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

TL;DR

TFZ is a novel compression framework that preserves the topology of 2D tensor fields, ensuring critical features remain intact during lossy compression for scientific visualization and analysis.

Contribution

The paper introduces TFZ, a topology-preserving compression method specifically designed for 2D symmetric and asymmetric tensor fields on flat meshes, addressing a key challenge in scientific data compression.

Findings

TFZ effectively preserves topological features during compression.

TFZ enhances existing compressors SZ3 and SPERR.

TFZ maintains global topological guarantees through local cell analysis.

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.