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A Physics-Informed Loss Function for Boundary-Consistent and Robust Artery Segmentation in DSA Sequences

Muhammad Irfan, Nasir Rahim, Khalid Mahmood Malik

TL;DR

This work tackles cerebral artery segmentation in dynamic DSA sequences and introduces a Physics-Informed Loss (PIL) that models boundary interaction as an elastic energy between the predicted and ground-truth contours, improving boundary coherence and robustness across architectures. PIL is formulated as an energy term $\mathcal{L}_{EI}$ and computed efficiently with FFT, enabling plug-and-play integration into existing networks without architectural changes. Evaluations on DIAS and DSCA show consistent improvements over conventional losses across U-Net, U-Net++, SegFormer, and MedFormer, with MedFormer + PIL delivering the strongest performance and boundary coherence. The study demonstrates that physics-informed boundary regularization can enhance both precision and robustness in vascular segmentation for dynamic angiographic imaging and provides open-source code for reproducibility.

Abstract

Accurate extraction and segmentation of the cerebral arteries from digital subtraction angiography (DSA) sequences is essential for developing reliable clinical management models of complex cerebrovascular diseases. Conventional loss functions often rely solely on pixel-wise overlap, overlooking the geometric and physical consistency of vascular boundaries, which can lead to fragmented or unstable vessel predictions. To overcome this limitation, we propose a novel \textit{Physics-Informed Loss} (PIL) that models the interaction between the predicted and ground-truth boundaries as an elastic process inspired by dislocation theory in materials physics. This formulation introduces a physics-based regularization term that enforces smooth contour evolution and structural consistency, allowing the network to better capture fine vascular geometry. The proposed loss is integrated into several segmentation architectures, including U-Net, U-Net++, SegFormer, and MedFormer, and evaluated on two public benchmarks: DIAS and DSCA. Experimental results demonstrate that PIL consistently outperforms conventional loss functions such as Cross-Entropy, Dice, Active Contour, and Surface losses, achieving superior sensitivity, F1 score, and boundary coherence. These findings confirm that the incorporation of physics-based boundary interactions into deep neural networks improves both the precision and robustness of vascular segmentation in dynamic angiographic imaging. The implementation of the proposed method is publicly available at https://github.com/irfantahir301/Physicsis_loss.

A Physics-Informed Loss Function for Boundary-Consistent and Robust Artery Segmentation in DSA Sequences

TL;DR

This work tackles cerebral artery segmentation in dynamic DSA sequences and introduces a Physics-Informed Loss (PIL) that models boundary interaction as an elastic energy between the predicted and ground-truth contours, improving boundary coherence and robustness across architectures. PIL is formulated as an energy term and computed efficiently with FFT, enabling plug-and-play integration into existing networks without architectural changes. Evaluations on DIAS and DSCA show consistent improvements over conventional losses across U-Net, U-Net++, SegFormer, and MedFormer, with MedFormer + PIL delivering the strongest performance and boundary coherence. The study demonstrates that physics-informed boundary regularization can enhance both precision and robustness in vascular segmentation for dynamic angiographic imaging and provides open-source code for reproducibility.

Abstract

Accurate extraction and segmentation of the cerebral arteries from digital subtraction angiography (DSA) sequences is essential for developing reliable clinical management models of complex cerebrovascular diseases. Conventional loss functions often rely solely on pixel-wise overlap, overlooking the geometric and physical consistency of vascular boundaries, which can lead to fragmented or unstable vessel predictions. To overcome this limitation, we propose a novel \textit{Physics-Informed Loss} (PIL) that models the interaction between the predicted and ground-truth boundaries as an elastic process inspired by dislocation theory in materials physics. This formulation introduces a physics-based regularization term that enforces smooth contour evolution and structural consistency, allowing the network to better capture fine vascular geometry. The proposed loss is integrated into several segmentation architectures, including U-Net, U-Net++, SegFormer, and MedFormer, and evaluated on two public benchmarks: DIAS and DSCA. Experimental results demonstrate that PIL consistently outperforms conventional loss functions such as Cross-Entropy, Dice, Active Contour, and Surface losses, achieving superior sensitivity, F1 score, and boundary coherence. These findings confirm that the incorporation of physics-based boundary interactions into deep neural networks improves both the precision and robustness of vascular segmentation in dynamic angiographic imaging. The implementation of the proposed method is publicly available at https://github.com/irfantahir301/Physicsis_loss.

Paper Structure

This paper contains 11 sections, 5 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Proposed Method
  3. Conventional Approaches to DNN Optimization
  4. Energy Interaction--Based Loss Optimization
  5. Efficient Computation of the Elastic Loss
  6. Experiments
  7. Dataset
  8. Experimental Setup
  9. Benchmark Comparison and Discussion
  10. Comparison with SOTA Methods
  11. Conclusion

Figures (1)

  • Figure 1: Qualitative comparison with state-of-the-art segmentation networks, where M1 denotes Attention-UNet, M2 denotes TransAttUNet, M3 represents AGNR, and M4 corresponds to the proposed MedFormer integrated with the Physics-Informed Loss (PIL). The results clearly highlight the enhanced vascular structure delineation achieved by the proposed MedFormer + PIL framework.