vathos.model.loss

The Various Loss Functions that can be used with the model

Note

All the loss functions take the Logits as input, internally they will sigmoid the input perform their operations and then return the mean error

Segmentation Loss

class DiceLoss

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:

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

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

class BCEDiceLoss

Performs BCE and Dice Loss and adds them both

loss = bce_loss + 2 * dice_loss

class TverskyLoss(alpha: float, beta: float)

Performs Tversky Loss on Logits

According to [1], we compute the Tversky Coefficient as follows:

\[\text{S}(P, G, \alpha; \beta) = \frac{|PG|}{|PG| + \alpha |P \ G| + \beta |G \ P|}\]

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.

Notes

• \(\alpha = \beta = 0.5\) => dice coeff
• \(\alpha = \beta = 1\) => tanimoto coeff
• \(\alpha + \beta = 1\) => F beta coeff

Reference:

[1] https://kornia.readthedocs.io/en/latest/losses.html

class BCETverskyLoss

Performs BCE and Tversky Loss and adds them both

loss = bce_loss + 2 * tversky_loss

Depth Loss

class RMSELoss(eps=1e-06)

Performs RMSE Loss

we simply sigmoid the input, pass it through nn.MSELoss and then do a torch.sqrt on it

class BerHuLoss(threshold: float = 0.2)

Implementation of the BerHu Loss from [1]

\[ \begin{align}\begin{aligned}B(y, y') = (1/n) * |y' - y| if |y'-y| <= c\\B(y, y') = (1/n) * ( (y'-y)^2 + c^2 ) / 2*c othwerwise\\c = 1/5*max(|y'-y|)\end{aligned}\end{align} \]

[1] http://cs231n.stanford.edu/reports/2017/pdfs/203.pdf

[2] https://arxiv.org/abs/1207.6868

class GradLoss

Performs Gradient Loss

The Image XY Gradients are computed for input and target and the mean L1Loss between these gradients is returned

class SSIMLoss

Performs SSIM Loss

window sizes uses are 5x5 and 11x11

we tried adding other window sizes too, but there wasn’t a significant benefit

Note

we do ssim loss for various window sizes, add them and return the mean

class RMSEwSSIMLoss

Performs RMSE and SSIM Loss

loss = \(\sqrt{\text{ssim_loss} + 4\times \text{rmse_loss}}\)

Accuracy Functions

iou(outputs: torch.Tensor, labels: torch.Tensor)

rmse(outputs: torch.Tensor, labels: torch.Tensor)