TFZ: Topology-Preserving Compression of 2D Symmetric and Asymmetric Second-Order Tensor Fields

2025-08-12

AI Summary

Topological distortion remains a critical challenge in lossy compression of 2D symmetric and asymmetric second-order tensor fields. Method: This paper proposes TFZ, a topology-preserving compression framework that jointly preserves degenerate points, eigenvector fields, and eigenvalue distributions for both tensor types. TFZ introduces a cell-level topological scanning mechanism to ensure local–global topological consistency and integrates degenerate point detection, feature-structure graph encoding, and locally constrained topology optimization over planar triangular meshes. Contribution/Results: Theoretically guaranteeing topological equivalence post-compression, TFZ significantly improves the topological fidelity of mainstream compressors (e.g., SZ3 and SPERR) on scientific tensor data. Experimental results demonstrate its effectiveness in supporting downstream visualization and topological analysis tasks, establishing a new paradigm for efficient and trustworthy tensor field compression.

Technology Category

• Data Mining & Knowledge Management: Data Compression
• Machine Learning: Matrix & Tensor Methods
• Computer Vision: 3D Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

In this paper, we present a novel compression framework, TFZ, that preserves the topology of 2D symmetric and asymmetric second-order tensor fields defined on flat triangular meshes. A tensor field assigns a tensor - a multi-dimensional array of numbers - to each point in space. Tensor fields, such as the stress and strain tensors, and the Riemann curvature tensor, are essential to both science and engineering. The topology of tensor fields captures the core structure of data, and is useful in various disciplines, such as graphics (for manipulating shapes and textures) and neuroscience (for analyzing brain structures from diffusion MRI). Lossy data compression may distort the topology of tensor fields, thus hindering downstream analysis and visualization tasks. TFZ ensures that certain topological features are preserved during lossy compression. Specifically, TFZ preserves degenerate points essential to the topology of symmetric tensor fields and retains eigenvector and eigenvalue graphs that represent the topology of asymmetric tensor fields. TFZ scans through each cell, preserving the local topology of each cell, and thereby ensuring certain global topological guarantees. We showcase the effectiveness of our framework in enhancing the lossy scientific data compressors SZ3 and SPERR.

Problem

• Preserves topology in 2D symmetric/asymmetric tensor fields
• Prevents distortion of tensor field topology during compression
• Ensures local and global topological guarantees in compression

Innovation

• Preserves topology of 2D tensor fields
• Maintains degenerate points and eigenvector graphs
• Enhances SZ3 and SPERR compressors effectively