kornia.losses

Reconstruction

kornia.losses.ssim_loss(img1, img2, window_size, max_val=1.0, eps=1e-12, reduction='mean')[source]

Function that computes a loss based on the SSIM measurement.

The loss, or the Structural dissimilarity (DSSIM) is described as:

\[\text{loss}(x, y) = \frac{1 - \text{SSIM}(x, y)}{2}\]

See ssim() for details about SSIM.

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

  • reduction (str, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Default: 'mean'

Return type

Tensor

Returns

The loss based on the ssim index.

Examples

>>> input1 = torch.rand(1, 4, 5, 5)
>>> input2 = torch.rand(1, 4, 5, 5)
>>> loss = ssim_loss(input1, input2, 5)
kornia.losses.psnr_loss(input, target, max_val)[source]

Function that computes the PSNR loss.

The loss is computed as follows:

\[\text{loss} = -\text{psnr(x, y)}\]

See psnr() for details abut PSNR.

Parameters
  • input (Tensor) – the input image with shape \((*)\).

  • labels – the labels image with 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_loss(ones, 1.2 * ones, 2.) # 10 * log(4/((1.2-1)**2)) / log(10)
tensor(-20.0000)
kornia.losses.total_variation(img)[source]

Function that computes Total Variation according to [1].

Parameters

img (Tensor) – the input image with shape \((N, C, H, W)\) or \((C, H, W)\).

Return type

Tensor

Returns

a scalar with the computer loss.

Examples

>>> total_variation(torch.ones(3, 4, 4))
tensor(0.)

Note

See a working example here.

Reference:

[1] https://en.wikipedia.org/wiki/Total_variation

kornia.losses.inverse_depth_smoothness_loss(idepth, image)[source]

Criterion that computes image-aware inverse depth smoothness loss.

\[\text{loss} = \left | \partial_x d_{ij} \right | e^{-\left \| \partial_x I_{ij} \right \|} + \left | \partial_y d_{ij} \right | e^{-\left \| \partial_y I_{ij} \right \|}\]
Parameters
  • idepth (Tensor) – tensor with the inverse depth with shape \((N, 1, H, W)\).

  • image (Tensor) – tensor with the input image with shape \((N, 3, H, W)\).

Return type

Tensor

Returns

a scalar with the computed loss.

Examples

>>> idepth = torch.rand(1, 1, 4, 5)
>>> image = torch.rand(1, 3, 4, 5)
>>> loss = inverse_depth_smoothness_loss(idepth, image)

Semantic Segmentation

kornia.losses.binary_focal_loss_with_logits(input, target, alpha=0.25, gamma=2.0, reduction='none', eps=None)[source]

Function that computes Binary Focal loss.

\[\text{FL}(p_t) = -\alpha_t (1 - p_t)^{\gamma} \, \text{log}(p_t)\]
where:
  • \(p_t\) is the model’s estimated probability for each class.

Parameters
  • input (Tensor) – input data tensor of arbitrary shape.

  • target (Tensor) – the target tensor with shape matching input.

  • alpha (float, optional) – Weighting factor for the rare class \(\alpha \in [0, 1]\). Default: 0.25

  • gamma (float, optional) – Focusing parameter \(\gamma >= 0\). Default: 2.0

  • reduction (str, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Default: 'none'

  • eps (Optional[float], optional) – Deprecated: scalar for numerically stability when dividing. This is no longer used. Default: None

Return type

Tensor

Returns

the computed loss.

Examples

>>> kwargs = {"alpha": 0.25, "gamma": 2.0, "reduction": 'mean'}
>>> logits = torch.tensor([[[6.325]],[[5.26]],[[87.49]]])
>>> labels = torch.tensor([[[1.]],[[1.]],[[0.]]])
>>> binary_focal_loss_with_logits(logits, labels, **kwargs)
tensor(21.8725)
kornia.losses.focal_loss(input, target, alpha, gamma=2.0, reduction='none', eps=None)[source]

Criterion that computes Focal loss.

