap_around,
seed=0)
print('endpoints with wrap_around:',
image_unwrap_wrap_around[index_first],
image_unwrap_wrap_around[index_last])
# with wrap around, the endpoints of the image should be equal
assert_almost_equal(image_unwrap_wrap_around[index_first],
image_unwrap_wrap_around[index_last])
dim_axis = [(ndim, axis) for ndim in (2, 3) for axis in range(ndim)]
@skipif(sys.version_info[:2] == (3, 4),
reason="Doesn't work with python 3.4. See issue #3079")
@testing.parametrize("ndim, axis", dim_axis)
def test_wrap_around(ndim, axis):
check_wrap_around(ndim, axis)
def test_mask():
length = 100
ramps = [np.linspace(0, 4 * np.pi, length),
np.linspace(0, 8 * np.pi, length),
np.linspace(0, 6 * np.pi, length)]
image = np.vstack(ramps)
mask_1d = np.ones((length,), dtype=bool)
mask_1d[0] = mask_1d[-1] = False
for i in range(len(ramps)):
# mask all ramps but the i'th one
mask = np.zeros(image.shape, dtype=bool)
mask |= mask_1d.reshape(1, -1)
mask[i, :] = False # unmask i'th ramp
image_wrapped = np.ma.array(np.angle(np.exp(1j * image)), mask=mask)
image_unwrapped = unwrap_phase(image_wrapped)
image_unwrapped -= image_unwrapped[0, 0] # remove phase shift
# The end of the unwrapped array should have value equal to the
# endpoint of the unmasked ramp
assert_array_almost_equal_nulp(image_unwrapped[:, -1], image[i, -1])
assert_(np.ma.isMaskedArray(image_unwrapped))
# Same tests, but forcing use of the 3D unwrapper by reshaping
with expected_warnings(['length 1 dimension']):
shape = (1,) + image_wrapped.shape
image_wrapped_3d = image_wrapped.reshape(shape)
image_unwrapped_3d = unwrap_phase(image_wrapped_3d)
# remove phase shift
image_unwrapped_3d -= image_unwrapped_3d[0, 0, 0]
assert_array_almost_equal_nulp(image_unwrapped_3d[:, :, -1],
image[i, -1])
def test_invalid_input():
with testing.raises(ValueError):
unwrap_phase(np.zeros([]))
with testing.raises(ValueError):
unwrap_phase(np.zeros((1, 1, 1, 1)))
with testing.raises(ValueError):
unwrap_phase(np.zeros((1, 1)), 3 * [False])
with testing.raises(ValueError):
unwrap_phase(np.zeros((1, 1)), 'False')
def test_unwrap_3d_middle_wrap_around():
# Segmentation fault in 3D unwrap phase with middle dimension connected
# GitHub issue #1171
image = np.zeros((20, 30, 40), dtype=np.float32)
unwrap = unwrap_phase(image, wrap_around=[False, True, False])
assert_(np.all(unwrap == 0))
def test_unwrap_2d_compressed_mask():
# ValueError when image is masked array with a compressed mask (no masked
# elements). GitHub issue #1346
image = np.ma.zeros((10, 10))
unwrap = unwrap_phase(image)
assert_(np.all(unwrap == 0))
def test_unwrap_2d_all_masked():
# Segmentation fault when image is masked array with a all elements masked
# GitHub issue #1347
# all elements masked
image = np.ma.zeros((10, 10))
image[:] = np.ma.masked
unwrap = unwrap_phase(image)
assert_(np.ma.isMaskedArray(unwrap))
assert_(np.all(unwrap.mask))
# 1 unmasked element, still zero edges
image = np.ma.zeros((10, 10))
image[:] = np.ma.masked
image[0, 0] = 0
unwrap = unwrap_phase(image)
assert_(np.ma.isMaskedArray(unwrap))
assert_(np.sum(unwrap.mask) == 99) # all but one masked
assert_(unwrap[0, 0] == 0)
def test_unwrap_3d_all_masked():
# all elements masked
image = np.ma.zeros((10, 10, 10))
image[:] = np.ma.masked
unwrap = unwrap_phase(image)
assert_(np.ma.isMaskedArray(unwrap))
assert_(np.all(unwrap.mask))
# 1 unmasked element, still zero edges
image = np.ma.zeros((10, 10, 10))
image[:] = np.ma.masked
image[0, 0, 0] = 0
unwrap = unwrap_phase(image)
assert_(np.ma.isMaskedArray(unwrap))
assert_(np.sum(unwrap.mask) == 999) # all but one masked
assert_(unwrap[0, 0, 0] == 0)

View File

@@ -1,454 +0,0 @@
r"""Function of unitary fourier transform (uft) and utilities
This module implements the unitary fourier transform, also known as
the ortho-normal transform. It is especially useful for convolution
[1], as it respects the Parseval equality. The value of the null
frequency is equal to
.. math:: \frac{1}{\sqrt{n}} \sum_i x_i
so the Fourier transform has the same energy as the original image
(see ``image_quad_norm`` function). The transform is applied from the
last axis for performance (assuming a C-order array input).
