mirror of
https://github.com/wassname/scikit-image.git
synced 2026-06-29 03:04:42 +08:00
Johannes Schönberger
246 lines
7.1 KiB
Python
246 lines
7.1 KiB
Python
import numpy as np
|
|
from skimage import img_as_float
|
|
from skimage._shared.utils import deprecated
|
|
|
|
|
|
def _denoise_tv_3d(im, weight=100, eps=2.e-4, n_iter_max=200):
|
|
"""Perform total-variation denoising on 3-D arrays.
|
|
|
|
Parameters
|
|
----------
|
|
im: ndarray
|
|
3-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
|
|
|
|
n_iter_max: int, optional
|
|
Maximal number of iterations used for the optimization.
|
|
|
|
Returns
|
|
-------
|
|
out: ndarray
|
|
Denoised array of floats.
|
|
|
|
Notes
|
|
-----
|
|
Rudin, Osher and Fatemi algorithm.
|
|
|
|
Examples
|
|
---------
|
|
First build synthetic noisy data
|
|
>>> x, y, z = np.ogrid[0:40, 0:40, 0:40]
|
|
>>> 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_3d(mask, weight=100)
|
|
"""
|
|
px = np.zeros_like(im)
|
|
py = np.zeros_like(im)
|
|
pz = np.zeros_like(im)
|
|
gx = np.zeros_like(im)
|
|
gy = np.zeros_like(im)
|
|
gz = np.zeros_like(im)
|
|
d = np.zeros_like(im)
|
|
i = 0
|
|
while i < n_iter_max:
|
|
d = - px - py - pz
|
|
d[1:] += px[:-1]
|
|
d[:, 1:] += py[:, :-1]
|
|
d[:, :, 1:] += pz[:, :, :-1]
|
|
|
|
out = im + d
|
|
E = (d**2).sum()
|
|
|
|
gx[:-1] = np.diff(out, axis=0)
|
|
gy[:, :-1] = np.diff(out, axis=1)
|
|
gz[:, :, :-1] = np.diff(out, axis=2)
|
|
norm = np.sqrt(gx**2 + gy**2 + gz**2)
|
|
E += weight * norm.sum()
|
|
norm *= 0.5 / weight
|
|
norm += 1.
|
|
px -= 1. / 6. * gx
|
|
px /= norm
|
|
py -= 1. / 6. * gy
|
|
py /= norm
|
|
pz -= 1 / 6. * gz
|
|
pz /= norm
|
|
E /= float(im.size)
|
|
if i == 0:
|
|
E_init = E
|
|
E_previous = E
|
|
else:
|
|
if np.abs(E_previous - E) < eps * E_init:
|
|
break
|
|
else:
|
|
E_previous = E
|
|
i += 1
|
|
return out
|
|
|
|
|
|
def _denoise_tv_2d(im, weight=50, eps=2.e-4, n_iter_max=200):
|
|
"""Perform total-variation denoising.
|
|
|
|
Parameters
|
|
----------
|
|
im: ndarray
|
|
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
|
|
|
|
n_iter_max: int, optional
|
|
Maximal number of iterations used for the optimization.
|
|
|
|
Returns
|
|
-------
|
|
out: ndarray
|
|
Denoised array of floats.
|
|
|
|
Notes
|
|
-----
|
|
The principle of total variation denoising is explained in
|
|
http://en.wikipedia.org/wiki/Total_variation_denoising.
|
|
|
|
This code is an implementation of the algorithm of Rudin, Fatemi and Osher
|
|
that was proposed by Chambolle in [1]_.
|
|
|
|
References
|
|
----------
|
|
.. [1] A. Chambolle, An algorithm for total variation minimization and
|
|
applications, Journal of Mathematical Imaging and Vision,
|
|
Springer, 2004, 20, 89-97.
|
|
|
|
Examples
|
|
---------
|
|
>>> import scipy
|
|
>>> lena = scipy.lena()
|
|
>>> import scipy
|
|
>>> lena = scipy.lena().astype(np.float)
|
|
>>> lena += 0.5 * lena.std()*np.random.randn(*lena.shape)
|
|
>>> denoised_lena = denoise_tv(lena, weight=60.0)
|
|
"""
|
|
px = np.zeros_like(im)
|
|
py = np.zeros_like(im)
|
|
gx = np.zeros_like(im)
|
|
gy = np.zeros_like(im)
|
|
d = np.zeros_like(im)
|
|
i = 0
|
|
while i < n_iter_max:
|
|
d = -px - py
|
|
d[1:] += px[:-1]
|
|
d[:, 1:] += py[:, :-1]
|
|
|
|
out = im + d
|
|
E = (d**2).sum()
|
|
gx[:-1] = np.diff(out, axis=0)
|
|
gy[:, :-1] = np.diff(out, axis=1)
|
|
norm = np.sqrt(gx**2 + gy**2)
|
|
E += weight * norm.sum()
|
|
norm *= 0.5 / weight
|
|
norm += 1
|
|
px -= 0.25 * gx
|
|
px /= norm
|
|
py -= 0.25 * gy
|
|
py /= norm
|
|
E /= float(im.size)
|
|
if i == 0:
|
|
E_init = E
|
|
E_previous = E
|
|
else:
|
|
if np.abs(E_previous - E) < eps * E_init:
|
|
break
|
|
else:
|
|
E_previous = E
|
|
i += 1
|
|
return out
|
|
|
|
|
|
def denoise_tv(im, weight=50, eps=2.e-4, n_iter_max=200):
|
|
"""Perform total-variation denoising on 2-d and 3-d images.
|
|
|
|
Parameters
|
|
----------
|
|
im: ndarray (2d or 3d) 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 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
|
|
|
|
n_iter_max: int, optional
|
|
Maximal number of iterations used for the optimization.
|
|
|
|
Returns
|
|
-------
|
|
out: ndarray
|
|
Denoised array of floats.
|
|
|
|
Notes
|
|
-----
|
|
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 [1]_.
|
|
|
|
References
|
|
----------
|
|
.. [1] A. Chambolle, An algorithm for total variation minimization and
|
|
applications, Journal of Mathematical Imaging and Vision,
|
|
Springer, 2004, 20, 89-97.
|
|
|
|
Examples
|
|
---------
|
|
>>> import scipy
|
|
>>> # 2D example using lena
|
|
>>> lena = scipy.lena()
|
|
>>> import scipy
|
|
>>> lena = scipy.lena().astype(np.float)
|
|
>>> lena += 0.5 * lena.std()*np.random.randn(*lena.shape)
|
|
>>> denoised_lena = denoise_tv(lena, weight=60)
|
|
>>> # 3D example on synthetic data
|
|
>>> x, y, z = np.ogrid[0:40, 0:40, 0:40]
|
|
>>> 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_3d(mask, weight=100)
|
|
"""
|
|
im_type = im.dtype
|
|
if not im_type.kind == 'f':
|
|
im = img_as_float(im)
|
|
|
|
if im.ndim == 2:
|
|
out = _denoise_tv_2d(im, weight, eps, n_iter_max)
|
|
elif im.ndim == 3:
|
|
out = _denoise_tv_3d(im, weight, eps, n_iter_max)
|
|
else:
|
|
raise ValueError('only 2-d and 3-d images may be denoised with this '
|
|
'function')
|
|
return out
|
|
|
|
|
|
tv_denoise = deprecated('skimage.filter.denoise_tv')(denoise_tv)
|