mirror of
https://github.com/wassname/scikit-image.git
synced 2026-06-29 01:11:56 +08:00
Johannes Schönberger
348 lines
11 KiB
Python
348 lines
11 KiB
Python
# coding: utf-8
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import numpy as np
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from skimage import img_as_float
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from skimage.restoration._denoise_cy import _denoise_bilateral, \
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_denoise_tv_bregman
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def denoise_bilateral(image, win_size=5, sigma_range=None, sigma_spatial=1,
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bins=10000, mode='constant', cval=0):
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"""Denoise image using bilateral filter.
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This is an edge-preserving and noise reducing denoising filter. It averages
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pixels based on their spatial closeness and radiometric similarity.
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Spatial closeness is measured by the gaussian function of the euclidian
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distance between two pixels and a certain standard deviation
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(`sigma_spatial`).
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Radiometric similarity is measured by the gaussian function of the euclidian
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distance between two color values and a certain standard deviation
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(`sigma_range`).
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Parameters
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----------
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image : ndarray
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Input image.
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win_size : int
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Window size for filtering.
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sigma_range : float
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Standard deviation for grayvalue/color distance (radiometric
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similarity). A larger value results in averaging of pixels with larger
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radiometric differences. Note, that the image will be converted using
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the `img_as_float` function and thus the standard deviation is in
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respect to the range `[0, 1]`.
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sigma_spatial : float
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Standard deviation for range distance. A larger value results in
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averaging of pixels with larger spatial differences.
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bins : int
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Number of discrete values for gaussian weights of color filtering.
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A larger value results in improved accuracy.
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mode : string
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How to handle values outside the image borders. See
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`scipy.ndimage.map_coordinates` for detail.
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cval : string
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Used in conjunction with mode 'constant', the value outside
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the image boundaries.
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Returns
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-------
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denoised : ndarray
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Denoised image.
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References
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----------
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.. [1] http://users.soe.ucsc.edu/~manduchi/Papers/ICCV98.pdf
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"""
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return _denoise_bilateral(image, win_size, sigma_range, sigma_spatial,
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bins, mode, cval)
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def denoise_tv_bregman(image, weight, max_iter=100, eps=1e-3, isotropic=True):
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"""Perform total-variation denoising using split-Bregman optimization.
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Total-variation denoising (also know as total-variation regularization)
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tries to find an image with less total-variation under the constraint
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of being similar to the input image, which is controlled by the
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regularization parameter.
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Parameters
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----------
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image : ndarray
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Input data to be denoised (converted using img_as_float`).
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weight : float, optional
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Denoising weight. The smaller the `weight`, the more denoising (at
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the expense of less similarity to the `input`). The regularization
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parameter `lambda` is chosen as `2 * weight`.
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eps : float, optional
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Relative difference of the value of the cost function that determines
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the stop criterion. The algorithm stops when::
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SUM((u(n) - u(n-1))**2) < eps
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max_iter : int, optional
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Maximal number of iterations used for the optimization.
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isotropic : boolean, optional
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Switch between isotropic and anisotropic TV denoising.
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Returns
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-------
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u : ndarray
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Denoised image.
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References
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----------
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.. [1] http://en.wikipedia.org/wiki/Total_variation_denoising
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.. [2] Tom Goldstein and Stanley Osher, "The Split Bregman Method For L1
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Regularized Problems",
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ftp://ftp.math.ucla.edu/pub/camreport/cam08-29.pdf
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.. [3] Pascal Getreuer, "Rudin–Osher–Fatemi Total Variation Denoising
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using Split Bregman" in Image Processing On Line on 2012–05–19,
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http://www.ipol.im/pub/art/2012/g-tvd/article_lr.pdf
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.. [4] http://www.math.ucsb.edu/~cgarcia/UGProjects/BregmanAlgorithms_JacquelineBush.pdf
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"""
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return _denoise_tv_bregman(image, weight, max_iter, eps, isotropic)
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def _denoise_tv_chambolle_3d(im, weight=100, eps=2.e-4, n_iter_max=200):
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"""Perform total-variation denoising on 3D images.
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Parameters
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----------
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im : ndarray
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3-D input data to be denoised.
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weight : float, optional
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Denoising weight. The greater `weight`, the more denoising (at
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the expense of fidelity to `input`).
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eps : float, optional
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Relative difference of the value of the cost function that determines
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the stop criterion. The algorithm stops when:
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(E_(n-1) - E_n) < eps * E_0
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n_iter_max : int, optional
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Maximal number of iterations used for the optimization.
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Returns
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-------
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out : ndarray
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Denoised array of floats.
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Notes
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-----
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Rudin, Osher and Fatemi algorithm.
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"""
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px = np.zeros_like(im)
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py = np.zeros_like(im)
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pz = np.zeros_like(im)
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gx = np.zeros_like(im)
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gy = np.zeros_like(im)
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gz = np.zeros_like(im)
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d = np.zeros_like(im)
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i = 0
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while i < n_iter_max:
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d = - px - py - pz
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d[1:] += px[:-1]
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d[:, 1:] += py[:, :-1]
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d[:, :, 1:] += pz[:, :, :-1]
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out = im + d
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E = (d**2).sum()
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gx[:-1] = np.diff(out, axis=0)
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gy[:, :-1] = np.diff(out, axis=1)
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gz[:, :, :-1] = np.diff(out, axis=2)
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norm = np.sqrt(gx**2 + gy**2 + gz**2)
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E += weight * norm.sum()
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norm *= 0.5 / weight
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norm += 1.
