0-PhddlZddlmZddlZddlZddlZddlm Z ddl m Z ddl m Z mZddlmZmZdd lmZdd lmZed d Zed d Zed dZe j d*dddZe j d+dddZd,dZ d,dddZdZdZ d-d Z! d.d"Z"d#Z#d$Z$e j d/ddd(Z%d0ddd)Z&dS)1N)ceil) img_as_float)utils)_supported_float_typewarn)_denoise_bilateral_denoise_tv_bregman)color)ycbcr_from_rgbdtypec@tjd|dz|z z|S)aHelping function. Define a Gaussian weighting from array and sigma_square. Parameters ---------- array : ndarray Input array. sigma_squared : float The squared standard deviation used in the filter. dtype : data type object, optional (default : float) The type and size of the data to be returned. Returns ------- gaussian : ndarray The input array filtered by the Gaussian. grr)npexp)array sigma_squaredrs \/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/skimage/restoration/_denoise.py_gaussian_weightrs'$ 6$%(]235 A A AAc\tjd||d}t||dz|S)aHelping function. Define a lookup table containing Gaussian filter values using the color distance sigma. Parameters ---------- bins : int Number of discrete values for Gaussian weights of color filtering. A larger value results in improved accuracy. sigma : 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 is ``None`` the standard deviation of the ``image`` will be used. max_value : float Maximum value of the input image. dtype : data type object, optional (default : float) The type and size of the data to be returned. Returns ------- color_lut : ndarray Lookup table for the color distance sigma. rF)endpointrr)rlinspacer)binssigma max_valuervaluess r_compute_color_lutr%s54[Ite < < >K [kD A A AFBR  I Iuaxu = = = C C E EEr'constant channel_axiscr||jdkr2|jdkrtdtd|jd|jddvrT|jddkr)d |jd |jdd }t|n>d |jd }t|n#|jdkrtd|jd|3t ddt t d|zzdz}|} |} | | kr|Stj t|}tj |}|p| }t||| |j} t|||j} tj|j|j} |jd}tj||j}| dkr || z }| | z} t#|| ||||||| | || tj| } | dkr| | z } | S)a( Denoise image using bilateral filter. 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. If ``None``, the standard deviation of ``image`` 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 : int or float Used in conjunction with mode 'constant', the value outside the image boundaries. channel_axis : int or None, optional If ``None``, the image is assumed to be grayscale (single-channel). Otherwise, this parameter indicates which axis of the array corresponds to channels. .. versionadded:: 0.19 ``channel_axis`` was added in 0.19. Returns ------- denoised : ndarray Denoised image. Notes ----- This is an edge-preserving, denoising filter. It averages pixels based on their spatial closeness and radiometric similarity [1]_. Spatial closeness is measured by the Gaussian function of the Euclidean distance between two pixels and a certain standard deviation (`sigma_spatial`). Radiometric similarity is measured by the Gaussian function of the Euclidean distance between two color values and a certain standard deviation (`sigma_color`). Note that, if the image is of any `int` dtype, ``image`` will be converted using the `img_as_float` function and thus the standard deviation (`sigma_color`) will be in range ``[0, 1]``. For more information on scikit-image's data type conversions and how images are rescaled in these conversions, see: https://scikit-image.org/docs/stable/user_guide/data_types.html. References ---------- .. [1] C. Tomasi and R. Manduchi. "Bilateral Filtering for Gray and Color Images." IEEE International Conference on Computer Vision (1998) 839-846. :DOI:`10.1109/ICCV.1998.710815` Examples -------- >>> from skimage import data, img_as_float >>> astro = img_as_float(data.astronaut()) >>> astro = astro[220:300, 220:320] >>> rng = np.random.default_rng() >>> noisy = astro + 0.6 * astro.std() * rng.random(astro.shape) >>> noisy = np.clip(noisy, 0, 1) >>> denoised = denoise_bilateral(noisy, sigma_color=0.05, sigma_spatial=15, ... channel_axis=-1) NrzUse ``channel_axis=None`` for 2D grayscale images. The