According to [LGG+18], the Focal loss is computed as follows:

\[\text{FL}(p_t) = -\alpha_t (1 - p_t)^{\gamma} \, \text{log}(p_t)\]
Where:
  • \(p_t\) is the model’s estimated probability for each class.

Parameters
  • input (Tensor) – logits tensor with shape \((N, C, *)\) where C = number of classes.

  • target (Tensor) – labels tensor with shape \((N, *)\) where each value is \(0 ≤ targets[i] ≤ C−1\).

  • alpha (float) – Weighting factor \(\alpha \in [0, 1]\).

  • gamma (float, optional) – Focusing parameter \(\gamma >= 0\). Default: 2.0

  • reduction (str, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Default: 'none'

  • eps (Optional[float], optional) – Deprecated: scalar to enforce numerical stabiliy. This is no longer used. Default: None

Return type

Tensor

Returns

the computed loss.

Example

>>> N = 5  # num_classes
>>> input = torch.randn(1, N, 3, 5, requires_grad=True)
>>> target = torch.empty(1, 3, 5, dtype=torch.long).random_(N)
>>> output = focal_loss(input, target, alpha=0.5, gamma=2.0, reduction='mean')
>>> output.backward()
kornia.losses.dice_loss(input, target, eps=1e-08)[source]

Criterion that computes Sørensen-Dice Coefficient loss.

According to [1], we compute the Sørensen-Dice Coefficient as follows:

\[\text{Dice}(x, class) = \frac{2 |X| \cap |Y|}{|X| + |Y|}\]
Where:
  • \(X\) expects to be the scores of each class.

  • \(Y\) expects to be the one-hot tensor with the class labels.

the loss, is finally computed as:

\[\text{loss}(x, class) = 1 - \text{Dice}(x, class)\]
Reference:

[1] https://en.wikipedia.org/wiki/S%C3%B8rensen%E2%80%93Dice_coefficient

Parameters
  • input (Tensor) – logits tensor with shape \((N, C, H, W)\) where C = number of classes.

  • labels – labels tensor with shape \((N, H, W)\) where each value is \(0 ≤ targets[i] ≤ C−1\).

  • eps (float, optional) – Scalar to enforce numerical stabiliy. Default: 1e-08

Return type

Tensor

Returns

the computed loss.

Example

>>> N = 5  # num_classes
>>> input = torch.randn(1, N, 3, 5, requires_grad=True)
>>> target = torch.empty(1, 3, 5, dtype=torch.long).random_(N)
>>> output = dice_loss(input, target)
>>> output.backward()
kornia.losses.tversky_loss(input, target, alpha, beta, eps=1e-08)[source]

Criterion that computes Tversky Coefficient loss.

According to [SEG17], we compute the Tversky Coefficient as follows:

\[\text{S}(P, G, \alpha; \beta) = \frac{|PG|}{|PG| + \alpha |P \setminus G| + \beta |G \setminus P|}\]
Where:
  • \(P\) and \(G\) are the predicted and ground truth binary labels.

  • \(\alpha\) and \(\beta\) control the magnitude of the penalties for FPs and FNs, respectively.

Note

  • \(\alpha = \beta = 0.5\) => dice coeff

  • \(\alpha = \beta = 1\) => tanimoto coeff

  • \(\alpha + \beta = 1\) => F beta coeff

Parameters
  • input (Tensor) – logits tensor with shape \((N, C, H, W)\) where C = number of classes.

  • target (Tensor) – labels tensor with shape \((N, H, W)\) where each value is \(0 ≤ targets[i] ≤ C−1\).

  • alpha (float) – the first coefficient in the denominator.

  • beta (float) – the second coefficient in the denominator.

  • eps (float, optional) – scalar for numerical stability. Default: 1e-08

Return type

Tensor

Returns

the computed loss.

