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.

Modern simulations and observations generate vast amounts of data, fueling a growing interest in replacing discrete data with continuous surrogate models, such as functional models and implicit neural networks, to enhance data storage, transfer, analysis, and visualization. To that end, kernel regression is a well-known class of non-parametric techniques useful for surrogate modeling. In this paper, we propose a new framework to use coresets for kernel regression-a small dataset that is used as a proxy for the original data-in scientific visualization. Using kernel regression as a surrogate for scientific data, we construct an optimized coreset that is both compact and highly accurate, reducing errors from randomly-sampled and grid-based coresets by orders of magnitude. We evaluate our framework on large spatial datasets and demonstrate that it incurs negligible error while preserving the underlying topological features.

Topological descriptors such as contour trees are widely utilized in scientific data analysis and visualization, with applications from materials science to climate simulations. It is desirable to preserve topological descriptors when data compression is part of the scientific workflow for these applications. However, classic error-bounded lossy compressors for volumetric data do not guarantee the preservation of topological descriptors, despite imposing strict pointwise error bounds. In this work, we introduce a general framework for augmenting any lossy compressor to preserve the topology of the data during compression. Specifically, our framework quantifies the adjustments (to the decompressed data) needed to preserve the contour tree and then employs a custom variable-precision encoding scheme to store these adjustments. We demonstrate the utility of our framework in augmenting classic compressors (such as SZ3, TTHRESH, and ZFP) and deep learning-based compressors (such as Neurcomp) with topological guarantees.