/
non_local_means.py
187 lines (161 loc) · 7.54 KB
/
non_local_means.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
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=0.0,
*,
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