ITSRS: An Inverse Taylor Series Adaptive Loss Based on Synergized Regional-Structural Information for Medical Image Segmentation.

Medical image segmentation is fundamental for accurate diagnosis, treatment planning, and disease monitoring. The design of loss functions plays a central role in advancing medical image segmentation. Due to computing gradients across the entire image, global loss functions are susceptible to interference from irrelevant regions. In contrast, region-specific losses reduce such noise but risk fragmenting anatomical continuity by ignoring long-range structural relationships. Thus, we propose an Inverse Taylor Synergized Regional-Structural (ITSRS) Loss, which can address the above trade-off and adaptively obtain better hyperparameters to segment more accurately. Specifically, we design a Synergized Regional-Structural (SRS) loss function, which leverages overlapping local regions to preserve both regional specificity and global continuity in gradient propagation. Furthermore, we develop an Inverse Taylor-based (IT) adaptive mechanism to further improve SRS and form the ITSRS, which transforms higher-order error proportions through inverse Taylor expansion to adaptively balance false positives (FP) and false negatives (FN) via a cross-dependent weighting scheme. IT adaptive mechanism can also improve stability, responsiveness to imbalance, and fine-grained structural awareness. Across six medical image segmentation datasets, ITSRS shows generally improved performance; for example, on the Kvasir-SEG dataset, the mean Dice increases from 83.03 to 87.15%, while HD95 decreases from 6.826 to 6.464. Extensive experiments on six medical image datasets demonstrate that ITSRS consistently outperforms existing loss functions, yielding improved accuracy and robustness across varying modalities and tasks. The code for this paper is available at https://github.com/HanRu1/ITSRS .