Multi-Tier Preservation of Discrete Morse Smale Complexes in Error-Bounded Lossy Compression

Abstract: 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.