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：现有的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，但通常不显式保留数据中的拓扑特征。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以获得拓扑一致且正确的科学见解。本文提出TopoSZ——一种能够保持二维和三维标量场拓扑特征的误差有界有损压缩方法。具体而言，我们旨在保留局部极值的类型和位置，以及解压数据中等值线树所捕捉的临界点之间的水平集关系。核心思想是从数据域的等值线树诱导分割中推导拓扑约束，并将此类约束与经典SZ压缩器中定制的误差控制量化策略相结合。我们的方法允许用户通过全局误差界和持久性阈值，在压缩过程中控制逐点误差和拓扑特征的损失。