restoration
Module: restoration
Image restoration module.
References
[R303] |
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) http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-7-1593 |
[R304] | Richardson, William Hadley, “Bayesian-Based Iterative Method of Image Restoration”. JOSA 62 (1): 55–59. doi:10.1364/JOSA.62.000055, 1972 |
[R305] | 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 |
skimage.restoration.denoise_bilateral (image) | Denoise image using bilateral filter. |
skimage.restoration.denoise_nl_means (image) | Perform non-local means denoising on 2-D or 3-D grayscale images, and 2-D RGB images. |
skimage.restoration.denoise_tv_bregman (...) | Perform total-variation denoising using split-Bregman optimization. |
skimage.restoration.denoise_tv_chambolle (im) | Perform total-variation denoising on n-dimensional images. |
skimage.restoration.nl_means_denoising (...) |
Deprecated function. Use skimage.restoration.denoise_nl_means instead. |
skimage.restoration.richardson_lucy (image, psf) | Richardson-Lucy deconvolution. |
skimage.restoration.unsupervised_wiener (...) | Unsupervised Wiener-Hunt deconvolution. |
skimage.restoration.unwrap_phase (image[, ...]) | Recover the original from a wrapped phase image. |
skimage.restoration.wiener (image, psf, balance) | Wiener-Hunt deconvolution |
denoise_bilateral
-
skimage.restoration.denoise_bilateral(image, win_size=None, sigma_color=None, sigma_spatial=1, bins=10000, mode='constant', cval=0, multichannel=True, sigma_range=None)
[source] -
Denoise image using bilateral filter.
This is an edge-preserving and noise reducing denoising filter. It averages pixels based on their spatial closeness and radiometric similarity.
Spatial closeness is measured by the gaussian function of the euclidian distance between two pixels and a certain standard deviation (
sigma_spatial
).Radiometric similarity is measured by the gaussian function of the euclidian distance between two color values and a certain standard deviation (
sigma_color
).Parameters: image : ndarray, shape (M, N[, 3])
Input image, 2D grayscale or RGB.
win_size : int
Window size for filtering. If win_size is not specified, it is calculated as max(5, 2*ceil(3*sigma_spatial)+1)
sigma_color : float
Standard deviation for grayvalue/color distance (radiometric similarity). A larger value results in averaging of pixels with larger radiometric differences. Note, that the image will be converted using the
img_as_float
function and thus the standard deviation is in respect to the range[0, 1]
. If the value isNone
the standard deviation of theimage
will be used.sigma_spatial : float
Standard deviation for range distance. A larger value results in averaging of pixels with larger spatial differences.
bins : int
Number of discrete values for gaussian weights of color filtering. A larger value results in improved accuracy.
mode : {‘constant’, ‘edge’, ‘symmetric’, ‘reflect’, ‘wrap’}
How to handle values outside the image borders. See
numpy.pad
for detail.cval : string
Used in conjunction with mode ‘constant’, the value outside the image boundaries.
multichannel : bool
Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension.
Returns: denoised : ndarray
Denoised image.
References
[R324] http://users.soe.ucsc.edu/~manduchi/Papers/ICCV98.pdf Examples
>>> from skimage import data, img_as_float >>> astro = img_as_float(data.astronaut()) >>> astro = astro[220:300, 220:320] >>> noisy = astro + 0.6 * astro.std() * np.random.random(astro.shape) >>> noisy = np.clip(noisy, 0, 1) >>> denoised = denoise_bilateral(noisy, sigma_color=0.05, sigma_spatial=15)
denoise_nl_means
-
skimage.restoration.denoise_nl_means(image, patch_size=7, patch_distance=11, h=0.1, multichannel=True, fast_mode=True)
[source] -
Perform non-local means denoising on 2-D or 3-D grayscale images, and 2-D 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
multichannel
parameter).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.
multichannel : bool, optional
Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension. Set to
False
for 3-D images.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.
