标题： TFZ：二维对称和非对称二阶张量场的拓扑保持压缩 显示英文标题

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

摘要： 在本文中，我们提出了一种新的压缩框架TFZ，该框架保留了定义在平坦三角形网格上的二维对称和非对称二阶张量场的拓扑结构。 张量场为空间中的每个点分配一个张量——一个数字的多维数组。 如应力和应变张量以及黎曼曲率张量等张量场，在科学和工程中都是至关重要的。 张量场的拓扑结构捕捉了数据的核心结构，并在各种学科中很有用，例如图形学（用于操作形状和纹理）和神经科学（用于从扩散MRI分析大脑结构）。 有损数据压缩可能会扭曲张量场的拓扑结构，从而阻碍后续的分析和可视化任务。 TFZ确保在有损压缩过程中保留某些拓扑特征。 具体来说，TFZ保留对称张量场拓扑至关重要的退化点，并保留表示非对称张量场拓扑的特征向量和特征值图。 TFZ遍历每个单元，保留每个单元的局部拓扑结构，从而确保某些全局拓扑保证。 我们展示了我们的框架在增强有损科学数据压缩器SZ3和SPERR方面的有效性。 显示英文摘要

摘要： 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.