We propose a novel method to preserve key topological structures (extrema, saddles, separatrices, and persistence diagrams) associated with Morse Smale complexes in error-bounded lossy compressed scalar fields. Existing error bounded lossy compressors rarely consider preserving topological structures such as discrete Morse Smale complexes, leading to significant inaccuracies in data interpretation and potentially resulting in incorrect scientific conclusions. This paper mainly focuses on preserving the Morse-Smale complexes in 2D/3D discrete scalar fields by precisely preserving critical points (cells) and the separatrices that connect them. Our approach generates a series of (discrete) edits during compression time, which are applied to the decompressed data to accurately reconstruct the complexes while maintaining the error within prescribed bounds. We design a workflow that iteratively fixes critical cells and separatrices in alternating steps until convergence within finite iterations. Our approach addresses diverse application needs by offering users multitier options to balance compression efficiency and feature preservation. To enable effective integration with lossy compressors, we use GPU parallelism to enhance the performance of each workflow component. We conduct experiments on various datasets to demonstrate the effectiveness of our method in accurately preserving Morse-Smale complexes.

翻译：我们提出了一种新颖方法，用于在误差有界有损压缩的标量场中保持与Morse-Smale复形相关的关键拓扑结构（极值点、鞍点、分界线及持久性图）。现有的误差有界有损压缩器很少考虑保持离散Morse-Smale复形等拓扑结构，这导致数据解释存在显著误差，并可能引发错误的科学结论。本文主要关注通过精确保持临界点（胞腔）及连接它们的分界线，来保持二维/三维离散标量场中的Morse-Smale复形。我们的方法在压缩阶段生成一系列（离散）编辑操作，这些操作应用于解压后的数据，以在将误差维持在预设范围内的同时精确重建复形。我们设计了一个工作流程，通过交替步骤迭代修正临界胞腔和分界线，直至在有限迭代次数内收敛。该方法通过为用户提供多层选项来平衡压缩效率与特征保持能力，从而满足多样化的应用需求。为实现与有损压缩器的有效集成，我们利用GPU并行化提升各工作流组件的性能。我们在多个数据集上进行了实验，证明了本方法在精确保持Morse-Smale复形方面的有效性。