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 neighbourhood, 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 [R325], corresponding to
fast=False
, the computational complexity isimage.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 [R326] is used, corresponding to a complexity ofimage.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 [R325]. Therefore, this algorithm executes faster than the classic algorith (
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. [R327].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 ofskimage.util.pad
before denoising.References
[R325] (1, 2, 3) Buades, A., Coll, B., & Morel, J. M. (2005, June). A non-local algorithm for image denoising. In CVPR 2005, Vol. 2, pp. 60-65, IEEE. [R326] (1, 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. [R327] (1, 2) Jacques Froment. Parameter-Free Fast Pixelwise Non-Local Means Denoising. Image Processing On Line, 2014, vol. 4, p. 300-326. Examples
>>> a = np.zeros((40, 40)) >>> a[10:-10, 10:-10] = 1. >>> a += 0.3 * np.random.randn(*a.shape) >>> denoised_a = denoise_nl_means(a, 7, 5, 0.1)
denoise_tv_bregman
-
skimage.restoration.denoise_tv_bregman(image, weight, max_iter=100, eps=0.001, isotropic=True)
[source] -
Perform total-variation denoising using split-Bregman optimization.
Total-variation denoising (also know as total-variation regularization) tries to find an image with less total-variation under the constraint of being similar to the input image, which is controlled by the regularization parameter.
Parameters: image : ndarray
Input data to be denoised (converted using img_as_float`).
weight : float
Denoising weight. The smaller the
weight
, the more denoising (at the expense of less similarity to theinput
). The regularization parameterlambda
is chosen as2 * weight
.eps : float, optional
Relative difference of the value of the cost function that determines the stop criterion. The algorithm stops when:
SUM((u(n) - u(n-1))**2) < eps
max_iter : int, optional
Maximal number of iterations used for the optimization.
isotropic : boolean, optional
Switch between isotropic and anisotropic TV denoising.
Returns: u : ndarray
Denoised image.
References
[R328] http://en.wikipedia.org/wiki/Total_variation_denoising [R329] Tom Goldstein and Stanley Osher, “The Split Bregman Method For L1 Regularized Problems”, ftp://ftp.math.ucla.edu/pub/camreport/cam08-29.pdf [R330] Pascal Getreuer, “Rudin–Osher–Fatemi Total Variation Denoising using Split Bregman” in Image Processing On Line on 2012–05–19, http://www.ipol.im/pub/art/2012/g-tvd/article_lr.pdf [R331] http://www.math.ucsb.edu/~cgarcia/UGProjects/BregmanAlgorithms_JacquelineBush.pdf
denoise_tv_chambolle
-
skimage.restoration.denoise_tv_chambolle(im, weight=0.1, eps=0.0002, n_iter_max=200, multichannel=False)
[source] -
Perform total-variation denoising on n-dimensional images.
Parameters: im : ndarray of ints, uints or floats
Input data to be denoised.
im
can be of any numeric type, but it is cast into an ndarray of floats for the computation of the denoised image.weight : float, optional
Denoising weight. The greater
weight
, the more denoising (at the expense of fidelity toinput
).eps : float, optional
Relative difference of the value of the cost function that determines the stop criterion. The algorithm stops when:
(E_(n-1) - E_n) < eps * E_0
n_iter_max : int, optional
Maximal number of iterations used for the optimization.
multichannel : bool, optional
Apply total-variation denoising separately for each channel. This option should be true for color images, otherwise the denoising is also applied in the channels dimension.
Returns: out : ndarray
Denoised image.
Notes
Make sure to set the multichannel parameter appropriately for color images.
The principle of total variation denoising is explained in http://en.wikipedia.org/wiki/Total_variation_denoising
The principle of total variation denoising is to minimize the total variation of the image, which can be roughly described as the integral of the norm of the image gradient. Total variation denoising tends to produce “cartoon-like” images, that is, piecewise-constant images.
This code is an implementation of the algorithm of Rudin, Fatemi and Osher that was proposed by Chambolle in [R332].
References
[R332] (1, 2) A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, Springer, 2004, 20, 89-97. Examples
2D example on astronaut image:
>>> from skimage import color, data >>> img = color.rgb2gray(data.astronaut())[:50, :50] >>> img += 0.5 * img.std() * np.random.randn(*img.shape) >>> denoised_img = denoise_tv_chambolle(img, weight=60)
3D example on synthetic data:
>>> x, y, z = np.ogrid[0:20, 0:20, 0:20] >>> mask = (x - 22)**2 + (y - 20)**2 + (z - 17)**2 < 8**2 >>> mask = mask.astype(np.float) >>> mask += 0.2*np.random.randn(*mask.shape) >>> res = denoise_tv_chambolle(mask, weight=100)
nl_means_denoising
-
skimage.restoration.nl_means_denoising(*args, **kwargs)
[source] -
Deprecated function. Use
skimage.restoration.denoise_nl_means
instead.Perform non-local means denoising on 2-D or 3-D grayscale images, and 2-D 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
multichannel
parameter).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.
multichannel : bool, optional
Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension. Set to
False
for 3-D images.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.
