233 lines
7.8 KiB
Python
233 lines
7.8 KiB
Python
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from warnings import warn
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import numpy as np
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from scipy.ndimage import uniform_filter, gaussian_filter
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from ..util.dtype import dtype_range
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from ..util.arraycrop import crop
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from .._shared.utils import warn, check_shape_equality
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__all__ = ['structural_similarity']
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def structural_similarity(im1, im2,
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*,
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win_size=None, gradient=False, data_range=None,
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multichannel=False, gaussian_weights=False,
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full=False, **kwargs):
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"""
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Compute the mean structural similarity index between two images.
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Parameters
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----------
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im1, im2 : ndarray
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Images. Any dimensionality with same shape.
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win_size : int or None, optional
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The side-length of the sliding window used in comparison. Must be an
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odd value. If `gaussian_weights` is True, this is ignored and the
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window size will depend on `sigma`.
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gradient : bool, optional
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If True, also return the gradient with respect to im2.
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data_range : float, optional
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The data range of the input image (distance between minimum and
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maximum possible values). By default, this is estimated from the image
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data-type.
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multichannel : bool, optional
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If True, treat the last dimension of the array as channels. Similarity
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calculations are done independently for each channel then averaged.
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gaussian_weights : bool, optional
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If True, each patch has its mean and variance spatially weighted by a
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normalized Gaussian kernel of width sigma=1.5.
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full : bool, optional
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If True, also return the full structural similarity image.
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Other Parameters
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----------------
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use_sample_covariance : bool
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If True, normalize covariances by N-1 rather than, N where N is the
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number of pixels within the sliding window.
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K1 : float
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Algorithm parameter, K1 (small constant, see [1]_).
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K2 : float
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Algorithm parameter, K2 (small constant, see [1]_).
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sigma : float
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Standard deviation for the Gaussian when `gaussian_weights` is True.
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Returns
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-------
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mssim : float
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The mean structural similarity index over the image.
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grad : ndarray
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The gradient of the structural similarity between im1 and im2 [2]_.
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This is only returned if `gradient` is set to True.
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S : ndarray
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The full SSIM image. This is only returned if `full` is set to True.
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Notes
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-----
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To match the implementation of Wang et. al. [1]_, set `gaussian_weights`
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to True, `sigma` to 1.5, and `use_sample_covariance` to False.
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.. versionchanged:: 0.16
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This function was renamed from ``skimage.measure.compare_ssim`` to
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``skimage.metrics.structural_similarity``.
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References
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----------
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.. [1] Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P.
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(2004). Image quality assessment: From error visibility to
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structural similarity. IEEE Transactions on Image Processing,
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13, 600-612.
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https://ece.uwaterloo.ca/~z70wang/publications/ssim.pdf,
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:DOI:`10.1109/TIP.2003.819861`
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.. [2] Avanaki, A. N. (2009). Exact global histogram specification
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optimized for structural similarity. Optical Review, 16, 613-621.
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:arxiv:`0901.0065`
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:DOI:`10.1007/s10043-009-0119-z`
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"""
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check_shape_equality(im1, im2)
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if multichannel:
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# loop over channels
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args = dict(win_size=win_size,
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gradient=gradient,
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data_range=data_range,
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multichannel=False,
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gaussian_weights=gaussian_weights,
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full=full)
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args.update(kwargs)
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nch = im1.shape[-1]
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mssim = np.empty(nch)
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if gradient:
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G = np.empty(im1.shape)
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if full:
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S = np.empty(im1.shape)
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for ch in range(nch):
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ch_result = structural_similarity(im1[..., ch],
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im2[..., ch], **args)
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if gradient and full:
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mssim[..., ch], G[..., ch], S[..., ch] = ch_result
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elif gradient:
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mssim[..., ch], G[..., ch] = ch_result
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elif full:
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mssim[..., ch], S[..., ch] = ch_result
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else:
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mssim[..., ch] = ch_result
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mssim = mssim.mean()
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if gradient and full:
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return mssim, G, S
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elif gradient:
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return mssim, G
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elif full:
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return mssim, S
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else:
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return mssim
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K1 = kwargs.pop('K1', 0.01)
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K2 = kwargs.pop('K2', 0.03)
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sigma = kwargs.pop('sigma', 1.5)
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if K1 < 0:
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raise ValueError("K1 must be positive")
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if K2 < 0:
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raise ValueError("K2 must be positive")
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if sigma < 0:
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raise ValueError("sigma must be positive")
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use_sample_covariance = kwargs.pop('use_sample_covariance', True)
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if gaussian_weights:
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# Set to give an 11-tap filter with the default sigma of 1.5 to match
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# Wang et. al. 2004.
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truncate = 3.5
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if win_size is None:
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if gaussian_weights:
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# set win_size used by crop to match the filter size
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r = int(truncate * sigma + 0.5) # radius as in ndimage
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win_size = 2 * r + 1
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else:
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win_size = 7 # backwards compatibility
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if np.any((np.asarray(im1.shape) - win_size) < 0):
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raise ValueError(
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"win_size exceeds image extent. If the input is a multichannel "
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"(color) image, set multichannel=True.")
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if not (win_size % 2 == 1):
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raise ValueError('Window size must be odd.')
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if data_range is None:
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if im1.dtype != im2.dtype:
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warn("Inputs have mismatched dtype. Setting data_range based on "
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"im1.dtype.", stacklevel=2)
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dmin, dmax = dtype_range[im1.dtype.type]
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data_range = dmax - dmin
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ndim = im1.ndim
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if gaussian_weights:
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filter_func = gaussian_filter
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filter_args = {'sigma': sigma, 'truncate': truncate}
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else:
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filter_func = uniform_filter
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filter_args = {'size': win_size}
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# ndimage filters need floating point data
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im1 = im1.astype(np.float64)
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im2 = im2.astype(np.float64)
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NP = win_size ** ndim
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# filter has already normalized by NP
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if use_sample_covariance:
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cov_norm = NP / (NP - 1) # sample covariance
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else:
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cov_norm = 1.0 # population covariance to match Wang et. al. 2004
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# compute (weighted) means
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ux = filter_func(im1, **filter_args)
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uy = filter_func(im2, **filter_args)
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# compute (weighted) variances and covariances
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uxx = filter_func(im1 * im1, **filter_args)
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uyy = filter_func(im2 * im2, **filter_args)
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uxy = filter_func(im1 * im2, **filter_args)
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vx = cov_norm * (uxx - ux * ux)
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vy = cov_norm * (uyy - uy * uy)
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vxy = cov_norm * (uxy - ux * uy)
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R = data_range
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C1 = (K1 * R) ** 2
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C2 = (K2 * R) ** 2
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A1, A2, B1, B2 = ((2 * ux * uy + C1,
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2 * vxy + C2,
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ux ** 2 + uy ** 2 + C1,
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vx + vy + C2))
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D = B1 * B2
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S = (A1 * A2) / D
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# to avoid edge effects will ignore filter radius strip around edges
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pad = (win_size - 1) // 2
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# compute (weighted) mean of ssim
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mssim = crop(S, pad).mean()
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if gradient:
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# The following is Eqs. 7-8 of Avanaki 2009.
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grad = filter_func(A1 / D, **filter_args) * im1
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grad += filter_func(-S / B2, **filter_args) * im2
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grad += filter_func((ux * (A2 - A1) - uy * (B2 - B1) * S) / D,
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**filter_args)
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grad *= (2 / im1.size)
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if full:
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return mssim, grad, S
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else:
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return mssim, grad
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else:
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if full:
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return mssim, S
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else:
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return mssim
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