"""Module for calculating the Gradient Similarity Metric (GSM) metric.
Examples
--------
.. doctest-skip::
>>> import numpy as np
>>> from viqa import GSM
>>> img_r = np.random.rand(256, 256)
>>> img_m = np.random.rand(256, 256)
>>> gsm = GSM()
>>> gsm.score(img_r, img_m, data_range=1)
"""
# Authors
# -------
# Author: Lukas Behammer
# Research Center Wels
# University of Applied Sciences Upper Austria, 2023
# CT Research Group
#
# Modifications
# -------------
# Original code, 2024, Lukas Behammer
#
# License
# -------
# BSD-3-Clause License
from warnings import warn
import numpy as np
import scipy.ndimage as ndi
from tqdm.autonotebook import trange
from viqa._metrics import FullReferenceMetricsInterface
from viqa.kernels import *
from viqa.utils import _to_float
# Load the kernels as constants
KERNELS_3D = [
gsm_kernel_x(),
gsm_kernel_y(),
gsm_kernel_z(),
gsm_kernel_xy1(),
gsm_kernel_xy2(),
gsm_kernel_yz1(),
gsm_kernel_yz2(),
gsm_kernel_xz1(),
gsm_kernel_xz2(),
gsm_kernel_xyz1(),
gsm_kernel_xyz2(),
gsm_kernel_xyz3(),
gsm_kernel_xyz4(),
]
KERNELS_2D = [
gsm_kernel_2d_x(),
gsm_kernel_2d_y(),
gsm_kernel_2d_xy(),
gsm_kernel_2d_yx(),
]
[docs]
class GSM(FullReferenceMetricsInterface):
"""Calculate the gradient similarity (GSM) between two images.
Attributes
----------
score_val : float
GSM score value of the last calculation.
parameters : dict
Dictionary containing the parameters for GSM calculation.
Parameters
----------
data_range : {1, 255, 65535}, default=255
Data range of the returned data in data loading. Is used for image loading when
``normalize`` is True and for the GSM calculation. Passed to
:py:func:`viqa.utils.load_data` and
:py:func:`viqa.fr_metrics.gsm.gradient_similarity`.
normalize : bool, default=False
If True, the input images are normalized to the ``data_range`` argument.
**kwargs : optional
Additional parameters for data loading. The keyword arguments are passed to
:py:func:`.viqa.utils.load_data`.
Other Parameters
----------------
chromatic : bool, default False
If True, the input images are expected to be RGB images.
If False, the input images are converted to grayscale images if necessary.
Raises
------
ValueError
If ``data_range`` is not set.
Warnings
--------
This metric is not yet tested. The metric should be only used for experimental
purposes.
.. todo:: test
Notes
-----
GSM is a full reference IQA metric based on gradient similarity. It combines
luminosity information and contrast-structural information. For further details,
see [1]_. ``data_range`` for image loading is also used for the GSM calculation and
therefore must be set. The parameter is set through the constructor of the class and
is passed to :py:meth:`score`.
References
----------
.. [1] Liu, A., Lin, W., & Narwaria, M. (2012). Image quality assessment based on
gradient similarity. IEEE Transactions on Image Processing, 21(4), 1500–1512.
https://doi.org/10.1109/TIP.2011.2175935
"""
def __init__(self, data_range=255, normalize=False, **kwargs):
"""Construct method."""
if data_range is None:
raise ValueError("Parameter data_range must be set.")
super().__init__(data_range=data_range, normalize=normalize, **kwargs)
self._name = "GSM"
[docs]
def score(self, img_r, img_m, dim=None, im_slice=None, **kwargs):
"""Calculate the gradient similarity (GSM) between two images.
The metric can be calculated for 2D and 3D images. If the images are 3D, the
metric can be calculated for the full volume or for a given slice of the image
by setting ``dim`` to the desired dimension and ``im_slice`` to the desired
slice number.
Parameters
----------
img_r : np.ndarray or Tensor or str or os.PathLike
Reference image to calculate score against.
img_m : np.ndarray or Tensor or str or os.PathLike
Distorted image to calculate score of.
dim : {0, 1, 2}, optional
GSM for 3D images is calculated as mean over all slices of the given
dimension.
im_slice : int, optional
If given, GSM is calculated only for the given slice of the 3D image.
**kwargs : optional
Additional parameters for GSM calculation. The keyword arguments are passed
to :py:func:`.viqa.fr_metrics.gsm.gradient_similarity`.
