import functools
import numpy as np
from scipy.ndimage import uniform_filter
from .._shared import utils
from .._shared.filters import gaussian
from .._shared.utils import _supported_float_type, check_shape_equality, warn
from ..util.arraycrop import crop
from ..util.dtype import dtype_range
__all__ = ['structural_similarity']
[文档]
def structural_similarity(
im1,
im2,
*,
win_size=None,
gradient=False,
data_range=None,
channel_axis=None,
gaussian_weights=False,
full=False,
**kwargs,
):
"""
Compute the mean structural similarity index between two images.
Please pay attention to the `data_range` parameter with floating-point 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 (difference between maximum and
minimum possible values). By default, this is estimated from the image
data type. This estimate may be wrong for floating-point image data.
Therefore it is recommended to always pass this scalar value explicitly
(see note below).
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.
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
-----
If `data_range` is not specified, the range is automatically guessed
based on the image data type. However for floating-point image data, this
estimate yields a result double the value of the desired range, as the
`dtype_range` in `skimage.util.dtype.py` has defined intervals from -1 to
+1. This yields an estimate of 2, instead of 1, which is most often
required when working with image data (as negative light intensities are
nonsensical). In case of working with YCbCr-like color data, note that
these ranges are different per channel (Cb and Cr have double the range
of Y), so one cannot calculate a channel-averaged SSIM with a single call
to this function, as identical ranges are assumed for each channel.
To match the implementation of Wang et al. [1]_, set `gaussian_weights`
to True, `sigma` to 1.5, `use_sample_covariance` to False, and
specify the `data_range` argument.
.. 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)
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. '
'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 np.issubdtype(im1.dtype, np.floating) or np.issubdtype(
im2.dtype, np.floating
):
raise ValueError(
'Since image dtype is floating point, you must specify '
'the data_range parameter. Please read the documentation '
'carefully (including the note). It is recommended that '
'you always specify the data_range anyway.'
)
if im1.dtype != im2.dtype:
warn(
"Inputs have mismatched dtypes. Setting data_range based on im1.dtype.",
stacklevel=2,
)
dmin, dmax = dtype_range[im1.dtype.type]
data_range = dmax - dmin
if np.issubdtype(im1.dtype, np.integer) and (im1.dtype != np.uint8):
warn(
"Setting data_range based on im1.dtype. "
+ f"data_range = {data_range:.0f}. "
+ "Please specify data_range explicitly to avoid mistakes.",
stacklevel=2,
)
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
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. Use float64 for accuracy.
mssim = crop(S, pad).mean(dtype=np.float64)
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