Example

>>> N = 5  # num_classes
>>> input = torch.randn(1, N, 3, 5, requires_grad=True)
>>> target = torch.empty(1, 3, 5, dtype=torch.long).random_(N)
>>> output = tversky_loss(input, target, alpha=0.5, beta=0.5)
>>> output.backward()

Distributions

kornia.losses.js_div_loss_2d(input, target, reduction='mean')[source]

Calculate the Jensen-Shannon divergence loss between heatmaps.

Parameters
  • input (Tensor) – the input tensor with shape \((B, N, H, W)\).

  • target (Tensor) – the target tensor with shape \((B, N, H, W)\).

  • reduction (str, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Default: 'mean'

Examples

>>> input = torch.full((1, 1, 2, 4), 0.125)
>>> loss = js_div_loss_2d(input, input)
>>> loss.item()
0.0
kornia.losses.kl_div_loss_2d(input, target, reduction='mean')[source]

Calculate the Kullback-Leibler divergence loss between heatmaps.

Parameters
  • input (Tensor) – the input tensor with shape \((B, N, H, W)\).

  • target (Tensor) – the target tensor with shape \((B, N, H, W)\).

  • reduction (str, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Default: 'mean'

Examples

>>> input = torch.full((1, 1, 2, 4), 0.125)
>>> loss = js_div_loss_2d(input, input)
>>> loss.item()
0.0

Morphology

class kornia.losses.HausdorffERLoss(alpha=2.0, k=10, reduction='mean')[source]

Binary Hausdorff loss based on morphological erosion.

Hausdorff Distance loss measures the maximum distance of a predicted segmentation boundary to the nearest ground-truth edge pixel. For two segmentation point sets X and Y , the one-sided HD from X to Y is defined as:

\[hd(X,Y) = \max_{x \in X} \min_{y \in Y}||x - y||_2\]

Furthermore, the bidirectional HD is:

\[HD(X,Y) = max(hd(X, Y), hd(Y, X))\]

This is an Hausdorff Distance (HD) Loss that based on morphological erosion, which provided a differentiable approximation of Hausdorff distance as stated in [KS19]. The code is refactored on top of here.

Parameters
  • alpha (float, optional) – controls the erosion rate in each iteration. Default: 2.0

  • k (int, optional) – the number of iterations of erosion. Default: 10

  • reduction (str, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the weighted mean of the output is taken, ‘sum’: the output will be summed. Default: 'mean'

Examples

>>> hdloss = HausdorffERLoss()
>>> input = torch.randn(5, 3, 20, 20)
>>> target = (torch.rand(5, 1, 20, 20) * 2).long()
>>> res = hdloss(input, target)
class kornia.losses.HausdorffERLoss3D(alpha=2.0, k=10, reduction='mean')[source]

Binary 3D Hausdorff loss based on morphological erosion.

Hausdorff Distance loss measures the maximum distance of a predicted segmentation boundary to the nearest ground-truth edge pixel. For two segmentation point sets X and Y , the one-sided HD from X to Y is defined as:

\[hd(X,Y) = \max_{x \in X} \min_{y \in Y}||x - y||_2\]

Furthermore, the bidirectional HD is:

\[HD(X,Y) = max(hd(X, Y), hd(Y, X))\]

This is a 3D Hausdorff Distance (HD) Loss that based on morphological erosion, which provided a differentiable approximation of Hausdorff distance as stated in [KS19]. The code is refactored on top of here.

Parameters
  • alpha (float, optional) – controls the erosion rate in each iteration. Default: 2.0

  • k (int, optional) – the number of iterations of erosion. Default: 10

  • reduction (str, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the weighted mean of the output is taken, ‘sum’: the output will be summed. Default: 'mean'

Examples

>>> hdloss = HausdorffERLoss3D()
>>> input = torch.randn(5, 3, 20, 20, 20)
>>> target = (torch.rand(5, 1, 20, 20, 20) * 2).long()
>>> res = hdloss(input, target)

Module

class kornia.losses.DiceLoss(eps=1e-08)[source]

Criterion that computes Sørensen-Dice Coefficient loss.

