Topologically Controlled Lossy Compression
Topologically Controlled Lossy Compression
复制标题
拓扑控制有损压缩
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Julien Tierny
中科院分区：
文献类型：
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作者：
Maxime Soler;Mélanie Plainchault;B. Conche;Julien Tierny
本文提出了一种对二维或三维规则网格上的标量数据进行有损压缩的新算法。某些技术允许用户控制由压缩引起的逐点误差。然而，在许多情况下，希望以类似的方式控制更高级别概念（如拓扑特征）的保留，以便为事后数据分析的结果提供保证。本文提出了第一个压缩技术的标量数据，支持严格控制的拓扑特征的损失。它为用户提供了关于重要特征的保留和在压缩期间破坏的较小特征的大小的具体保证。特别是，我们提出了一个简单的压缩策略的基础上的拓扑自适应量化的范围。我们的算法提供了强有力的保证之间的瓶颈距离持久性图表的输入和解压数据，特别是那些与极值。我们的策略的一个简单的扩展还可以控制逐点错误。我们还展示了如何将我们的方法与最先进的压缩机联合收割机相结合，以进一步改善几何重建。大量的实验，可比的压缩率，证明了我们的算法在拓扑特征的保存方面的优越性。我们展示了我们的方法的实用性，说明事后拓扑数据分析管道的输出之间的兼容性，执行输入和解压数据，模拟或采集的数据集。我们还提供了一个轻量级的基于VTK的C++实现我们的方法用于再现的目的。
This paper presents a new algorithm for the lossy compression of scalar data defined on 2D or 3D regular grids, with topological control. Certain techniques allow users to control the pointwise error induced by the compression. However, in many scenarios it is desirable to control in a similar way the preservation of higher-level notions, such as topological features, in order to provide guarantees on the outcome of post-hoc data analyses. This paper presents the first compression technique for scalar data which supports a strictly controlled loss of topological features. It provides users with specific guarantees both on the preservation of the important features and on the size of the smaller features destroyed during compression. In particular, we present a simple compression strategy based on a topologically adaptive quantization of the range. Our algorithm provides strong guarantees on the bottleneck distance between persistence diagrams of the input and decompressed data, specifically those associated with extrema. A simple extension of our strategy additionally enables a control on the pointwise error. We also show how to combine our approach with state-of-the-art compressors, to further improve the geometrical reconstruction. Extensive experiments, for comparable compression rates, demonstrate the superiority of our algorithm in terms of the preservation of topological features. We show the utility of our approach by illustrating the compatibility between the output of post-hoc topological data analysis pipelines, executed on the input and decompressed data, for simulated or acquired data sets. We also provide a lightweight VTK-based C++ implementation of our approach for reproduction purposes.