mmagic.datasets.transforms.blur_kernels 源代码
# This code is referenced from BasicSR with modifications.
# Reference: https://github.com/xinntao/BasicSR/blob/master/basicsr/data/degradations.py # noqa
# Original license: Copyright (c) 2020 xinntao, under the Apache 2.0 license.
import numpy as np
from scipy import special
[文档]def get_rotated_sigma_matrix(sig_x, sig_y, theta):
"""Calculate the rotated sigma matrix (two dimensional matrix).
Args:
sig_x (float): Standard deviation along the horizontal direction.
sig_y (float): Standard deviation along the vertical direction.
theta (float): Rotation in radian.
Returns:
np.ndarray: Rotated sigma matrix.
"""
diag = np.array([[sig_x**2, 0], [0, sig_y**2]]).astype(np.float32)
rot = np.array([[np.cos(theta), -np.sin(theta)],
[np.sin(theta), np.cos(theta)]]).astype(np.float32)
return np.matmul(rot, np.matmul(diag, rot.T))
[文档]def _mesh_grid(kernel_size):
"""Generate the mesh grid, centering at zero.
Args:
kernel_size (int): The size of the kernel.
Returns:
x_grid (np.ndarray): x-coordinates with shape
(kernel_size, kernel_size).
y_grid (np.ndarray): y-coordinates with shape
(kernel_size, kernel_size).
xy_grid (np.ndarray): stacked coordinates with shape
(kernel_size, kernel_size, 2).
"""
range_ = np.arange(-kernel_size // 2 + 1., kernel_size // 2 + 1.)
x_grid, y_grid = np.meshgrid(range_, range_)
xy_grid = np.hstack((x_grid.reshape((kernel_size * kernel_size, 1)),
y_grid.reshape(kernel_size * kernel_size,
1))).reshape(kernel_size, kernel_size,
2)
return xy_grid, x_grid, y_grid
[文档]def calculate_gaussian_pdf(sigma_matrix, grid):
"""Calculate PDF of the bivariate Gaussian distribution.
Args:
sigma_matrix (np.ndarray): The variance matrix with shape (2, 2).
grid (np.ndarray): Coordinates generated by :func:`_mesh_grid`,
with shape (K, K, 2), where K is the kernel size.
Returns:
kernel (np.ndarray): Un-normalized kernel.
"""
inverse_sigma = np.linalg.inv(sigma_matrix)
kernel = np.exp(-0.5 * np.sum(np.matmul(grid, inverse_sigma) * grid, 2))
return kernel
[文档]def bivariate_gaussian(kernel_size,
sig_x,
sig_y=None,
theta=None,
grid=None,
is_isotropic=True):
"""Generate a bivariate isotropic or anisotropic Gaussian kernel.
In isotropic mode, only `sig_x` is used. `sig_y` and `theta` are
ignored.
Args:
kernel_size (int): The size of the kernel
sig_x (float): Standard deviation along horizontal direction.
sig_y (float | None, optional): Standard deviation along the vertical
direction. If it is None, 'is_isotropic' must be set to True.
Default: None.
theta (float | None, optional): Rotation in radian. If it is None,
'is_isotropic' must be set to True. Default: None.
grid (ndarray, optional): Coordinates generated by :func:`_mesh_grid`,
with shape (K, K, 2), where K is the kernel size. Default: None
is_isotropic (bool, optional): Whether to use an isotropic kernel.
Default: True.
Returns:
kernel (np.ndarray): normalized kernel (i.e. sum to 1).
"""
if grid is None:
grid, _, _ = _mesh_grid(kernel_size)
if is_isotropic:
sigma_matrix = np.array([[sig_x**2, 0], [0,
sig_x**2]]).astype(np.float32)
else:
if sig_y is None:
raise ValueError('"sig_y" cannot be None if "is_isotropic" is '
'False.')
sigma_matrix = get_rotated_sigma_matrix(sig_x, sig_y, theta)
kernel = calculate_gaussian_pdf(sigma_matrix, grid)
kernel = kernel / np.sum(kernel)
return kernel
[文档]def bivariate_generalized_gaussian(kernel_size,
sig_x,
sig_y=None,
theta=None,
beta=1,
grid=None,
is_isotropic=True):
"""Generate a bivariate generalized Gaussian kernel.
Described in `Parameter Estimation For Multivariate Generalized
Gaussian Distributions` by Pascal et. al (2013). In isotropic mode,
only `sig_x` is used. `sig_y` and `theta` is ignored.
Args:
kernel_size (int): The size of the kernel
sig_x (float): Standard deviation along horizontal direction
sig_y (float | None, optional): Standard deviation along the vertical
direction. If it is None, 'is_isotropic' must be set to True.
