Polynomial Dice Loss for Medical Image Segmentation

Region-based loss functions, such as the Dice loss, have established themselves as the de facto standard for highly class- and region-imbalanced segmentation tasks. However, models trained using region-based loss functions are notoriously miscalibrated and typically yield over-confident predictions. In medical imaging applications, such as defining tumor resection margins, this miscalibration is hindering clinical adoption. In this work, we outline a novel gradient perspective on this overconfidence and show how it affects region-based loss functions. We propose a "surgery" on the gradient vector field as a simple, yet effective intervention to mitigate calibration issues. This surgery adds a factor to the loss's partial derivative, scaling the gradient's magnitude linearly with the prediction error. In empirical evaluations across 2D and 3D medical segmentation tasks, we demonstrate the effectiveness of this intervention while maintaining high prediction accuracy when used in conjunction with any region-based loss function.

Instance-sensitive losses for semantic segmentation such as blob loss and CC loss were designed to address instance imbalance, ensuring small lesions generate the same gradient as large ones, but operate only on single-class segmentation. In multi-class settings, class imbalance poses an additional problem: rare classes with few instances receive a disproportionately small share of the training signal. We show that extending instance-sensitive losses to multi-class segmentation via a one-vs-rest class decomposition repurposes them to also address class imbalance, as uniform averaging over classes ensures each class contributes equally regardless of frequency. We further show that inverse-size weighting, which destabilizes training when applied globally due to weight imbalances across rare and common classes, becomes effective when integrated within the per-component loss, confining the reweighting to each component's spatial context. On the BraTS-METS 2025 dataset (260 test cases), multi-class CC loss improves foreground Dice (0.64 +/- 0.26 vs. 0.59 +/- 0.27 baseline) and rare-class Dice, while maintaining Panoptic Quality at DSC threshold 0.5. Multi-class blob loss achieves the best Panoptic Quality at threshold 0.5 (0.40 +/- 0.24 vs. 0.38 +/- 0.25 baseline) and recognition quality (0.53 +/- 0.29 vs. 0.49 +/- 0.30). Integrating inverse-size weighting within the per-component loss increases rare-class Dice to 0.44 +/- 0.36 at the cost of reduced detection quality.

Accurate image segmentation remains challenging, particularly in generating sharp, confident boundaries. While modern architectures have advanced the field, many of them still rely on standard loss functions like Cross-Entropy and Dice, which often neglect the discriminative structure of learned features, leading to inaccurate boundaries. This work introduces Deep Discriminant Analysis (DDA), a differentiable, architecture-agnostic loss function that embeds classical discriminant principles for network training. DDA explicitly maximizes between-class variance while minimizing within-class one, promoting compact and separable feature distributions without increasing inference cost. Evaluations on the DIS5K benchmark demonstrate that DDA consistently improves segmentation accuracy, boundary sharpness, and model confidence across various architectures. Our results show that integrating discriminant analysis offers a simple, effective path for building more robust segmentation models.