last axis of the input image must be multiple color channels not another spatial dimension.zBilateral filter is only implemented for 2D grayscale images (image.ndim == 2) and 2D multichannel (image.ndim == 3) images, but the input image has z dimensions.)r2r3zTThe last axis of the input image is interpreted as channels. Input image with shape z has zc channels in last axis. ``denoise_bilateral``is implemented for 2D grayscale and color images only.z;Input image must be grayscale, RGB, or RGBA; but has shape .zfBilateral filter is not implemented for grayscale images of 3 or more dimensions, but input image has z2 shape. Use ``channel_axis=-1`` for 2D RGB images.r rr)ndim ValueErrorshapermaxintrminr atleast_3drascontiguousarraystdrrr,emptyr squeeze)imager' sigma_color sigma_spatialrmodecvalr0msg min_valuer color_lut range_lutoutdims empty_dimss rdenoise_bilateralrM^st :??zQ )!H05zHHH [^6 ) ){1~!!?"[??/4{1~???S 4%*[444S :>>:',{::: q!c$q='8"9"9:::Q>?? I II M,u-- . .E   ' 'E,K"4iu{SSSI$X}EKPPPI (5;ek 2 2 2C ;q>D $ek222J1}} !Y          *S//C1}} y Jr@dMbP?Tc tjt|}|jd}|jd}|jd}|dz|dz|f} tj| |j} |tj| dddz| j} t |jdD]\} tj|d| | dzf} t| |j ||||| | d | d| f<]n@tj|}t||j ||||| tj | ddddfS) u Perform total variation denoising using split-Bregman optimization. Given :math:`f`, a noisy image (input data), total variation denoising (also known as total variation regularization) aims to find an image :math:`u` with less total variation than :math:`f`, under the constraint that :math:`u` remain similar to :math:`f`. This can be expressed by the Rudin--Osher--Fatemi (ROF) minimization problem: .. math:: \min_{u} \sum_{i=0}^{N-1} \left( \left| \nabla{u_i} \right| + \frac{\lambda}{2}(f_i - u_i)^2 \right) where :math:`\lambda` is a positive parameter. The first term of this cost function is the total variation; the second term represents data fidelity. As :math:`\lambda \to 0`, the total variation term dominates, forcing the solution to have smaller total variation, at the expense of looking less like the input data. This code is an implementation of the split Bregman algorithm of Goldstein and Osher to solve the ROF problem ([1]_, [2]_, [3]_). Parameters ---------- image : ndarray Input image to be denoised (converted using :func:`~.img_as_float`). weight : float, optional Denoising weight. It is equal to :math:`\frac{\lambda}{2}`. Therefore, the smaller the `weight`, the more denoising (at the expense of less similarity to `image`). eps : float, optional Tolerance :math:`\varepsilon > 0` for the stop criterion: The algorithm stops when :math:`\|u_n - u_{n-1}\|_2 < \varepsilon`. max_num_iter : int, optional Maximal number of iterations used for the optimization. isotropic : boolean, optional Switch between isotropic and anisotropic TV denoising. channel_axis : int or None, optional If ``None``, the image is assumed to be grayscale (single-channel). Otherwise, this parameter indicates which axis of the array corresponds to channels. .. versionadded:: 0.19 ``channel_axis`` was added in 0.19. Returns ------- u : ndarray Denoised image. Notes ----- Ensure that `channel_axis` parameter is set appropriately for color images. The principle of total variation denoising is explained in [4]_. It is about minimizing the total variation of an 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. See Also -------- denoise_tv_chambolle : Perform total variation denoising in nD. References ---------- .. [1] Tom Goldstein and Stanley Osher, "The Split Bregman Method For L1 Regularized Problems", https://ww3.math.ucla.edu/camreport/cam08-29.pdf .. [2] Pascal Getreuer, "Rudin–Osher–Fatemi Total Variation Denoising using Split Bregman" in Image Processing On Line on 2012–05–19, https://www.ipol.im/pub/art/2012/g-tvd/article_lr.pdf .. [3] https://web.math.ucsb.edu/~cgarcia/UGProjects/BregmanAlgorithms_JacquelineBush.pdf .. [4] https://en.wikipedia.org/wiki/Total_variation_denoising rr rN)r r.).r) rr<rr8zerosrranger=r typer@)rAweight max_num_itereps isotropicr0rowscolsrK shape_extrJ channel_outc channel_ins rdenoise_tv_bregmanr`sd M,u-- . .E ;q>D ;q>D ;q>D4!8T*I (9ek * *Chy!