According to [1], we compute the Sørensen-Dice Coefficient as follows:

\[\text{Dice}(x, class) = \frac{2 |X| \cap |Y|}{|X| + |Y|}\]
Where:
  • \(X\) expects to be the scores of each class.

  • \(Y\) expects to be the one-hot tensor with the class labels.

the loss, is finally computed as:

\[\text{loss}(x, class) = 1 - \text{Dice}(x, class)\]
Reference:

[1] https://en.wikipedia.org/wiki/S%C3%B8rensen%E2%80%93Dice_coefficient

Parameters

eps (float, optional) – Scalar to enforce numerical stabiliy. Default: 1e-08

Shape:
  • Input: \((N, C, H, W)\) where C = number of classes.

  • Target: \((N, H, W)\) where each value is \(0 ≤ targets[i] ≤ C−1\).

Example

>>> N = 5  # num_classes
>>> criterion = DiceLoss()
>>> input = torch.randn(1, N, 3, 5, requires_grad=True)
>>> target = torch.empty(1, 3, 5, dtype=torch.long).random_(N)
>>> output = criterion(input, target)
>>> output.backward()
class kornia.losses.TverskyLoss(alpha, beta, eps=1e-08)[source]

Criterion that computes Tversky Coefficient loss.

According to [SEG17], we compute the Tversky Coefficient as follows:

\[\text{S}(P, G, \alpha; \beta) = \frac{|PG|}{|PG| + \alpha |P \setminus G| + \beta |G \setminus P|}\]
Where:
  • \(P\) and \(G\) are the predicted and ground truth binary labels.

  • \(\alpha\) and \(\beta\) control the magnitude of the penalties for FPs and FNs, respectively.

Note

  • \(\alpha = \beta = 0.5\) => dice coeff

  • \(\alpha = \beta = 1\) => tanimoto coeff

  • \(\alpha + \beta = 1\) => F beta coeff

Parameters
  • alpha (float) – the first coefficient in the denominator.

  • beta (float) – the second coefficient in the denominator.

  • eps (float, optional) – scalar for numerical stability. Default: 1e-08

Shape:
  • Input: \((N, C, H, W)\) where C = number of classes.

  • Target: \((N, H, W)\) where each value is \(0 ≤ targets[i] ≤ C−1\).

Examples

>>> N = 5  # num_classes
>>> criterion = TverskyLoss(alpha=0.5, beta=0.5)
>>> input = torch.randn(1, N, 3, 5, requires_grad=True)
>>> target = torch.empty(1, 3, 5, dtype=torch.long).random_(N)
>>> output = criterion(input, target)
>>> output.backward()
class kornia.losses.FocalLoss(alpha, gamma=2.0, reduction='none', eps=None)[source]

Criterion that computes Focal loss.

According to [LGG+18], the Focal loss is computed as follows:

\[\text{FL}(p_t) = -\alpha_t (1 - p_t)^{\gamma} \, \text{log}(p_t)\]
Where:
  • \(p_t\) is the model’s estimated probability for each class.

Parameters
  • alpha (float) – Weighting factor \(\alpha \in [0, 1]\).

  • gamma (float, optional) – Focusing parameter \(\gamma >= 0\). Default: 2.0

  • reduction (str, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Default: 'none'

  • eps (Optional[float], optional) – Deprecated: scalar to enforce numerical stability. This is no longer used. Default: None

Shape:
  • Input: \((N, C, *)\) where C = number of classes.

  • Target: \((N, *)\) where each value is \(0 ≤ targets[i] ≤ C−1\).

Example

>>> N = 5  # num_classes
>>> kwargs = {"alpha": 0.5, "gamma": 2.0, "reduction": 'mean'}
>>> criterion = FocalLoss(**kwargs)
>>> input = torch.randn(1, N, 3, 5, requires_grad=True)
>>> target = torch.empty(1, 3, 5, dtype=torch.long).random_(N)
>>> output = criterion(input, target)
>>> output.backward()
class kornia.losses.SSIMLoss(window_size, max_val=1.0, eps=1e-12, reduction='mean')[source]

Create a criterion that computes a loss based on the SSIM measurement.