Default: None.
theta (float | None, optional): Rotation in radian. If it is None,
'is_isotropic' must be set to True. Default: None.
beta (float, optional): Shape parameter, beta = 1 is the normal
distribution. Default: 1.
grid (ndarray, optional): Coordinates generated by :func:`_mesh_grid`,
with shape (K, K, 2), where K is the kernel size. Default: None
is_isotropic (bool, optional): Whether to use an isotropic kernel.
Default: True.
Returns:
kernel (np.ndarray): normalized kernel.
"""
if grid is None:
grid, _, _ = _mesh_grid(kernel_size)
if is_isotropic:
sigma_matrix = np.array([[sig_x**2, 0], [0,
sig_x**2]]).astype(np.float32)
else:
sigma_matrix = get_rotated_sigma_matrix(sig_x, sig_y, theta)
inverse_sigma = np.linalg.inv(sigma_matrix)
kernel = np.exp(
-0.5 *
np.power(np.sum(np.matmul(grid, inverse_sigma) * grid, 2), beta))
kernel = kernel / np.sum(kernel)
return kernel
[文档]def bivariate_plateau(kernel_size,
sig_x,
sig_y,
theta,
beta,
grid=None,
is_isotropic=True):
"""Generate a plateau-like anisotropic kernel.
This kernel has a form of 1 / (1+x^(beta)).
Ref: https://stats.stackexchange.com/questions/203629/is-there-a-plateau-shaped-distribution # noqa
In the isotropic mode, only `sig_x` is used. `sig_y` and `theta` is ignored.
Args:
kernel_size (int): The size of the kernel
sig_x (float): Standard deviation along horizontal direction
sig_y (float): Standard deviation along the vertical direction.
theta (float): Rotation in radian.
beta (float): Shape parameter, beta = 1 is the normal distribution.
grid (np.ndarray, optional): Coordinates generated by :func:`_mesh_grid`,
with shape (K, K, 2), where K is the kernel size. Default: None
is_isotropic (bool, optional): Whether to use an isotropic kernel.
Default: True.
Returns:
kernel (np.ndarray): normalized kernel (i.e. sum to 1).
"""
if grid is None:
grid, _, _ = _mesh_grid(kernel_size)
if is_isotropic:
sigma_matrix = np.array([[sig_x**2, 0], [0,
sig_x**2]]).astype(np.float32)
else:
sigma_matrix = get_rotated_sigma_matrix(sig_x, sig_y, theta)
inverse_sigma = np.linalg.inv(sigma_matrix)
kernel = np.reciprocal(
np.power(np.sum(np.matmul(grid, inverse_sigma) * grid, 2), beta) + 1)
kernel = kernel / np.sum(kernel)
return kernel
[文档]def random_bivariate_gaussian_kernel(kernel_size,
sigma_x_range,
sigma_y_range,
rotation_range,
noise_range=None,
is_isotropic=True):
"""Randomly generate bivariate isotropic or anisotropic Gaussian kernels.
In the isotropic mode, only `sigma_x_range` is used. `sigma_y_range` and
`rotation_range` is ignored.
Args:
kernel_size (int): The size of the kernel.
sigma_x_range (tuple): The range of the standard deviation along the
horizontal direction. Default: [0.6, 5]
sigma_y_range (tuple): The range of the standard deviation along the
vertical direction. Default: [0.6, 5]
rotation_range (tuple): Range of rotation in radian.
noise_range (tuple, optional): Multiplicative kernel noise.
Default: None.
is_isotropic (bool, optional): Whether to use an isotropic kernel.
Default: True.
Returns:
kernel (np.ndarray): The kernel whose parameters are sampled from the
specified range.
"""
assert kernel_size % 2 == 1, 'Kernel size must be an odd number.'
assert sigma_x_range[0] <= sigma_x_range[1], 'Wrong sigma_x_range.'
sigma_x = np.random.uniform(sigma_x_range[0], sigma_x_range[1])
if is_isotropic is False:
assert sigma_y_range[0] <= sigma_y_range[1], 'Wrong sigma_y_range.'
assert rotation_range[0] <= rotation_range[1], 'Wrong rotation_range.'
sigma_y = np.random.uniform(sigma_y_range[0], sigma_y_range[1])
rotation = np.random.uniform(rotation_range[0], rotation_range[1])
else:
sigma_y = sigma_x
rotation = 0
kernel = bivariate_gaussian(
kernel_size, sigma_x, sigma_y, rotation, is_isotropic=is_isotropic)
# add multiplicative noise
if noise_range is not None:
assert noise_range[0] <= noise_range[1], 'Wrong noise range.'
noise = np.random.uniform(
noise_range[0], noise_range[1], size=kernel.shape)
kernel = kernel * noise
kernel = kernel / np.sum(kernel)
return kernel
[文档]def random_bivariate_generalized_gaussian_kernel(kernel_size,
sigma_x_range,
sigma_y_range,
rotation_range,
beta_range,
noise_range=None,
is_isotropic=True):
"""Randomly generate bivariate generalized Gaussian kernels.