References
----------
.. [1] B. R. Hunt "A matrix theory proof of the discrete convolution
theorem", IEEE Trans. on Audio and Electroacoustics,
vol. au-19, no. 4, pp. 285-288, dec. 1971
"""
import numpy as np
import scipy.fft as fft
from .._shared.utils import _supported_float_type
def ufftn(inarray, dim=None):
"""N-dimensional unitary Fourier transform.
Parameters
----------
inarray : ndarray
The array to transform.
dim : int, optional
The last axis along which to compute the transform. All
axes by default.
Returns
-------
outarray : ndarray (same shape than inarray)
The unitary N-D Fourier transform of ``inarray``.
Examples
--------
>>> input = np.ones((3, 3, 3))
>>> output = ufftn(input)
>>> np.allclose(np.sum(input) / np.sqrt(input.size), output[0, 0, 0])
True
>>> output.shape
(3, 3, 3)
"""
if dim is None:
dim = inarray.ndim
outarray = fft.fftn(inarray, axes=range(-dim, 0), norm='ortho')
return outarray
def uifftn(inarray, dim=None):
"""N-dimensional unitary inverse Fourier transform.
Parameters
----------
inarray : ndarray
The array to transform.
dim : int, optional
The last axis along which to compute the transform. All
axes by default.
Returns
-------
outarray : ndarray (same shape than inarray)
The unitary inverse N-D Fourier transform of ``inarray``.
Examples
--------
>>> input = np.ones((3, 3, 3))
>>> output = uifftn(input)
>>> np.allclose(np.sum(input) / np.sqrt(input.size), output[0, 0, 0])
True
>>> output.shape
(3, 3, 3)
"""
if dim is None:
dim = inarray.ndim
outarray = fft.ifftn(inarray, axes=range(-dim, 0), norm='ortho')
return outarray
def urfftn(inarray, dim=None):
"""N-dimensional real unitary Fourier transform.
This transform considers the Hermitian property of the transform on
real-valued input.
Parameters
----------
inarray : ndarray, shape (M, N, ..., P)
The array to transform.
dim : int, optional
The last axis along which to compute the transform. All
axes by default.
Returns
-------
outarray : ndarray, shape (M, N, ..., P / 2 + 1)
The unitary N-D real Fourier transform of ``inarray``.
Notes
-----
The ``urfft`` functions assume an input array of real
values. Consequently, the output has a Hermitian property and
redundant values are not computed or returned.
Examples
--------
>>> input = np.ones((5, 5, 5))
>>> output = urfftn(input)
>>> np.allclose(np.sum(input) / np.sqrt(input.size), output[0, 0, 0])
True
>>> output.shape
(5, 5, 3)
"""
if dim is None:
dim = inarray.ndim
outarray = fft.rfftn(inarray, axes=range(-dim, 0), norm='ortho')
return outarray
def uirfftn(inarray, dim=None, shape=None):
"""N-dimensional inverse real unitary Fourier transform.
This transform considers the Hermitian property of the transform
from complex to real input.
Parameters
----------
inarray : ndarray
The array to transform.
dim : int, optional
The last axis along which to compute the transform. All
axes by default.
shape : tuple of int, optional
The shape of the output. The shape of ``rfft`` is ambiguous in
case of odd-valued input shape. In this case, this parameter
should be provided. See ``np.fft.irfftn``.
Returns
-------
outarray : ndarray
The unitary N-D inverse real Fourier transform of ``inarray``.
