Existing error-bounded lossy compression techniques control the pointwise error during compression to guarantee the integrity of the decompressed data. However, they typically do not explicitly preserve the topological features in data. When performing post hoc analysis with decompressed data using topological methods, preserving topology in the compression process to obtain topologically consistent and correct scientific insights is desirable. In this paper, we introduce TopoSZ, an error-bounded lossy compression method that preserves the topological features in 2D and 3D scalar fields. Specifically, we aim to preserve the types and locations of local extrema as well as the level set relations among critical points captured by contour trees in the decompressed data. The main idea is to derive topological constraints from contour-tree-induced segmentation from the data domain, and incorporate such constraints with a customized error-controlled quantization strategy from the classic SZ compressor.Our method allows users to control the pointwise error and the loss of topological features during the compression process with a global error bound and a persistence threshold.

翻译：现有误差有界有损压缩技术通过控制压缩过程中的逐点误差来保证解压数据的完整性，但通常未明确保持数据中的拓扑特征。当使用拓扑方法对解压数据进行事后分析时，希望在压缩过程中保持拓扑结构，从而获得拓扑一致且正确的科学洞察。本文提出TopoSZ——一种在二维和三维标量场中保持拓扑特征的误差有界有损压缩方法。具体而言，我们旨在解压数据中保持局部极值的类型与位置，以及由等高线树捕获的临界点之间的水平集关系。核心思想是从数据域的等高线树诱导分割中导出拓扑约束，并将此类约束与经典SZ压缩器中定制化的误差控制量化策略相结合。该方法允许用户通过全局误差界和持续阈值，在压缩过程中同时控制逐点误差与拓扑特征的损失。