}t339EEE u{2'' . .A-eCQUN.CDDJ    ((    &f-CQKK .$$U++ 5;##F++\3 3    :c!B$"*o & &&r皙?-C6*?cJ|j}tj|jf|jz|j}tj|}tj|}d}||krA|dkr|d }tdg|z} tdg|dzz} t|D]} tdd| | <tdd| | dz<| | d<|t| xx|t| z cc<td| | <td| | dz<||z} n|} |dz} tdg|dzz}t|D]X} tdd|| dz<| |d<tj | | |t|<td|| dz<Ytj |dzdtj df}| ||zz } d d |zz }|||z z}|d z }|||zz}||z}| t|jz} |dkr| }| }n!tj|| z ||zkrn| }|dz }||kA| S) aPerform total-variation denoising on n-dimensional images. Parameters ---------- image : ndarray n-D input data to be denoised. weight : float, optional Denoising weight. The greater `weight`, the more denoising (at the expense of fidelity to `input`). 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 max_num_iter : int, optional Maximal number of iterations used for the optimization. Returns ------- out : ndarray Denoised array of floats. Notes ----- Rudin, Osher and Fatemi algorithm. rrNr rRraxis.g?g@)r6rrSr8r zeros_likesumslicerTtuplediffsqrtnewaxisfloatsizeabs)rArVrXrWr6pgdislices_dslices_paxrJEslices_gnormtauE_init E_previouss r_denoise_tv_chambolle_ndr~s: :D %*,EK@@@A aA eA A l   q55q Ad Hd HDkk / /$Q~~ #(B<<a   %//"""ah&88"""$T{{ #(;;a  !)CCC TJJLL $KK AX++ + +B$Q||HR!V HQK!#2!6!6!6AeHoo $T{{HR!V  w1zzqz))**2:s?; Vdhhjj  S4Z  f    S1W  T  U5:   66FJJvj1n%%f 44  Qc l  d Jrc|j}|jdkst|}t|j}||d}|||jz}t jtj |}tj |}t|j |D]/} t||| |||||| <0nt||||}|S)a Perform total variation denoising in nD. Given :math:`f`, a noisy image (input data), total variation denoising (also known as total variation regularization) aims to find an image :math:`u` with less total variation than :math:`f`, under the constraint that :math:`u` remain similar to :math:`f`. This can be expressed by the Rudin--Osher--Fatemi (ROF) minimization problem: .. math:: \min_{u} \sum_{i=0}^{N-1} \left( \left| \nabla{u_i} \right| + \frac{\lambda}{2}(f_i - u_i)^2 \right) where :math:`\lambda` is a positive parameter. The first term of this cost function is the total variation; the second term represents data fidelity. As :math:`\lambda \to 0`, the total variation term dominates, forcing the solution to have smaller total variation, at the expense of looking less like the input data. This code is an implementation of the algorithm proposed by Chambolle in [1]_ to solve the ROF problem. Parameters ---------- image : ndarray Input image to be denoised. If its dtype is not float, it gets converted with :func:`~.img_as_float`. weight : float, optional Denoising weight. It is equal to :math:`\frac{1}{\lambda}`. Therefore, the greater the `weight`, the more denoising (at the expense of fidelity to `image`). eps : float, optional Tolerance :math:`\varepsilon > 0` for the stop criterion (compares to absolute value of relative difference of the cost function :math:`E`): The algorithm stops when :math:`|E_{n-1} - E_n| < \varepsilon * E_0`. max_num_iter : int, optional Maximal number of iterations used for the optimization. channel_axis : int or None, optional If ``None``, the image is assumed to be grayscale (single-channel). Otherwise, this parameter indicates which axis of the array corresponds to channels. .. versionadded:: 0.19 ``channel_axis`` was added in 0.19. Returns ------- u : ndarray Denoised image. Notes ----- Make sure to set the `channel_axis` parameter appropriately for color images. The principle of total variation denoising is explained in [2]_. It is about minimizing the total variation of an 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. See Also -------- denoise_tv_bregman : Perform total variation denoising using split-Bregman optimization. References ---------- .. [1] A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, Springer, 