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