用于图像数据高效拓扑保持的稀疏立方复形

中文摘要 AI 辅助

持久同调（PH）是提取和保留图像数据拓扑信息的常用工具，尤其在拓扑结构保留至关重要的图像分割领域。然而，尽管PH在维度、领域和目标结构上具有普遍适用性，基于PH的方法的运行成本往往使其实际应用不可行。在本工作中，我们认为这种运行成本主要由处理对下游应用（如优化目标）不重要的信息所驱动。我们提出稀疏立方过滤作为PH计算的一种替代基础，在真实数据集上将后续计算成本降低高达100倍。我们展示了其与稠密对应物的优化信号高度一致，并在其他基于PH的目标实际无法运作的现实训练场景（即具有大块尺寸的3D数据）中，实证评估了我们解决方案作为优化目标的有效性。我们展示了我们的解决方案在六个不同数据集上将拓扑精度提高高达80%，同时保持基于像素和区域的精度。

英文摘要

Persistent homology (PH) is a frequently used tool for extracting and preserving topological information from image data, particularly in image segmentation, where preservation of topological structures is important. However, despite its general applicability across dimensionality, domains, and target structures, the runtime cost of PH-based methods often makes their practical use infeasible. In this work, we argue that this runtime cost is largely driven by processing information that is unimportant for downstream application (e.g. as optimization objective). We propose sparse cubical filtrations as an alternative foundation for PH computation, reducing subsequent computational costs by factors of up to 100 on real datasets. We show close agreement with the optimization signal of the dense counterpart and empirically evaluate our solution's effectiveness as an optimization objective in realistic training regimes where other PH-based objectives can practically not operate (i.e., 3D data with large patch sizes). We show how our solution improves topological accuracy by up to 80\% across six diverse datasets while maintaining pixel- and region-based accuracy.

发表机构

• Weill Cornell Medicine（威尔康奈尔医学院）
• Technical University of Munich（慕尼黑工业大学）
• Imperial College London（伦敦帝国理工学院）
• Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）
• Cornell Tech（康奈尔科技校区）
• Munich Data Science Institute（慕尼黑数据科学研究所）

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