Image quality#

kornia.metrics.psnr(image, target, max_val)[source]#

Create a function that calculates the PSNR between 2 images.

PSNR is Peek Signal to Noise Ratio, which is similar to mean squared error. Given an m x n image, the PSNR is:

\[\text{PSNR} = 10 \log_{10} \bigg(\frac{\text{MAX}_I^2}{MSE(I,T)}\bigg)\]

where

\[\text{MSE}(I,T) = \frac{1}{mn}\sum_{i=0}^{m-1}\sum_{j=0}^{n-1} [I(i,j) - T(i,j)]^2\]

and \(\text{MAX}_I\) is the maximum possible input value (e.g for floating point images \(\text{MAX}_I=1\)).

Parameters:

image (Tensor) – the input image with arbitrary shape \((*)\).
target (Tensor) – the labels image with arbitrary shape \((*)\).
max_val (float) – The maximum value in the input tensor.

Return type:

Tensor

Returns:

the computed loss as a scalar.

Examples

>>> ones = torch.ones(1)
>>> psnr(ones, 1.2 * ones, 2.) # 10 * log(4/((1.2-1)**2)) / log(10)
tensor(20.0000)

Reference:: https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio#Definition

kornia.metrics.ssim(img1, img2, window_size, max_val=1.0, eps=1e-12, padding='same')[source]#

Compute 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:

\[\text{SSIM}(x, y) = \frac{(2\mu_x\mu_y+c_1)(2\sigma_{xy}+c_2)} {(\mu_x^2+\mu_y^2+c_1)(\sigma_x^2+\sigma_y^2+c_2)}\]

where:

\(c_1=(k_1 L)^2\) and \(c_2=(k_2 L)^2\) are two variables to stabilize the division with weak denominator.
\(L\) is the dynamic range of the pixel-values (typically this is \(2^{\#\text{bits per pixel}}-1\)).

Parameters:

img1 (Tensor) – the first input image with shape \((B, C, H, W)\).
img2 (Tensor) – the second input image with shape \((B, C, H, W)\).
window_size (int) – the size of the gaussian kernel to smooth the images.
max_val (float, optional) – the dynamic range of the images. Default: 1.0
eps (float, optional) – Small value for numerically stability when dividing. Default: 1e-12
padding (str, optional) – 'same' | 'valid'. Whether to only use the “valid” convolution area to compute SSIM to match the MATLAB implementation of original SSIM paper. Default: "same"

Return type:

Tensor

Returns:

The ssim index map with shape \((B, C, H, W)\).

Examples

>>> input1 = torch.rand(1, 4, 5, 5)
>>> input2 = torch.rand(1, 4, 5, 5)
>>> ssim_map = ssim(input1, input2, 5)  # 1x4x5x5

kornia.metrics.ssim3d(img1, img2, window_size, max_val=1.0, eps=1e-12, padding='same')[source]#

Compute 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:

\[\text{SSIM}(x, y) = \frac{(2\mu_x\mu_y+c_1)(2\sigma_{xy}+c_2)} {(\mu_x^2+\mu_y^2+c_1)(\sigma_x^2+\sigma_y^2+c_2)}\]

torch.where:

\(c_1=(k_1 L)^2\) and \(c_2=(k_2 L)^2\) are two variables to stabilize the division with weak denominator.
\(L\) is the dynamic range of the pixel-values (typically this is \(2^{\#\text{bits per pixel}}-1\)).

Parameters:

img1 (Tensor) – the first input image with shape \((B, C, D, H, W)\).
img2 (Tensor) – the second input image with shape \((B, C, D, H, W)\).
window_size (int) – the size of the gaussian kernel to smooth the images.
max_val (float, optional) – the dynamic range of the images. Default: 1.0
eps (float, optional) – Small value for numerically stability when dividing. Default: 1e-12
padding (str, optional) – 'same' | 'valid'. Whether to only use the “valid” convolution area to compute SSIM to match the MATLAB implementation of original SSIM paper. Default: "same"

Return type:

Tensor

Returns:

The ssim index map with shape \((B, C, D, H, W)\).

Examples

>>> input1 = torch.rand(1, 4, 5, 5, 5)
>>> input2 = torch.rand(1, 4, 5, 5, 5)
>>> ssim_map = ssim3d(input1, input2, 5)  # 1x4x5x5x5

class kornia.metrics.SSIM(window_size, max_val=1.0, eps=1e-12, padding='same')[source]#

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:

\[\text{SSIM}(x, y) = \frac{(2\mu_x\mu_y+c_1)(2\sigma_{xy}+c_2)} {(\mu_x^2+\mu_y^2+c_1)(\sigma_x^2+\sigma_y^2+c_2)}\]

where:

\(c_1=(k_1 L)^2\) and \(c_2=(k_2 L)^2\) are two variables to stabilize the division with weak denominator.
\(L\) is the dynamic range of the pixel-values (typically this is \(2^{\#\text{bits per pixel}}-1\)).

Parameters:

window_size (int) – the size of the gaussian kernel to smooth the images.
max_val (float, optional) – the dynamic range of the images. Default: 1.0
eps (float, optional) – Small value for numerically stability when dividing. Default: 1e-12
padding (str, optional) – 'same' | 'valid'. Whether to only use the “valid” convolution area to compute SSIM to match the MATLAB implementation of original SSIM paper. Default: "same"

Shape:

Input: \((B, C, H, W)\).
Target \((B, C, H, W)\).
Output: \((B, C, H, W)\).

Examples

>>> input1 = torch.rand(1, 4, 5, 5)
>>> input2 = torch.rand(1, 4, 5, 5)
>>> ssim = SSIM(5)
>>> ssim_map = ssim(input1, input2)  # 1x4x5x5

class kornia.metrics.SSIM3D(window_size, max_val=1.0, eps=1e-12, padding='same')[source]#

Create a module that computes the Structural Similarity (SSIM) index between two 3D images.

Measures the (SSIM) index between each element in the input x and target y.

The index can be described as:

\[\text{SSIM}(x, y) = \frac{(2\mu_x\mu_y+c_1)(2\sigma_{xy}+c_2)} {(\mu_x^2+\mu_y^2+c_1)(\sigma_x^2+\sigma_y^2+c_2)}\]

torch.where:

\(c_1=(k_1 L)^2\) and \(c_2=(k_2 L)^2\) are two variables to stabilize the division with weak denominator.
\(L\) is the dynamic range of the pixel-values (typically this is \(2^{\#\text{bits per pixel}}-1\)).

Parameters:

window_size (int) – the size of the gaussian kernel to smooth the images.
max_val (float, optional) – the dynamic range of the images. Default: 1.0
eps (float, optional) – Small value for numerically stability when dividing. Default: 1e-12
padding (str, optional) – 'same' | 'valid'. Whether to only use the “valid” convolution area to compute SSIM to match the MATLAB implementation of original SSIM paper. Default: "same"

Shape:

Input: \((B, C, D, H, W)\).
Target \((B, C, D, H, W)\).
Output: \((B, C, D, H, W)\).

Examples

>>> input1 = torch.rand(1, 4, 5, 5, 5)
>>> input2 = torch.rand(1, 4, 5, 5, 5)
>>> ssim = SSIM3D(5)
>>> ssim_map = ssim(input1, input2)  # 1x4x5x5x5