Notes
-----
The ``uirfft`` function assumes that the output array is
real-valued. Consequently, the input is assumed to have a Hermitian
property and redundant values are implicit.
Examples
--------
>>> input = np.ones((5, 5, 5))
>>> output = uirfftn(urfftn(input), shape=input.shape)
>>> np.allclose(input, output)
True
>>> output.shape
(5, 5, 5)
"""
if dim is None:
dim = inarray.ndim
outarray = fft.irfftn(inarray, shape, axes=range(-dim, 0), norm='ortho')
return outarray
def ufft2(inarray):
"""2-dimensional unitary Fourier transform.
Compute the Fourier transform on the last 2 axes.
Parameters
----------
inarray : ndarray
The array to transform.
Returns
-------
outarray : ndarray (same shape as inarray)
The unitary 2-D Fourier transform of ``inarray``.
See Also
--------
uifft2, ufftn, urfftn
Examples
--------
>>> input = np.ones((10, 128, 128))
>>> output = ufft2(input)
>>> np.allclose(np.sum(input[1, ...]) / np.sqrt(input[1, ...].size),
... output[1, 0, 0])
True
>>> output.shape
(10, 128, 128)
"""
return ufftn(inarray, 2)
def uifft2(inarray):
"""2-dimensional inverse unitary Fourier transform.
Compute the inverse Fourier transform on the last 2 axes.
Parameters
----------
inarray : ndarray
The array to transform.
Returns
-------
outarray : ndarray (same shape as inarray)
The unitary 2-D inverse Fourier transform of ``inarray``.
See Also
--------
uifft2, uifftn, uirfftn
Examples
--------
>>> input = np.ones((10, 128, 128))
>>> output = uifft2(input)
>>> np.allclose(np.sum(input[1, ...]) / np.sqrt(input[1, ...].size),
... output[0, 0, 0])
True
>>> output.shape
(10, 128, 128)
"""
return uifftn(inarray, 2)
def urfft2(inarray):
"""2-dimensional real unitary Fourier transform
Compute the real Fourier transform on the last 2 axes. This
transform considers the Hermitian property of the transform from
complex to real-valued input.
Parameters
----------
inarray : ndarray, shape (M, N, ..., P)
The array to transform.
Returns
-------
outarray : ndarray, shape (M, N, ..., 2 * (P - 1))
The unitary 2-D real Fourier transform of ``inarray``.
See Also
--------
ufft2, ufftn, urfftn
Examples
--------
>>> input = np.ones((10, 128, 128))
>>> output = urfft2(input)
>>> np.allclose(np.sum(input[1,...]) / np.sqrt(input[1,...].size),
... output[1, 0, 0])
True
>>> output.shape
(10, 128, 65)
"""
return urfftn(inarray, 2)
def uirfft2(inarray, shape=None):
"""2-dimensional inverse real unitary Fourier transform.
Compute the real inverse Fourier transform on the last 2 axes.
This transform considers the Hermitian property of the transform
from complex to real-valued input.
Parameters
----------
inarray : ndarray, shape (M, N, ..., P)
The array to transform.
shape : tuple of int, optional
The shape of the output. The shape of ``rfft`` is ambiguous in
case of odd-valued input shape. In this case, this parameter
should be provided. See ``np.fft.irfftn``.
Returns
-------
outarray : ndarray, shape (M, N, ..., 2 * (P - 1))
The unitary 2-D inverse real Fourier transform of ``inarray``.
See Also
--------
urfft2, uifftn, uirfftn
Examples
--------
>>> input = np.ones((10, 128, 128))
>>> output = uirfftn(urfftn(input), shape=input.shape)
>>> np.allclose(input, output)
True
>>> output.shape
(10, 128, 128)
"""
return uirfftn(inarray, 2, shape=shape)
def image_quad_norm(inarray):
"""Return the quadratic norm of images in Fourier space.
This function detects whether the input image satisfies the
Hermitian property.
Parameters
----------
inarray : ndarray
Input image. The image data should reside in the final two
axes.
Returns
-------
norm : float
The quadratic norm of ``inarray``.