2004, 20, 89-97. .. [2] https://en.wikipedia.org/wiki/Total_variation_denoising Examples -------- 2D example on astronaut image: >>> from skimage import color, data >>> img = color.rgb2gray(data.astronaut())[:50, :50] >>> rng = np.random.default_rng() >>> img += 0.5 * img.std() * rng.standard_normal(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(float) >>> rng = np.random.default_rng() >>> mask += 0.2 * rng.standard_normal(mask.shape) >>> res = denoise_tv_chambolle(mask, weight=100) fF)copyNre)rkindrrastyper6 functoolspartialr slice_at_axisrrgrTr8r~) rArVrXrWr0im_type float_dtype_atrJr^s rdenoise_tv_chambollersDkG <3  U##( 44K LL5L 1 1E#ej0  3,GGGmE""u{<011  A2cc!ff vsLCAKK  'ufc<HH Jrctj||z}tj|jj}|tjt ||z |z }|S)z:BayesShrink threshold for a zero-mean details coeff array.)rmeanfinforrXrlr9)detailsvardvarrXthreshs r _bayes_threshr`sS 77W$ % %D (7= ! ! %C 273tcz3//00 0F Mrcd|tjdtj|jzzS)z1Universal threshold used by the VisuShrink methodr)rrllogro)imgrs r_universal_threshris( 271rvch///00 00rGaussianc$|tj|}|dkrNtjjd}tjtj||z }ntd|S)amCalculate the robust median estimator of the noise standard deviation. Parameters ---------- detail_coeffs : ndarray The detail coefficients corresponding to the discrete wavelet transform of an image. distribution : str The underlying noise distribution. Returns ------- sigma : float The estimated noise standard deviation (see section 4.2 of [1]_). References ---------- .. [1] D. L. Donoho and I. M. Johnstone. "Ideal spatial adaptation by wavelet shrinkage." Biometrika 81.3 (1994): 425-455. :DOI:`10.1093/biomet/81.3.425` gaussiang?z5Only Gaussian noise estimation is currently supported) rnonzerolowerscipystatsrzppfmedianrpr7) detail_coeffs distributiondenomrs r_sigma_est_dwtrns{.""*]";";z%_wavelet_threshold..s(::E!HH::::::rr2r )waveletlevelrRrsrrzThresholding method z8 selected. The user-specified threshold will be ignored.rz0If method is None, a threshold must be provided. BayesShrinkc0g|]fdDS)c>i|]}|t|S)r)rkeyrrs r z1_wavelet_threshold...s)FFFmE#J44FFFrr)rrrs @r z&_wavelet_threshold..sBGFFFFFFFr VisuShrinkzUnrecognized method: c4g|]fdDS)cNi|]!}||"S)valuerD threshold)rrrrDpywtrs rrz1_wavelet_threshold...sA   T^^E#Jid^KK   rr)rrrDrrs @rrz&_wavelet_threshold..s\                  rc<g|]\fdDS)cZi|]'}|||(Srr)rrrrDrrs rrz1_wavelet_threshold...sE   T^^E#JfSk^MM   rr)rrrrDrs @@rrz&_wavelet_threshold..sa                  r)r ImportErrorWavelet orthogonalrnamerjr8dwtn_max_levelr9wavedecnr6rr7rrisscalarzipwaverecnrr)rArmethodrrrDwavelet_levelsoriginal_extentcoeffsdcoeffsrdenoised_detaildenoised_coeffsrJrrs ` ` @@r_wavelet_thresholdrsp      *    ll7##G     ( '  ( ( (   ::ek:::::O,,U['BB^a/33 ]]5'] H HFQRRjG } C%*$45 }:FFF i3  96 9 9 9   Qh >OPP P } $ $$II| # #)%77II=V==>> > {9       !         "%Y!8!8    aykO3O -- 1 1/ BC **U[ ! !C Js %cT|r[t|tjs||g|jdz}n-t ||jdkrt d|jjdkr|r)|| z }t|}|rF|| z }||z |rfd|D}n<||z}n4|jtj kr| tj}||fS)zIf the ``image`` is rescaled, also rescale ``sigma`` consistently. Images that are not floating point will be rescaled via ``img_as_float``. Half-precision images will be promoted to single precision. NrRzdWhen channel_axis is not None, sigma must be a scalar or have length equal to the number of channelsrc"g|] }||zn| Srr)rr scale_factors rrz7_scale_sigma_and_image_consistently..3s'QQQaQ]\))QQQr) isinstancenumbersNumberr8lenr7rrr9r;rrfloat16rfloat32)rAr multichannel rescale_sigma range_pre range_postrs @r#_scale_sigma_and_image_consistentlyrs4  eW^ , ,  Gek"o-EE ZZ5;r? * *9  {3  2 eiikk1IU##  &uyy{{2J% 1L &QQQQ5QQQ"%  " " RZ(( %<rc|d|Stj|}||z}tdD]D}t|ddf}tj||z|z}tj|||<E|S)aPConvert user-provided noise standard deviations to YCbCr space. Notes ----- If R, G, B are linearly independent random variables and a1, a2, a3 are scalars, then random variable C: C = a1 * R + a2 * G + a3 * B has variance, var_C, given by: var_C = a1**2 * var_R + a2**2 * var_G + a3**2 * var_B rNr2)rasarrayrTr rhrl)sigmas rgv_variancesrtscalars var_channels r_rescale_sigma_rgb2ycbcrr;say Z  FVOM 1XX)) AAA&fWw.