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structural_similarity.py
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structural_similarity.py
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import functools
import numpy as np
from scipy.ndimage import uniform_filter
from skimage._shared import utils
from skimage._shared.filters import gaussian
from skimage._shared.utils import (
_supported_float_type, check_shape_equality, warn)
from skimage.util.arraycrop import crop
from skimage.util.dtype import dtype_range
__all__ = ['structural_similarity']
@utils.deprecate_multichannel_kwarg()
def structural_similarity(im1, im2,
*,
win_size=None, gradient=False, data_range=None,
channel_axis=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.
channel_axis : int or None, optional
If None, the image is assumed to be a grayscale (single channel) image.
Otherwise, this parameter indicates which axis of the array corresponds
to channels.
.. versionadded:: 0.19
``channel_axis`` was added in 0.19.
multichannel : bool, optional
If True, treat the last dimension of the array as channels. Similarity
calculations are done independently for each channel then averaged.
This argument is deprecated: specify `channel_axis` instead.
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)
float_type = _supported_float_type(im1.dtype)
if channel_axis is not None:
# loop over channels
args = dict(win_size=win_size,
gradient=gradient,
data_range=data_range,
channel_axis=None,
gaussian_weights=gaussian_weights,
full=full)
args.update(kwargs)
nch = im1.shape[channel_axis]
mssim = np.empty(nch, dtype=float_type)
if gradient:
G = np.empty(im1.shape, dtype=float_type)
if full:
S = np.empty(im1.shape, dtype=float_type)
channel_axis = channel_axis % im1.ndim
_at = functools.partial(utils.slice_at_axis, axis=channel_axis)
for ch in range(nch):
ch_result = structural_similarity(im1[_at(ch)],
im2[_at(ch)], **args)
if gradient and full:
mssim[ch], G[_at(ch)], S[_at(ch)] = ch_result
elif gradient:
mssim[ch], G[_at(ch)] = ch_result
elif full:
mssim[ch], S[_at(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)
K3 = kwargs.pop('K3', K2 / np.sqrt(2))
alpha = kwargs.pop('alpha', 1)
beta = kwargs.pop('beta', 1)
gamma = kwargs.pop('gamma', 1)
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 K3 < 0:
raise ValueError("K3 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. '
'Either ensure that your images are '
'at least 7x7; or pass win_size explicitly '
'in the function call, with an odd value '
'less than or equal to the smaller side of your '
'images. If your images are multichannel '
'(with color channels), set channel_axis to '
'the axis number corresponding to the channels.')
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_args = {'sigma': sigma, 'truncate': truncate, 'mode': 'reflect'}
else:
filter_func = uniform_filter
filter_args = {'size': win_size}
# ndimage filters need floating point data
im1 = im1.astype(float_type, copy=False)
im2 = im2.astype(float_type, copy=False)
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
C3 = (K3 * R) ** 2
sxsy = np.sqrt(np.clip(vx * vy, 0, None))
A1, A2, A3, B1, B2, B3 = ((
2 * ux * uy + C1,
2 * sxsy + C2,
vxy + C3,
ux ** 2 + uy ** 2 + C1,
vx + vy + C2,
sxsy + C3,
))
S = (A1/B1)**alpha * (A2/B2)**beta * (A3/B3)**gamma
# to avoid edge effects will ignore filter radius strip around edges
pad = (win_size - 1) // 2
# compute (weighted) mean of ssim. Use float64 for accuracy.
mssim = crop(S, pad).mean(dtype=np.float64)
if full:
return mssim, S
else:
return mssim