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Leveraging Persistence Image to Enhance Robustness and Performance in Curvilinear Structure Segmentation

Zhuangzhi Gao, Feixiang Zhou, He Zhao, Xiuju Chen, Xiaoxin Li, Qinkai Yu, Yitian Zhao, Alena Shantsila, Gregory Y. H. Lip, Eduard Shantsila, Yalin Zheng

TL;DR

This paper tackles robust segmentation of curvilinear medical structures by integrating topological information into deep networks. It introduces PIs-Regressor to approximate differentiable Persistence Images from images and Topology SegNet to fuse these features with image representations during both downsampling and upsampling. The method bypasses non-differentiable Persistence Diagrams and heavy topology-based losses, achieving state-of-the-art results on DRIVE, ER, and Optos in both pixel-level accuracy and topological fidelity, including reductions in Betti-number errors. The approach demonstrates enhanced robustness to challenging imaging conditions and offers a flexible framework that can be combined with other topology-based techniques.

Abstract

Segmenting curvilinear structures in medical images is essential for analyzing morphological patterns in clinical applications. Integrating topological properties, such as connectivity, improves segmentation accuracy and consistency. However, extracting and embedding such properties - especially from Persistence Diagrams (PD) - is challenging due to their non-differentiability and computational cost. Existing approaches mostly encode topology through handcrafted loss functions, which generalize poorly across tasks. In this paper, we propose PIs-Regressor, a simple yet effective module that learns persistence image (PI) - finite, differentiable representations of topological features - directly from data. Together with Topology SegNet, which fuses these features in both downsampling and upsampling stages, our framework integrates topology into the network architecture itself rather than auxiliary losses. Unlike existing methods that depend heavily on handcrafted loss functions, our approach directly incorporates topological information into the network structure, leading to more robust segmentation. Our design is flexible and can be seamlessly combined with other topology-based methods to further enhance segmentation performance. Experimental results show that integrating topological features enhances model robustness, effectively handling challenges like overexposure and blurring in medical imaging. Our approach on three curvilinear benchmarks demonstrate state-of-the-art performance in both pixel-level accuracy and topological fidelity.

Leveraging Persistence Image to Enhance Robustness and Performance in Curvilinear Structure Segmentation

TL;DR

This paper tackles robust segmentation of curvilinear medical structures by integrating topological information into deep networks. It introduces PIs-Regressor to approximate differentiable Persistence Images from images and Topology SegNet to fuse these features with image representations during both downsampling and upsampling. The method bypasses non-differentiable Persistence Diagrams and heavy topology-based losses, achieving state-of-the-art results on DRIVE, ER, and Optos in both pixel-level accuracy and topological fidelity, including reductions in Betti-number errors. The approach demonstrates enhanced robustness to challenging imaging conditions and offers a flexible framework that can be combined with other topology-based techniques.

Abstract

Segmenting curvilinear structures in medical images is essential for analyzing morphological patterns in clinical applications. Integrating topological properties, such as connectivity, improves segmentation accuracy and consistency. However, extracting and embedding such properties - especially from Persistence Diagrams (PD) - is challenging due to their non-differentiability and computational cost. Existing approaches mostly encode topology through handcrafted loss functions, which generalize poorly across tasks. In this paper, we propose PIs-Regressor, a simple yet effective module that learns persistence image (PI) - finite, differentiable representations of topological features - directly from data. Together with Topology SegNet, which fuses these features in both downsampling and upsampling stages, our framework integrates topology into the network architecture itself rather than auxiliary losses. Unlike existing methods that depend heavily on handcrafted loss functions, our approach directly incorporates topological information into the network structure, leading to more robust segmentation. Our design is flexible and can be seamlessly combined with other topology-based methods to further enhance segmentation performance. Experimental results show that integrating topological features enhances model robustness, effectively handling challenges like overexposure and blurring in medical imaging. Our approach on three curvilinear benchmarks demonstrate state-of-the-art performance in both pixel-level accuracy and topological fidelity.
Paper Structure (4 sections, 3 figures, 2 tables)

This paper contains 4 sections, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Experiments and Results
  4. Conclusion

Figures (3)

  • Figure 1: Illustration of the process for obtaining stable topological feature representations—specifically, the persistence image (PI) from segmentation results. The traditional pipeline, as depicted in (a) to (f), often suffers from issues such as non-differentiability and high computational cost.
  • Figure 2: Overview of the proposed framework. From top to bottom and left to right: (1) overall model diagram, (2) Topology SegNet architecture, (3) PIs-Regressor network for extracting persistence images, and (4) details of Topology SegNet during downsampling and upsampling
  • Figure 3: Visualization of segmentation results from different models on the DRIVE, ER, and Optos datasets.