Examples
--------
>>> input = np.ones((5, 5))
>>> image_quad_norm(ufft2(input)) == np.sum(np.abs(input)**2)
True
>>> image_quad_norm(ufft2(input)) == image_quad_norm(urfft2(input))
True
"""
# If there is a Hermitian symmetry
if inarray.shape[-1] != inarray.shape[-2]:
return (2 * np.sum(np.sum(np.abs(inarray) ** 2, axis=-1), axis=-1) -
np.sum(np.abs(inarray[..., 0]) ** 2, axis=-1))
else:
return np.sum(np.sum(np.abs(inarray) ** 2, axis=-1), axis=-1)
def ir2tf(imp_resp, shape, dim=None, is_real=True):
"""Compute the transfer function of an impulse response (IR).
This function makes the necessary correct zero-padding, zero
convention, correct fft2, etc... to compute the transfer function
of IR. To use with unitary Fourier transform for the signal (ufftn
or equivalent).
Parameters
----------
imp_resp : ndarray
The impulse responses.
shape : tuple of int
A tuple of integer corresponding to the target shape of the
transfer function.
dim : int, optional
The last axis along which to compute the transform. All
axes by default.
is_real : boolean, optional
If True (default), imp_resp is supposed real and the Hermitian property
is used with rfftn Fourier transform.
Returns
-------
y : complex ndarray
The transfer function of shape ``shape``.
See Also
--------
ufftn, uifftn, urfftn, uirfftn
Examples
--------
>>> np.all(np.array([[4, 0], [0, 0]]) == ir2tf(np.ones((2, 2)), (2, 2)))
True
>>> ir2tf(np.ones((2, 2)), (512, 512)).shape == (512, 257)
True
>>> ir2tf(np.ones((2, 2)), (512, 512), is_real=False).shape == (512, 512)
True
Notes
-----
The input array can be composed of multiple-dimensional IR with
an arbitrary number of IR. The individual IR must be accessed
through the first axes. The last ``dim`` axes contain the space
definition.
"""
if not dim:
dim = imp_resp.ndim
# Zero padding and fill
irpadded_dtype = _supported_float_type(imp_resp)
irpadded = np.zeros(shape, dtype=irpadded_dtype)
irpadded[tuple([slice(0, s) for s in imp_resp.shape])] = imp_resp
# Roll for zero convention of the fft to avoid the phase
# problem. Work with odd and even size.
for axis, axis_size in enumerate(imp_resp.shape):
if axis >= imp_resp.ndim - dim:
irpadded = np.roll(irpadded,
shift=-int(np.floor(axis_size / 2)),
axis=axis)
func = fft.rfftn if is_real else fft.fftn
out = func(irpadded, axes=(range(-dim, 0)))
# TODO: remove .astype call once SciPy >= 1.4 is required
cplx_dtype = np.promote_types(irpadded_dtype, np.complex64)
return out.astype(cplx_dtype, copy=False)
def laplacian(ndim, shape, is_real=True):
"""Return the transfer function of the Laplacian.
Laplacian is the second order difference, on row and column.
Parameters
----------
ndim : int
The dimension of the Laplacian.
shape : tuple
The support on which to compute the transfer function.
is_real : boolean, optional
If True (default), imp_resp is assumed to be real-valued and
the Hermitian property is used with rfftn Fourier transform
to return the transfer function.
Returns
-------
tf : array_like, complex
The transfer function.
impr : array_like, real
The Laplacian.
Examples
--------
>>> tf, ir = laplacian(2, (32, 32))
>>> np.all(ir == np.array([[0, -1, 0], [-1, 4, -1], [0, -1, 0]]))
True
>>> np.all(tf == ir2tf(ir, (32, 32)))
True
"""
impr = np.zeros([3] * ndim)
for dim in range(ndim):
idx = tuple([slice(1, 2)] * dim +
[slice(None)] +
[slice(1, 2)] * (ndim - dim - 1))
impr[idx] = np.array([-1.0,
0.0,
-1.0]).reshape([-1 if i == dim else 1
for i in range(ndim)])
impr[(slice(1, 2), ) * ndim] = 2.0 * ndim
return ir2tf(impr, shape, is_real=is_real), impr

View File

@@ -1,113 +0,0 @@
import numpy as np
from .._shared.utils import warn
from ._unwrap_1d import unwrap_1d
from ._unwrap_2d import unwrap_2d
from ._unwrap_3d import unwrap_3d
def unwrap_phase(image, wrap_around=False, seed=None):
'''Recover the original from a wrapped phase image.