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px -= 1. / 6. * gx
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px /= norm
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py -= 1. / 6. * gy
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py /= norm
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pz -= 1 / 6. * gz
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pz /= norm
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E /= float(im.size)
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if i == 0:
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E_init = E
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E_previous = E
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else:
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if np.abs(E_previous - E) < eps * E_init:
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break
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else:
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E_previous = E
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i += 1
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return out
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def _denoise_tv_chambolle_2d(im, weight=50, eps=2.e-4, n_iter_max=200):
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"""Perform total-variation denoising on 2D images.
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Parameters
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----------
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im : ndarray
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Input data to be denoised.
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weight : float, optional
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Denoising weight. The greater `weight`, the more denoising (at
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the expense of fidelity to `input`)
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eps : float, optional
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Relative difference of the value of the cost function that determines
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the stop criterion. The algorithm stops when:
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(E_(n-1) - E_n) < eps * E_0
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n_iter_max : int, optional
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Maximal number of iterations used for the optimization.
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Returns
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-------
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out : ndarray
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Denoised array of floats.
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Notes
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-----
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The principle of total variation denoising is explained in
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http://en.wikipedia.org/wiki/Total_variation_denoising.
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This code is an implementation of the algorithm of Rudin, Fatemi and Osher
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that was proposed by Chambolle in [1]_.
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References
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----------
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.. [1] A. Chambolle, An algorithm for total variation minimization and
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applications, Journal of Mathematical Imaging and Vision,
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Springer, 2004, 20, 89-97.
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"""
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px = np.zeros_like(im)
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py = np.zeros_like(im)
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gx = np.zeros_like(im)
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gy = np.zeros_like(im)
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d = np.zeros_like(im)
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i = 0
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while i < n_iter_max:
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d = -px - py
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d[1:] += px[:-1]
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d[:, 1:] += py[:, :-1]
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out = im + d
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E = (d**2).sum()
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gx[:-1] = np.diff(out, axis=0)
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gy[:, :-1] = np.diff(out, axis=1)
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norm = np.sqrt(gx**2 + gy**2)
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E += weight * norm.sum()
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norm *= 0.5 / weight
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norm += 1
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px -= 0.25 * gx
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px /= norm
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py -= 0.25 * gy
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py /= norm
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E /= float(im.size)
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if i == 0:
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E_init = E
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E_previous = E
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else:
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if np.abs(E_previous - E) < eps * E_init:
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break
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else:
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E_previous = E
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i += 1
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return out
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def denoise_tv_chambolle(im, weight=50, eps=2.e-4, n_iter_max=200,
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multichannel=False):
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"""Perform total-variation denoising on 2D and 3D images.
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Parameters
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----------
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im : ndarray (2d or 3d) of ints, uints or floats
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Input data to be denoised. `im` can be of any numeric type,
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but it is cast into an ndarray of floats for the computation
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of the denoised image.
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weight : float, optional
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Denoising weight. The greater `weight`, the more denoising (at
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the expense of fidelity to `input`).
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eps : float, optional
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Relative difference of the value of the cost function that
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determines the stop criterion. The algorithm stops when:
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(E_(n-1) - E_n) < eps * E_0
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n_iter_max : int, optional
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Maximal number of iterations used for the optimization.
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multichannel : bool, optional
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Apply total-variation denoising separately for each channel. This
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option should be true for color images, otherwise the denoising is
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also applied in the 3rd dimension.
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Returns
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-------
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out : ndarray
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Denoised image.
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Notes
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-----
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Make sure to set the multichannel parameter appropriately for color images.
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The principle of total variation denoising is explained in
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http://en.wikipedia.org/wiki/Total_variation_denoising
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The principle of total variation denoising is to minimize the
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total variation of the image, which can be roughly described as
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the integral of the norm of the image gradient. Total variation
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denoising tends to produce "cartoon-like" images, that is,
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piecewise-constant images.
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This code is an implementation of the algorithm of Rudin, Fatemi and Osher
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that was proposed by Chambolle in [1]_.
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References
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----------
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.. [1] A. Chambolle, An algorithm for total variation minimization and
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applications, Journal of Mathematical Imaging and Vision,
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Springer, 2004, 20, 89-97.
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Examples
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--------
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2D example on Lena image:
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>>> from skimage import color, data
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>>> lena = color.rgb2gray(data.lena())[:50, :50]
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>>> lena += 0.5 * lena.std() * np.random.randn(*lena.shape)
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>>> denoised_lena = denoise_tv_chambolle(lena, weight=60)
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3D example on synthetic data:
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>>> x, y, z = np.ogrid[0:20, 0:20, 0:20]
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>>> mask = (x - 22)**2 + (y - 20)**2 + (z - 17)**2 < 8**2
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>>> mask = mask.astype(np.float)
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>>> mask += 0.2*np.random.randn(*mask.shape)
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>>> res = denoise_tv_chambolle(mask, weight=100)
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"""
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im_type = im.dtype
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if not im_type.kind == 'f':
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im = img_as_float(im)
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if im.ndim == 2:
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out = _denoise_tv_chambolle_2d(im, weight, eps, n_iter_max)
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elif im.ndim == 3:
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if multichannel:
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out = np.zeros_like(im)
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for c in range(im.shape[2]):
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out[..., c] = _denoise_tv_chambolle_2d(im[..., c], weight, eps,
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n_iter_max)
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else:
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out = _denoise_tv_chambolle_3d(im, weight, eps, n_iter_max)
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else:
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raise ValueError('only 2-d and 3-d images may be denoised with this '
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'function')
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return out
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