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 neighbourhood, 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 [R333], corresponding to
fast=False
, the computational complexity isimage.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 [R334] is used, corresponding to a complexity ofimage.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 [R333]. Therefore, this algorithm executes faster than the classic algorith (
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. [R335].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 ofskimage.util.pad
before denoising.References
[R333] (1, 2, 3) Buades, A., Coll, B., & Morel, J. M. (2005, June). A non-local algorithm for image denoising. In CVPR 2005, Vol. 2, pp. 60-65, IEEE. [R334] (1, 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. [R335] (1, 2) Jacques Froment. Parameter-Free Fast Pixelwise Non-Local Means Denoising. Image Processing On Line, 2014, vol. 4, p. 300-326. Examples
>>> a = np.zeros((40, 40)) >>> a[10:-10, 10:-10] = 1. >>> a += 0.3 * np.random.randn(*a.shape) >>> denoised_a = denoise_nl_means(a, 7, 5, 0.1)
richardson_lucy
-
skimage.restoration.richardson_lucy(image, psf, iterations=50, clip=True)
[source] -
Richardson-Lucy deconvolution.
Parameters: image : ndarray
Input degraded image (can be N dimensional).
psf : ndarray
The point spread function.
iterations : int
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.
Returns: im_deconv : ndarray
The deconvolved image.
References
[R336] http://en.wikipedia.org/wiki/Richardson%E2%80%93Lucy_deconvolution Examples
>>> from skimage import color, data, restoration >>> camera = color.rgb2gray(data.camera()) >>> from scipy.signal import convolve2d >>> psf = np.ones((5, 5)) / 25 >>> camera = convolve2d(camera, psf, 'same') >>> camera += 0.1 * camera.std() * np.random.standard_normal(camera.shape) >>> deconvolved = restoration.richardson_lucy(camera, psf, 5)
unsupervised_wiener
-
skimage.restoration.unsupervised_wiener(image, psf, reg=None, user_params=None, is_real=True, clip=True)
[source] -
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
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.
Returns: x_postmean : (M, N) ndarray
The deconvolved image (the posterior mean).
chains : dict
The keys
noise
andprior
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. 100 by default.
min_iter : int
The minimum number of iterations. 30 by default.
max_iter : int
The maximum number of iterations if
threshold
is not satisfied. 150 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.
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
[R337] 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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-7-1593
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') >>> img += 0.1 * img.std() * np.random.standard_normal(img.shape) >>> deconvolved_img = restoration.unsupervised_wiener(img, psf)
unwrap_phase
-
skimage.restoration.unwrap_phase(image, wrap_around=False, seed=None)
[source] -
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
.References
[R338] 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, [R339] 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. 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
wiener
-
skimage.restoration.wiener(image, psf, balance, reg=None, is_real=True, clip=True)
[source] -
Wiener-Hunt deconvolution
Return the deconvolution with a Wiener-Hunt approach (i.e. with Fourier diagonalisation).
Parameters: image : (M, N) ndarray
Input degraded image
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
(M, N)
ifis_real is True
,(M, N // 2 + 1)
otherwise (seenp.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
andreg
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 ifpsf
and/orreg
are provided as transfer function. For the hermitian property seeuft
module ornp.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.
Notes
This function applies the Wiener filter to a noisy and degraded image by an impulse response (or PSF). If the data model is
where is noise, the PSF and the unknown original image, the Wiener filter is
where and are the Fourier and inverse Fourier transfroms respectively, the transfer function (or the Fourier transfrom of the PSF, see [Hunt] below) and the filter to penalize the restored image frequencies (Laplacian by default, that is penalization of high frequency). The parameter 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 corresponds 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 , see [Hunt].
References
[R340] 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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-7-1593
[R341] 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 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') >>> img += 0.1 * img.std() * np.random.standard_normal(img.shape) >>> deconvolved_img = restoration.wiener(img, psf, 1100)
© 2011 the scikit-image team
Licensed under the BSD 3-clause License.
http://scikit-image.org/docs/0.12.x/api/skimage.restoration.html