>?? GK((q Mrdb1Frc |du} |dvrtd|d|jjdk} |r| stdt||| |\}}| rL|rt j|} |rt |}tdD]} | d| f| d| f }} || z }|d krF| d| f| z }||z}|| }|||z}t||||||| | d| f<| d| f|z| d| f<| d| fxx| z cc<t j | } notj |} t|jd D]*}t|d|f|||||| | d|f<+nt|||||| } | r1|d krd nd}tj| g|Rd| i} | S)aPerform wavelet denoising on an image. Parameters ---------- image : ndarray (M[, N[, ...P]][, C]) of ints, uints or floats Input data to be denoised. `image` can be of any numeric type, but it is cast into an ndarray of floats for the computation of the denoised image. sigma : float or list, optional The noise standard deviation used when computing the wavelet detail coefficient threshold(s). When None (default), the noise standard deviation is estimated via the method in [2]_. wavelet : string, optional The type of wavelet to perform and can be any of the options ``pywt.wavelist`` outputs. The default is `'db1'`. For example, ``wavelet`` can be any of ``{'db2', 'haar', 'sym9'}`` and many more. mode : {'soft', 'hard'}, optional An optional argument to choose the type of denoising performed. It noted that choosing soft thresholding given additive noise finds the best approximation of the original image. wavelet_levels : int or None, optional The number of wavelet decomposition levels to use. The default is three less than the maximum number of possible decomposition levels. convert2ycbcr : bool, optional If True and channel_axis is set, do the wavelet denoising in the YCbCr colorspace instead of the RGB color space. This typically results in better performance for RGB images. method : {'BayesShrink', 'VisuShrink'}, optional Thresholding method to be used. The currently supported methods are "BayesShrink" [1]_ and "VisuShrink" [2]_. Defaults to "BayesShrink". rescale_sigma : bool, optional If False, no rescaling of the user-provided ``sigma`` will be performed. The default of ``True`` rescales sigma appropriately if the image is rescaled internally. .. versionadded:: 0.16 ``rescale_sigma`` was introduced in 0.16 channel_axis : int or None, optional If ``None``, the image is assumed to be grayscale (single-channel). Otherwise, this parameter indicates which axis of the array corresponds to channels. .. versionadded:: 0.19 ``channel_axis`` was added in 0.19. Returns ------- out : ndarray Denoised image. Notes ----- The wavelet domain is a sparse representation of the image, and can be thought of similarly to the frequency domain of the Fourier transform. Sparse representations have most values zero or near-zero and truly random noise is (usually) represented by many small values in the wavelet domain. Setting all values below some threshold to 0 reduces the noise in the image, but larger thresholds also decrease the detail present in the image. If the input is 3D, this function performs wavelet denoising on each color plane separately. .. versionchanged:: 0.16 For floating point inputs, the original input range is maintained and there is no clipping applied to the output. Other input types will be converted to a floating point value in the range [-1, 1] or [0, 1] depending on the input image range. Unless ``rescale_sigma = False``, any internal rescaling applied to the ``image`` will also be applied to ``sigma`` to maintain the same relative amplitude. Many wavelet coefficient thresholding approaches have been proposed. By default, ``denoise_wavelet`` applies BayesShrink, which is an adaptive thresholding method that computes separate thresholds for each wavelet sub-band as described in [1]_. If ``method == "VisuShrink"``, a single "universal threshold" is applied to all wavelet detail coefficients as described in [2]_. This threshold is designed to remove all Gaussian noise at