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

2024-09-25

arXiv.org

AI Summary

Existing error-bounded scalar field compression methods fail to faithfully preserve critical topological structures of the discrete Morse–Smale (MS) complex—such as extrema, saddle points, separatrices, and persistence diagrams—leading to inaccurate scientific interpretation. This paper introduces the first multi-level topology-preserving framework for error-constrained compression. It designs a reversible topological editing sequence grounded in discrete Morse theory, enabling joint correction of critical cells and separatrices within a bounded number of GPU-accelerated iterations. We further propose an error-aware localization and tracking mechanism to support user-controllable fidelity-compression trade-offs. Evaluated on 2D/3D scientific datasets under absolute error bounds of 1%–5%, our method achieves >98% recall of critical topological features, reduces separatrix geometric deviation by 76%, improves compression ratios by 1.8–3.2×, and maintains end-to-end real-time performance.

Technology Category

• Data Mining & Knowledge Management: Data Compression
• Machine Learning: Learning on the Edge & Model Compression
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• Preserve Morse-Smale complexes in lossy compression
• Maintain critical points and separatrices accurately
• Balance compression efficiency and topological feature preservation

Innovation

• Preserves Morse-Smale complexes in compression
• Uses iterative workflow for critical feature correction
• Leverages GPU parallelism for performance enhancement