TD loss: Taylor expansion of Dice loss for robust medical image segmentation

Label noise poses significant challenges for medical image segmentation due to annotation subjectivity and intrinsic image complexity. To mitigate this issue, we propose TD loss, a noise-robust objective function derived from the Taylor expansion of the standard Dice loss. By decomposing the Dice loss into polynomial components, TD loss preserves the gradient characteristics of Dice loss while substantially enhancing robustness to noisy labels. Furthermore, we present an improved variant, TD loss₊, which employs a min-max optimization scheme to dynamically balance polynomial weights, thereby improving task adaptability. From a theoretical perspective, we establish the noise robustness of TD loss through a bounded risk difference analysis, proving its tolerance to both symmetric and asymmetric noise. Extensive experiments across four medical imaging datasets demonstrate that TD loss and its adaptive extension consistently outperform the original Dice loss under various noise conditions, achieving more robust segmentation results.