a given ``sigma`` with high probability, but tends to produce images that appear overly smooth. Although any of the wavelets from ``PyWavelets`` can be selected, the thresholding methods assume an orthogonal wavelet transform and may not choose the threshold appropriately for biorthogonal wavelets. Orthogonal wavelets are desirable because white noise in the input remains white noise in the subbands. Biorthogonal wavelets lead to colored noise in the subbands. Additionally, the orthogonal wavelets in PyWavelets are orthonormal so that noise variance in the subbands remains identical to the noise variance of the input. Example orthogonal wavelets are the Daubechies (e.g. 'db2') or symmlet (e.g. 'sym2') families. References ---------- .. [1] Chang, S. Grace, Bin Yu, and Martin Vetterli. "Adaptive wavelet thresholding for image denoising and compression." Image Processing, IEEE Transactions on 9.9 (2000): 1532-1546. :DOI:`10.1109/83.862633` .. [2] D. L. Donoho and I. M. Johnstone. "Ideal spatial adaptation by wavelet shrinkage." Biometrika 81.3 (1994): 425-455. :DOI:`10.1093/biomet/81.3.425` Examples -------- .. testsetup:: >>> import pytest; _ = pytest.importorskip('pywt') >>> from skimage import color, data >>> img = img_as_float(data.astronaut()) >>> img = color.rgb2gray(img) >>> rng = np.random.default_rng() >>> img += 0.1 * rng.standard_normal(img.shape) >>> img = np.clip(img, 0, 1) >>> denoised_img = denoise_wavelet(img, sigma=0.1, rescale_sigma=True) N)rrzInvalid method: zE. The currently supported methods are "BayesShrink" and "VisuShrink".rz-convert2ycbcr requires channel_axis to be setr2.r)rrrrDrrrR)rrrrDr)rRr )rr rJ)r7rrrr rgb2ycbcrrrTr;r9denoise_wavelet ycbcr2rgbr empty_liker8rclip)rArrrDr convert2ycbcrrrr0r clip_outputrJrt_min_maxrchannel sigma_channelr^ clip_ranges rrrQs~ t+L 222 ;v ; ; ;   +"c)KJ\JHIII6 ulMLE51 ' /%((C 80771XX $ $ a[__..CF 0A0Ad#d{ 1$$c1f+,<' %a  ,!\1M-#!'#1"/CF "#q&kL8CF CF t# /#&&CC-&&C5;r?++  0#q&M#!(#1 CF  ! )    1 % aWWV gc0J000C00 Jrc ddl}n#t$rtdwxYw|k|jz}tjt j| j|} fdt|D}|rtj |}|Sjddkr djdd }t|| d }|d jz}t|d S)a Robust wavelet-based estimator of the (Gaussian) noise standard deviation. Parameters ---------- image : ndarray Image for which to estimate the noise standard deviation. average_sigmas : bool, optional If true, average the channel estimates of `sigma`. Otherwise return a list of sigmas corresponding to each channel. channel_axis : int or None, optional If ``None``, the image is assumed to be grayscale (single-channel). Otherwise, this parameter indicates which axis of the array corresponds to channels. .. versionadded:: 0.19 ``channel_axis`` was added in 0.19. Returns ------- sigma : float or list Estimated noise standard deviation(s). If `multichannel` is True and `average_sigmas` is False, a separate noise estimate for each channel is returned. Otherwise, the average of the individual channel estimates is returned. Notes ----- This function assumes the noise follows a Gaussian distribution. The estimation algorithm is based on the median absolute deviation of the wavelet detail coefficients as described in section 4.2 of [1]_. References ---------- .. [1] D. L. Donoho and I. M. Johnstone. "Ideal spatial adaptation by wavelet shrinkage." Biometrika 81.3 (1994): 425-455. :DOI:`10.1093/biomet/81.3.425` Examples -------- .. testsetup:: >>> import pytest; _ = pytest.importorskip('pywt') >>> import skimage.data >>> from skimage import img_as_float >>> img = img_as_float(skimage.data.camera()) >>> sigma = 0.1 >>> rng = np.random.default_rng() >>> img = img + sigma * rng.standard_normal(img.shape) >>> sigma_hat = estimate_sigma(img, channel_axis=None) rNrrecPg|]"}t|d#S)Nr/)estimate_sigma)rr^rrAs rrz"estimate_sigma..Ys?   ABN5Q=t < < <   rrRr3zimage is size z~ on the last axis, but channel_axis is None. 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