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ENH: n-dimensional refactor of TV denoising.
_denoise_tv_chambolle_2d and _denoise_tv_chambolle_3d are replaced by _denoise_tv_chambolle_nd The restriction to 2D and 3D in denoies_tv_chambolle was removed.
This commit is contained in:
Gregory R. Lee
committed by
Gregory R. Lee
Gregory R. Lee
parent
b9c951335a
commit
2d326a464e
+36
-113
@@ -116,7 +116,7 @@ def denoise_tv_bregman(image, weight, max_iter=100, eps=1e-3, isotropic=True):
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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=0.2, eps=2.e-4, n_iter_max=200):
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def _denoise_tv_chambolle_nd(im, weight=0.2, 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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@@ -146,112 +146,41 @@ def _denoise_tv_chambolle_3d(im, weight=0.2, eps=2.e-4, n_iter_max=200):
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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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ndim = im.ndim
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p = np.zeros(im.shape + (im.ndim, ), dtype=im.dtype)
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g = np.zeros_like(p)
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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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if i > 0:
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d = -p.sum(-1)
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slices_d = [slice(None), ] * ndim
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slices_p = [slice(None), ] * (ndim + 1)
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for ax in range(ndim):
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slices_d[ax] = slice(1, None)
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slices_p[ax] = slice(0, -1)
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slices_p[-1] = ax
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d[slices_d] += p[slices_p]
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slices_d[ax] = slice(None)
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slices_p[ax] = slice(None)
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out = im + d
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else:
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out = im
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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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slices_g = [slice(None), ] * (ndim + 1)
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for ax in range(ndim):
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slices_g[ax] = slice(0, -1)
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slices_g[-1] = ax
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g[slices_g] = np.diff(out, axis=ax)
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slices_g[ax] = slice(None)
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norm = np.sqrt((g*g).sum(-1, keepdims=True))
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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=0.2, 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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p -= 1. / (2.*ndim) * g
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p /= 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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@@ -271,7 +200,7 @@ def denoise_tv_chambolle(im, weight=0.2, eps=2.e-4, n_iter_max=200,
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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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im : ndarray 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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@@ -289,7 +218,7 @@ def denoise_tv_chambolle(im, weight=0.2, eps=2.e-4, n_iter_max=200,
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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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also applied in the channels dimension.
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Returns
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-------
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@@ -341,17 +270,11 @@ def denoise_tv_chambolle(im, weight=0.2, eps=2.e-4, n_iter_max=200,
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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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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_nd(im[..., c], weight, eps,
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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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out = _denoise_tv_chambolle_nd(im, weight, eps, n_iter_max)
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return out
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