Returns
-------
score_val : float
GSM score value.
Raises
------
ValueError
If invalid dimension given in ``dim``. \n
If images are neither 2D nor 3D. \n
If images are 3D, but dim is not given. \n
If ``im_slice`` is given, but not an integer.
Warns
-----
RuntimeWarning
If ``dim`` or ``im_slice`` is given for 2D images. \n
If ``im_slice`` is not given, but ``dim`` is given for 3D images, GSM is
calculated for the full volume.
Notes
-----
For 3D images if ``dim`` is given, but ``im_slice`` is not, the GSM is
calculated for the full volume of the 3D image. This is implemented as `mean` of
the GSM values of all slices of the given dimension. If ``dim`` is given and
``im_slice`` is given, the GSM is calculated for the given slice of the given
dimension (represents a 2D metric of the given slice). This implementation is
adapted for 3D images if ``experimental=True``. Therefore, 12 kernels are used
instead of the original 4. The gradient is calculated by
.. math::
\\max_{n=1,2,...,N} \\lbrace \\pmb{I} * \\mathcal{K}_{n} \\rbrace
\\text{ instead of } \\max_{n=1,2,...,N} \\lbrace \\operatorname{mean2}
(\\lvert \\pmb{X} \\cdot \\mathcal{K}_{n} \\rvert) \\rbrace
with :math:`\\pmb{I}` denoting the Image, :math:`\\mathcal{K}_{n}` denoting the
Kernel `n` and :math:`\\pmb{X}` denoting an image block.
"""
img_r, img_m = self.load_images(img_r, img_m)
if img_r.ndim == 3:
if (
dim is not None and type(im_slice) is int
): # if dim and im_slice are given
# Calculate GSM for given slice of given dimension
match dim:
case 0:
score_val = gradient_similarity(
img_r[im_slice, :, :],
img_m[im_slice, :, :],
data_range=self.parameters["data_range"],
**kwargs,
)
case 1:
score_val = gradient_similarity(
img_r[:, im_slice, :],
img_m[:, im_slice, :],
data_range=self.parameters["data_range"],
**kwargs,
)
case 2:
score_val = gradient_similarity(
img_r[:, :, im_slice],
img_m[:, :, im_slice],
data_range=self.parameters["data_range"],
**kwargs,
)
case _:
raise ValueError(
"Invalid dim value. Must be integer of 0, 1 or 2."
)
elif (
dim is not None and im_slice is None
): # if dim is given, but im_slice is not, calculate GSM for full volume
warn(
"im_slice is not given. Calculating GSM for full volume.",
RuntimeWarning,
)
score_val = gradient_similarity_3d(
img_r,
img_m,
data_range=self.parameters["data_range"],
dim=dim,
**kwargs,
)
else:
if type(im_slice) is not int or None:
raise ValueError("im_slice must be an integer.")
raise ValueError(
"If images are 3D, dim and im_slice (optional) must be given."
)
elif img_r.ndim == 2:
if dim or im_slice:
warn("dim and im_slice are ignored for 2D images.", RuntimeWarning)
# Calculate GSM for 2D images
score_val = gradient_similarity(
img_r, img_m, data_range=self.parameters["data_range"], **kwargs
)
else:
raise ValueError("Images must be 2D or 3D.")
self.score_val = score_val
return score_val
[docs]
def print_score(self, decimals=2):
"""Print the GSM score value of the last calculation.
Parameters
----------
decimals : int, default=2
Number of decimal places to print the score value.
Warns
-----
RuntimeWarning
If :py:attr:`score_val` is not available.
"""
if self.score_val is not None:
print("GSM: {}".format(np.round(self.score_val, decimals)))
else:
warn("No score value for GSM. Run score() first.", RuntimeWarning)
[docs]
def gradient_similarity_3d(img_r, img_m, dim=0, experimental=False, **kwargs):
"""Calculate the gradient similarity (GSM) between two 3D images.
Parameters
----------
img_r : np.ndarray
Reference image to calculate score against
img_m : np.ndarray
Distorted image to calculate score of
dim : {0, 1, 2}, default=2
Dimension on which the slices are iterated.
experimental : bool, default=False
If ``True``, calculate GSM for the full volume with experimental 3D kernels. If
``False``, calculate GSM for all slices of the given dimension and calculate
mean over all single slice values.
