提出一种高效图结构方法，保证图像分割的拓扑正确性。
Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentation
- 构建组件图编码预测与真实标签的拓扑信息
- 提出严格拓扑度量，实现同伦等价判断
- 计算速度比持久同调方法快五倍，适用多类分割
拓扑正确性在诸多图像分割任务中至关重要，但多数网络采用像素级损失函数（如Dice）训练，忽视拓扑准确性。现有拓扑感知方法常缺乏鲁棒的拓扑保障，仅适用于特定场景或计算开销高。本文提出一种新型图基框架，实现拓扑精确的图像分割，兼具高效性与通用性。该方法构建组件图，完整编码预测与真实标签的拓扑信息，可高效识别拓扑关键区域，并基于局部邻域信息聚合损失。同时引入严格拓扑度量，捕捉预测与标签对的并集和交集之间的同伦等价关系。我们形式化证明了方法的拓扑保证，并在二值及多类别数据集上实证其有效性。所提损失在性能上达到当前最优，且计算速度较持久同调方法提升最高达五倍。
原文摘要 · Abstract (English)
Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust topological guarantees, are limited to specific use cases, or impose high computational costs. In this work, we propose a novel, graph-based framework for topologically accurate image segmentation that is both computationally efficient and generally applicable. Our method constructs a component graph that fully encodes the topological information of both the prediction and ground truth, allowing us to efficiently identify topologically critical regions and aggregate a loss based on local neighborhood information. Furthermore, we introduce a strict topological metric capturing the homotopy equivalence between the union and intersection of prediction-label pairs. We formally prove the topological guarantees of our approach and empirically validate its effectiveness on binary and multi-class datasets. Our loss demonstrates state-of-the-art performance with up to fivefold faster loss computation compared to persistent homology methods.
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