. 2024 Jan 29;11(2):130. doi: 10.3390/bioengineering11020130

Table 2.

Definitions of the examined losses along with their corresponding hyper-parameters, which were used in the process of training the 2D U-Net model for automatically delineating the spinal canal from WBDWI. TP = true positives, FP = false positives, FN = false negatives, y_n = true label for voxel n (0 = background, 1 = spinal canal), ${\hat{y}}_{n}$ = model-predicted label probability for voxel n.

Loss Name	Definition	Discussion
Log-cosh Dice	$L C D L = l n (c o s h (D L))$ $where D L = 1 - \frac{2 \cdot T P}{2 \cdot T P + F P + F N}$	This univariate transformation of the Dice loss, DL, has been suggested for improving medical image segmentation in the context of imbalanced distributions of labels [25].
Combo	$C L = D L - ω \frac{1}{N} \sum_{n = 1}^{N} y_{n} \cdot l n {\hat{y}}_{n}$ $+ (1 - y_{n}) \cdot l n (1 - {\hat{y}}_{n})$	A weighted sum of Dice and binary cross-entropy losses [26]. To identify the optimal weight $ω \in (0,1)$ between these two losses, training/validation of the U-Net model was compared using values of ω from 0 to 1 at increments of 0.1.
Tversky	$T L = 1 - \frac{T P}{T P + α \cdot F P + β \cdot F N}$	A generalised version of the Dice loss $(α = β = 0.5)$ , this loss provides more nuanced balancing between a requirement for high sensitivity $(α > β)$ or precision $(α < β)$ . The best trade-off was investigated by varying the values of α and β, from 0 to 1 with an increment of 0.1 [27].
Focal Tversky	$F T L = {T L}^{γ}$	A further generalisation of the Tversky loss, this loss employs a third parameter γ, which controls the non-linearity of the loss. In class-imbalanced data, small-scale segmentations might result in a high TL score; however, γ > 0 causes a higher gradient loss, forcing the model to focus on harder examples (small regions of interest that do not contribute to the loss significantly) [28]. We varied γ from 1 to 3 with an increment of 0.1 to determine the optimal value.