In the isotropic mode, only `sigma_x_range` is used. `sigma_y_range` and
`rotation_range` is ignored.
Args:
kernel_size (int): The size of the kernel.
sigma_x_range (tuple): The range of the standard deviation along the
horizontal direction. Default: [0.6, 5]
sigma_y_range (tuple): The range of the standard deviation along the
vertical direction. Default: [0.6, 5]
rotation_range (tuple): Range of rotation in radian.
beta_range (float): The range of the shape parameter, beta = 1 is the
normal distribution.
noise_range (tuple, optional): Multiplicative kernel noise.
Default: None.
is_isotropic (bool, optional): Whether to use an isotropic kernel.
Default: True.
Returns:
kernel (np.ndarray): Normalized kernel.
"""
assert kernel_size % 2 == 1, 'Kernel size must be an odd number.'
assert sigma_x_range[0] <= sigma_x_range[1], 'Wrong sigma_x_range.'
sigma_x = np.random.uniform(sigma_x_range[0], sigma_x_range[1])
if is_isotropic is False:
assert sigma_y_range[0] <= sigma_y_range[1], 'Wrong sigma_y_range.'
assert rotation_range[0] <= rotation_range[1], 'Wrong rotation_range.'
sigma_y = np.random.uniform(sigma_y_range[0], sigma_y_range[1])
rotation = np.random.uniform(rotation_range[0], rotation_range[1])
else:
sigma_y = sigma_x
rotation = 0
# assume beta_range[0] <= 1 <= beta_range[1]
if np.random.uniform() <= 0.5:
beta = np.random.uniform(beta_range[0], 1)
else:
beta = np.random.uniform(1, beta_range[1])
kernel = bivariate_generalized_gaussian(
kernel_size,
sigma_x,
sigma_y,
rotation,
beta,
is_isotropic=is_isotropic)
# add multiplicative noise
if noise_range is not None:
assert noise_range[0] <= noise_range[1], 'Wrong noise range.'
noise = np.random.uniform(
noise_range[0], noise_range[1], size=kernel.shape)
kernel = kernel * noise
kernel = kernel / np.sum(kernel)
return kernel
[文档]def random_bivariate_plateau_kernel(kernel_size,
sigma_x_range,
sigma_y_range,
rotation_range,
beta_range,
noise_range=None,
is_isotropic=True):
"""Randomly generate bivariate plateau kernels.
In the isotropic mode, only `sigma_x_range` is used. `sigma_y_range` and
`rotation_range` is ignored.
Args:
kernel_size (int): The size of the kernel.
sigma_x_range (tuple): The range of the standard deviation along the
horizontal direction. Default: [0.6, 5]
sigma_y_range (tuple): The range of the standard deviation along the
vertical direction. Default: [0.6, 5]
rotation_range (tuple): Range of rotation in radian.
beta_range (float): The range of the shape parameter, beta = 1 is the
normal distribution.
noise_range (tuple, optional): Multiplicative kernel noise.
Default: None.
is_isotropic (bool, optional): Whether to use an isotropic kernel.
Default: True.
Returns:
kernel (np.ndarray): Plateau kernel.
"""
assert kernel_size % 2 == 1, 'Kernel size must be an odd number.'
assert sigma_x_range[0] <= sigma_x_range[1], 'Wrong sigma_x_range.'
sigma_x = np.random.uniform(sigma_x_range[0], sigma_x_range[1])
if is_isotropic is False:
assert sigma_y_range[0] <= sigma_y_range[1], 'Wrong sigma_y_range.'
assert rotation_range[0] <= rotation_range[1], 'Wrong rotation_range.'
sigma_y = np.random.uniform(sigma_y_range[0], sigma_y_range[1])
rotation = np.random.uniform(rotation_range[0], rotation_range[1])
else:
sigma_y = sigma_x
rotation = 0
# TODO: this may be not proper
if np.random.uniform() <= 0.5:
beta = np.random.uniform(beta_range[0], 1)
else:
beta = np.random.uniform(1, beta_range[1])
kernel = bivariate_plateau(
kernel_size,
sigma_x,
sigma_y,
rotation,
beta,
is_isotropic=is_isotropic)
# add multiplicative noise
if noise_range is not None:
assert noise_range[0] <= noise_range[1], 'Wrong noise range.'
noise = np.random.uniform(
noise_range[0], noise_range[1], size=kernel.shape)
kernel = kernel * noise
kernel = kernel / np.sum(kernel)
return kernel
[文档]def random_circular_lowpass_kernel(omega_range, kernel_size, pad_to=0):
"""Generate a 2D Sinc filter.
