Category cross entropy
\(L(gt, pr) = - gt \cdot \log(pr)\)
Jacard loss
\(L(A, B) = 1 - \frac{A \cap B}{A \cup B}
\)
dice loss
\(L(precision, recall) = 1 - (1 + \beta^2) \frac{precision \cdot recall}
{\beta^2 \cdot precision + recall}\)
\(L(tp, fp, fn) = \frac{(1 + \beta^2) \cdot tp} {(1 + \beta^2) \cdot fp + \beta^2 \cdot fn + fp}
\)
binary cross entropy loss
\(L(gt, pr) = - gt \cdot \log(pr) - (1 - gt) \cdot \log(1 - pr)
\)
Focal loss
\(L(gt, pr) = - gt \cdot \alpha \cdot (1 - pr)^\gamma \cdot \log(pr)\) (categorical)
\(L(gt, pr) = - gt \alpha (1 - pr)^\gamma \log(pr) - (1 - gt) \alpha pr^\gamma \log(1 - pr)
\) (binary)
jaccard_loss = JaccardLoss()
dice_loss = DiceLoss()
binary_focal_loss = BinaryFocalLoss()
categorical_focal_loss = CategoricalFocalLoss()
binary_crossentropy = BinaryCELoss()
categorical_crossentropy = CategoricalCELoss()
# loss combinations
bce_dice_loss = binary_crossentropy + dice_loss
bce_jaccard_loss = binary_crossentropy + jaccard_loss
cce_dice_loss = categorical_crossentropy + dice_loss
cce_jaccard_loss = categorical_crossentropy + jaccard_loss
binary_focal_dice_loss = binary_focal_loss + dice_loss
binary_focal_jaccard_loss = binary_focal_loss + jaccard_loss
categorical_focal_dice_loss = categorical_focal_loss + dice_loss
categorical_focal_jaccard_loss = categorical_focal_loss + jaccard_loss
\(Dice\ loss\ =\ 1\ -\ \frac{2\sum_{pixels}^{ }y_{_{true}}\ y_{_{pred}}}{\sum_{pixels}^{ }y_{true\ }^{ }\ +\ y_{pred}^{ }}\)