From an image wrapped to lie in the interval [-pi, pi), recover the
original, unwrapped image.
Parameters
----------
image : 1D, 2D or 3D ndarray of floats, optionally a masked array
The values should be in the range [-pi, pi). If a masked array is
provided, the masked entries will not be changed, and their values
will not be used to guide the unwrapping of neighboring, unmasked
values. Masked 1D arrays are not allowed, and will raise a
`ValueError`.
wrap_around : bool or sequence of bool, optional
When an element of the sequence is `True`, the unwrapping process
will regard the edges along the corresponding axis of the image to be
connected and use this connectivity to guide the phase unwrapping
process. If only a single boolean is given, it will apply to all axes.
Wrap around is not supported for 1D arrays.
seed : int, optional
Unwrapping 2D or 3D images uses random initialization. This sets the
seed of the PRNG to achieve deterministic behavior.
Returns
-------
image_unwrapped : array_like, double
Unwrapped image of the same shape as the input. If the input `image`
was a masked array, the mask will be preserved.
Raises
------
ValueError
If called with a masked 1D array or called with a 1D array and
``wrap_around=True``.
Examples
--------
>>> c0, c1 = np.ogrid[-1:1:128j, -1:1:128j]
>>> image = 12 * np.pi * np.exp(-(c0**2 + c1**2))
>>> image_wrapped = np.angle(np.exp(1j * image))
>>> image_unwrapped = unwrap_phase(image_wrapped)
>>> np.std(image_unwrapped - image) < 1e-6 # A constant offset is normal
True
References
----------
.. [1] Miguel Arevallilo Herraez, David R. Burton, Michael J. Lalor,
and Munther A. Gdeisat, "Fast two-dimensional phase-unwrapping
algorithm based on sorting by reliability following a noncontinuous
path", Journal Applied Optics, Vol. 41, No. 35 (2002) 7437,
.. [2] Abdul-Rahman, H., Gdeisat, M., Burton, D., & Lalor, M., "Fast
three-dimensional phase-unwrapping algorithm based on sorting by
reliability following a non-continuous path. In W. Osten,
C. Gorecki, & E. L. Novak (Eds.), Optical Metrology (2005) 32--40,
International Society for Optics and Photonics.
'''
if image.ndim not in (1, 2, 3):
raise ValueError('Image must be 1, 2, or 3 dimensional')
if isinstance(wrap_around, bool):
wrap_around = [wrap_around] * image.ndim
elif (hasattr(wrap_around, '__getitem__')
and not isinstance(wrap_around, str)):
if len(wrap_around) != image.ndim:
raise ValueError('Length of `wrap_around` must equal the '
'dimensionality of image')
wrap_around = [bool(wa) for wa in wrap_around]
else:
raise ValueError('`wrap_around` must be a bool or a sequence with '
'length equal to the dimensionality of image')
if image.ndim == 1:
if np.ma.isMaskedArray(image):
raise ValueError('1D masked images cannot be unwrapped')
if wrap_around[0]:
raise ValueError('`wrap_around` is not supported for 1D images')
if image.ndim in (2, 3) and 1 in image.shape:
warn('Image has a length 1 dimension. Consider using an '
'array of lower dimensionality to use a more efficient '
'algorithm')
if np.ma.isMaskedArray(image):
mask = np.require(np.ma.getmaskarray(image), np.uint8, ['C'])
else:
mask = np.zeros_like(image, dtype=np.uint8, order='C')
image_not_masked = np.asarray(
np.ma.getdata(image), dtype=np.float64, order='C')
image_unwrapped = np.empty_like(image, dtype=np.float64, order='C',
subok=False)
if image.ndim == 1:
unwrap_1d(image_not_masked, image_unwrapped)
elif image.ndim == 2:
unwrap_2d(image_not_masked, mask, image_unwrapped,
wrap_around, seed)
elif image.ndim == 3:
unwrap_3d(image_not_masked, mask, image_unwrapped,
wrap_around, seed)
if np.ma.isMaskedArray(image):
return np.ma.array(image_unwrapped, mask=mask,
fill_value=image.fill_value)
else:
return image_unwrapped