.. attention::
This is experimental and the resulting values are not validated.
**kwargs : optional
Additional parameters for GSM calculation. The keyword arguments are passed
to :py:func:`viqa.fr_metrics.gsm.gradient_similarity`.
Returns
-------
gsm_score : float
GSM score value.
Raises
------
ValueError
If the ``dim`` is not an integer of 0, 1 or 2.
Warnings
--------
This metric is not yet tested. The metric should be only used for experimental
purposes.
.. todo:: test
See Also
--------
viqa.fr_metrics.gsm.gradient_similarity : Calculate the gradient similarity between
two images.
References
----------
.. [1] Liu, A., Lin, W., & Narwaria, M. (2012). Image quality assessment based on
gradient similarity. IEEE Transactions on Image Processing, 21(4), 1500–1512.
https://doi.org/10.1109/TIP.2011.2175935
"""
if not experimental:
x, y, z = img_r.shape # get image dimensions
scores = []
# Calculate GSM for all slices of the given dimension
match dim:
case 0:
for slice_ in trange(x):
scores.append(
gradient_similarity(
img_r[slice_, :, :], img_m[slice_, :, :], **kwargs
)
)
case 1:
for slice_ in trange(y):
scores.append(
gradient_similarity(
img_r[:, slice_, :], img_m[:, slice_, :], **kwargs
)
)
case 2:
for slice_ in trange(z):
scores.append(
gradient_similarity(
img_r[:, :, slice_], img_m[:, :, slice_], **kwargs
)
)
case _:
raise ValueError("Invalid dim value. Must be integer of 0, 1 or 2.")
return np.mean(np.array(scores))
else:
return gradient_similarity(img_r, img_m, **kwargs)
[docs]
def gradient_similarity(img_r, img_m, data_range=255, c=200, p=0.1):
"""Calculate the gradient similarity between two images.
Parameters
----------
img_r : np.ndarray
Reference image to calculate score against
img_m : np.ndarray
Distorted image to calculate score of
data_range : {1, 255, 65535}
Data range of the input images
c : int, default=200
Constant as masking parameter. Typically, :math:`200 \\leq c \\leq 1000`. See
[1] for details.
p : float, default=0.1
Constant for weighting between luminance and structure similarity. Can be
:math:`0 \\leq p \\leq 1`. Higher `p` means more accentuation of luminance.
Should be :math:`p \\ll 0.5`. See [1]_ for details.
Returns
-------
gsm_score : float
GSM score value.
Raises
------
ValueError
If the images are neither 2D nor 3D.
Warnings
--------
This metric is not yet tested. The metric should be only used for experimental
purposes.
.. todo:: test
See Also
--------
viqa.fr_metrics.gsm.gradient_similarity_3d : Calculate the gradient similarity
between two 3D images.
References
----------
.. [1] Liu, A., Lin, W., & Narwaria, M. (2012). Image quality assessment based on
gradient similarity. IEEE Transactions on Image Processing, 21(4), 1500–1512.
https://doi.org/10.1109/TIP.2011.2175935
"""
gradients_r = []
gradients_m = []
if img_r.ndim == 3:
kernels = KERNELS_3D
elif img_r.ndim == 2:
kernels = KERNELS_2D
else:
raise ValueError("Images must be 2D or 3D.")
for kernel in kernels:
gradients_r.append(ndi.correlate(img_r, kernel))
gradients_m.append(ndi.correlate(img_m, kernel))
# key for sorting the gradients by their mean of absolute values
def _mean_of_abs(input_array):
return np.mean(np.abs(input_array))
img_r_gradient = sorted(gradients_r, key=_mean_of_abs, reverse=True)[0]
img_m_gradient = sorted(gradients_m, key=_mean_of_abs, reverse=True)[0]
img_r_gradient = _to_float(img_r_gradient)
img_m_gradient = _to_float(img_m_gradient)
k = c / max(np.max(img_r_gradient), np.max(img_m_gradient))
r = np.abs(img_r_gradient - img_m_gradient) / max(
img_r_gradient, img_m_gradient, key=_mean_of_abs
)
con_struc_sim = ((2 * (1 - r)) + k) / (1 + (1 - r) ** 2 + k)
lum_sim = 1 - ((img_r - img_m) / data_range) ** 2
weight = p * con_struc_sim
quality = (1 - weight) * con_struc_sim + weight * lum_sim
gsm_score = np.nanmean(quality)
return gsm_score