Reference: https://dsp.stackexchange.com/questions/58301/2-d-circularly-symmetric-low-pass-filter # noqa
Args:
omega_range (tuple): The cutoff frequency in radian (pi is max).
kernel_size (int): The size of the kernel. It must be an odd number.
pad_to (int, optional): The size of the padded kernel. It must be odd
or zero. Default: 0.
Returns:
kernel (np.ndarray): The Sinc kernel with specified parameters.
"""
err = np.geterr()
np.seterr(divide='ignore', invalid='ignore')
assert kernel_size % 2 == 1, 'Kernel size must be an odd number.'
omega = np.random.uniform(omega_range[0], omega_range[-1])
kernel = np.fromfunction(
lambda x, y: omega * special.j1(omega * np.sqrt(
(x - (kernel_size - 1) / 2)**2 + (y - (kernel_size - 1) / 2)**2)) /
(2 * np.pi * np.sqrt((x - (kernel_size - 1) / 2)**2 +
(y - (kernel_size - 1) / 2)**2)),
[kernel_size, kernel_size])
kernel[(kernel_size - 1) // 2,
(kernel_size - 1) // 2] = omega**2 / (4 * np.pi)
kernel = kernel / np.sum(kernel)
if pad_to > kernel_size:
pad_size = (pad_to - kernel_size) // 2
kernel = np.pad(kernel, ((pad_size, pad_size), (pad_size, pad_size)))
np.seterr(**err)
return kernel
[文档]def random_mixed_kernels(kernel_list,
kernel_prob,
kernel_size,
sigma_x_range=[0.6, 5],
sigma_y_range=[0.6, 5],
rotation_range=[-np.pi, np.pi],
beta_gaussian_range=[0.5, 8],
beta_plateau_range=[1, 2],
omega_range=[0, np.pi],
noise_range=None):
"""Randomly generate a kernel.
Args:
kernel_list (list): A list of kernel types. Choices are
'iso', 'aniso', 'skew', 'generalized_iso', 'generalized_aniso',
'plateau_iso', 'plateau_aniso', 'sinc'.
kernel_prob (list): The probability of choosing of the corresponding
kernel.
kernel_size (int): The size of the kernel.
sigma_x_range (list, optional): The range of the standard deviation
along the horizontal direction. Default: (0.6, 5).
sigma_y_range (list, optional): The range of the standard deviation
along the vertical direction. Default: (0.6, 5).
rotation_range (list, optional): Range of rotation in radian.
Default: (-np.pi, np.pi).
beta_gaussian_range (list, optional): The range of the shape parameter
for generalized Gaussian. Default: (0.5, 8).
beta_plateau_range (list, optional): The range of the shape parameter
for plateau kernel. Default: (1, 2).
omega_range (list, optional): The range of omega used in Sinc kernel.
Default: (0, np.pi).
noise_range (list, optional): Multiplicative kernel noise.
Default: None.
Returns:
kernel (np.ndarray): The kernel whose parameters are sampled from the
specified range.
"""
kernel_type = np.random.choice(kernel_list, p=kernel_prob)
if kernel_type == 'iso':
kernel = random_bivariate_gaussian_kernel(
kernel_size,
sigma_x_range,
sigma_y_range,
rotation_range,
noise_range=noise_range,
is_isotropic=True)
elif kernel_type == 'aniso':
kernel = random_bivariate_gaussian_kernel(
kernel_size,
sigma_x_range,
sigma_y_range,
rotation_range,
noise_range=noise_range,
is_isotropic=False)
elif kernel_type == 'generalized_iso':
kernel = random_bivariate_generalized_gaussian_kernel(
kernel_size,
sigma_x_range,
sigma_y_range,
rotation_range,
beta_gaussian_range,
noise_range=noise_range,
is_isotropic=True)
elif kernel_type == 'generalized_aniso':
kernel = random_bivariate_generalized_gaussian_kernel(
kernel_size,
sigma_x_range,
sigma_y_range,
rotation_range,
beta_gaussian_range,
noise_range=noise_range,
is_isotropic=False)
elif kernel_type == 'plateau_iso':
kernel = random_bivariate_plateau_kernel(
kernel_size,
sigma_x_range,
sigma_y_range,
rotation_range,
beta_plateau_range,
noise_range=None,
is_isotropic=True)
elif kernel_type == 'plateau_aniso':
kernel = random_bivariate_plateau_kernel(
kernel_size,
sigma_x_range,
sigma_y_range,
rotation_range,
beta_plateau_range,
noise_range=None,
is_isotropic=False)
elif kernel_type == 'sinc':
kernel = random_circular_lowpass_kernel(omega_range, kernel_size)
return kernel