The loss, or the Structural dissimilarity (DSSIM) is described as:

\[\text{loss}(x, y) = \frac{1 - \text{SSIM}(x, y)}{2}\]

See ssim_loss() for details about SSIM.

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

  • reduction (str, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Default: 'mean'

Returns

The loss based on the ssim index.

Examples

>>> input1 = torch.rand(1, 4, 5, 5)
>>> input2 = torch.rand(1, 4, 5, 5)
>>> criterion = SSIMLoss(5)
>>> loss = criterion(input1, input2)
class kornia.losses.InverseDepthSmoothnessLoss[source]

Criterion that computes image-aware inverse depth smoothness loss.

\[\text{loss} = \left | \partial_x d_{ij} \right | e^{-\left \| \partial_x I_{ij} \right \|} + \left | \partial_y d_{ij} \right | e^{-\left \| \partial_y I_{ij} \right \|}\]
Shape:
  • Inverse Depth: \((N, 1, H, W)\)

  • Image: \((N, 3, H, W)\)

  • Output: scalar

Examples

>>> idepth = torch.rand(1, 1, 4, 5)
>>> image = torch.rand(1, 3, 4, 5)
>>> smooth = InverseDepthSmoothnessLoss()
>>> loss = smooth(idepth, image)
class kornia.losses.TotalVariation[source]

Compute the Total Variation according to [1].

Shape:
  • Input: \((N, C, H, W)\) or \((C, H, W)\).

  • Output: \((N,)\) or scalar.

Examples

>>> tv = TotalVariation()
>>> output = tv(torch.ones((2, 3, 4, 4), requires_grad=True))
>>> output.data
tensor([0., 0.])
>>> output.sum().backward()  # grad can be implicitly created only for scalar outputs
Reference:

[1] https://en.wikipedia.org/wiki/Total_variation

class kornia.losses.PSNRLoss(max_val)[source]

Create a criterion that calculates the PSNR loss.

The loss is computed as follows:

\[\text{loss} = -\text{psnr(x, y)}\]

See psnr() for details abut PSNR.

Parameters

max_val (float) – The maximum value in the input tensor.

Shape:
  • Input: arbitrary dimensional tensor \((*)\).

  • Target: arbitrary dimensional tensor \((*)\) same shape as input.

  • Output: a scalar.

Examples

>>> ones = torch.ones(1)
>>> criterion = PSNRLoss(2.)
>>> criterion(ones, 1.2 * ones) # 10 * log(4/((1.2-1)**2)) / log(10)
tensor(-20.0000)
class kornia.losses.BinaryFocalLossWithLogits(alpha, gamma=2.0, reduction='none')[source]

Criterion that computes Focal loss.

According to [LGG+18], the Focal loss is computed as follows:

\[\text{FL}(p_t) = -\alpha_t (1 - p_t)^{\gamma} \, \text{log}(p_t)\]
where:
  • \(p_t\) is the model’s estimated probability for each class.

Parameters
  • alpha) – Weighting factor for the rare class \(\alpha \in [0, 1]\).

  • gamma (float, optional) – Focusing parameter \(\gamma >= 0\). Default: 2.0

  • reduction (str, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. Default: 'none'

Shape:
  • Input: \((N, *)\).

  • Target: \((N, *)\).

Examples

>>> kwargs = {"alpha": 0.25, "gamma": 2.0, "reduction": 'mean'}
>>> loss = BinaryFocalLossWithLogits(**kwargs)
>>> input = torch.randn(1, 3, 5, requires_grad=True)
>>> target = torch.empty(1, 3, 5, dtype=torch.long).random_(2)
>>> output = loss(input, target)
>>> output.backward()