from typing import List
import torch
from torch import nn
from kornia.filters import filter2d_separable, get_gaussian_kernel1d
from kornia.filters.filter import _compute_padding
def _crop(img: torch.Tensor, cropping_shape: List[int]) -> torch.Tensor:
"""Crop out the part of "valid" convolution area."""
return torch.nn.functional.pad(
img, (-cropping_shape[2], -cropping_shape[3], -cropping_shape[0], -cropping_shape[1])
)
[docs]def ssim(
img1: torch.Tensor,
img2: torch.Tensor,
window_size: int,
max_val: float = 1.0,
eps: float = 1e-12,
padding: str = 'same',
) -> torch.Tensor:
r"""Function that computes the Structural Similarity (SSIM) index map between two images.
Measures the (SSIM) index between each element in the input `x` and target `y`.
The index can be described as:
.. math::
\text{SSIM}(x, y) = \frac{(2\mu_x\mu_y+c_1)(2\sigma_{xy}+c_2)}
{(\mu_x^2+\mu_y^2+c_1)(\sigma_x^2+\sigma_y^2+c_2)}
where:
- :math:`c_1=(k_1 L)^2` and :math:`c_2=(k_2 L)^2` are two variables to
stabilize the division with weak denominator.
- :math:`L` is the dynamic range of the pixel-values (typically this is
:math:`2^{\#\text{bits per pixel}}-1`).
Args:
img1: the first input image with shape :math:`(B, C, H, W)`.
img2: the second input image with shape :math:`(B, C, H, W)`.
window_size: the size of the gaussian kernel to smooth the images.
max_val: the dynamic range of the images.
eps: Small value for numerically stability when dividing.
padding: ``'same'`` | ``'valid'``. Whether to only use the "valid" convolution
area to compute SSIM to match the MATLAB implementation of original SSIM paper.
Returns:
The ssim index map with shape :math:`(B, C, H, W)`.
Examples:
>>> input1 = torch.rand(1, 4, 5, 5)
>>> input2 = torch.rand(1, 4, 5, 5)
>>> ssim_map = ssim(input1, input2, 5) # 1x4x5x5
"""
if not isinstance(img1, torch.Tensor):
raise TypeError(f"Input img1 type is not a torch.Tensor. Got {type(img1)}")
if not isinstance(img2, torch.Tensor):
raise TypeError(f"Input img2 type is not a torch.Tensor. Got {type(img2)}")
if not isinstance(max_val, float):
raise TypeError(f"Input max_val type is not a float. Got {type(max_val)}")
if not len(img1.shape) == 4:
raise ValueError(f"Invalid img1 shape, we expect BxCxHxW. Got: {img1.shape}")
if not len(img2.shape) == 4:
raise ValueError(f"Invalid img2 shape, we expect BxCxHxW. Got: {img2.shape}")
if not img1.shape == img2.shape:
raise ValueError(f"img1 and img2 shapes must be the same. Got: {img1.shape} and {img2.shape}")
# prepare kernel
kernel: torch.Tensor = get_gaussian_kernel1d(window_size, 1.5, device=img1.device, dtype=img1.dtype)
# compute coefficients
C1: float = (0.01 * max_val) ** 2
C2: float = (0.03 * max_val) ** 2
# compute local mean per channel
mu1: torch.Tensor = filter2d_separable(img1, kernel, kernel)
mu2: torch.Tensor = filter2d_separable(img2, kernel, kernel)
cropping_shape: List[int] = []
if padding == 'valid':
height = width = kernel.shape[-1]
cropping_shape = _compute_padding([height, width])
mu1 = _crop(mu1, cropping_shape)
mu2 = _crop(mu2, cropping_shape)
elif padding == 'same':
pass
mu1_sq = mu1**2
mu2_sq = mu2**2
mu1_mu2 = mu1 * mu2
mu_img1_sq = filter2d_separable(img1**2, kernel, kernel)
mu_img2_sq = filter2d_separable(img2**2, kernel, kernel)
mu_img1_img2 = filter2d_separable(img1 * img2, kernel, kernel)
if padding == 'valid':
mu_img1_sq = _crop(mu_img1_sq, cropping_shape)
mu_img2_sq = _crop(mu_img2_sq, cropping_shape)
mu_img1_img2 = _crop(mu_img1_img2, cropping_shape)
elif padding == 'same':
pass
# compute local sigma per channel
sigma1_sq = mu_img1_sq - mu1_sq
sigma2_sq = mu_img2_sq - mu2_sq
sigma12 = mu_img1_img2 - mu1_mu2
# compute the similarity index map
num: torch.Tensor = (2.0 * mu1_mu2 + C1) * (2.0 * sigma12 + C2)
den: torch.Tensor = (mu1_sq + mu2_sq + C1) * (sigma1_sq + sigma2_sq + C2)
return num / (den + eps)
[docs]class SSIM(nn.Module):
r"""Create a module that computes the Structural Similarity (SSIM) index between two images.
Measures the (SSIM) index between each element in the input `x` and target `y`.
The index can be described as:
.. math::
\text{SSIM}(x, y) = \frac{(2\mu_x\mu_y+c_1)(2\sigma_{xy}+c_2)}
{(\mu_x^2+\mu_y^2+c_1)(\sigma_x^2+\sigma_y^2+c_2)}
where:
- :math:`c_1=(k_1 L)^2` and :math:`c_2=(k_2 L)^2` are two variables to
stabilize the division with weak denominator.
- :math:`L` is the dynamic range of the pixel-values (typically this is
:math:`2^{\#\text{bits per pixel}}-1`).
Args:
window_size: the size of the gaussian kernel to smooth the images.
max_val: the dynamic range of the images.
eps: Small value for numerically stability when dividing.
padding: ``'same'`` | ``'valid'``. Whether to only use the "valid" convolution
area to compute SSIM to match the MATLAB implementation of original SSIM paper.
Shape:
- Input: :math:`(B, C, H, W)`.
- Target :math:`(B, C, H, W)`.
- Output: :math:`(B, C, H, W)`.
Examples:
>>> input1 = torch.rand(1, 4, 5, 5)
>>> input2 = torch.rand(1, 4, 5, 5)
>>> ssim = SSIM(5)
>>> ssim_map = ssim(input1, input2) # 1x4x5x5
"""
def __init__(self, window_size: int, max_val: float = 1.0, eps: float = 1e-12, padding: str = 'same') -> None:
super().__init__()
self.window_size: int = window_size
self.max_val: float = max_val
self.eps = eps
self.padding = padding
def forward(self, img1: torch.Tensor, img2: torch.Tensor) -> torch.Tensor:
return ssim(img1, img2, self.window_size, self.max_val, self.eps, self.padding)