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摘要翻译：
本文提出了一种基于拓扑控制的二维或三维规则网格标量数据有损压缩的新算法。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的概念（如拓扑特征）的保存，以便为后Hoc数据分析的结果提供保证。本文提出了第一种支持严格控制拓扑特征丢失的标量数据压缩技术。它为用户提供了特定的保证，既保证了重要特征的保存，又保证了压缩过程中被破坏的较小特征的大小。特别地，我们提出了一种基于拓扑自适应量化范围的简单压缩策略。我们的算法对输入数据和解压缩数据的持久化图之间的瓶颈距离提供了有力的保证，特别是与极值相关的持久化图。我们的策略的一个简单扩展还支持对逐点错误的控制。我们还展示了如何将我们的方法与最先进的压缩器相结合，以进一步改善几何重建。大量的实验表明，对于可比较的压缩比，我们的算法在保持拓扑特征方面的优越性。对于模拟或获取的数据集，我们通过说明在输入和解压缩数据上执行的post-hoc拓扑数据分析流水线的输出之间的兼容性来说明我们方法的效用。我们还提供了一个轻量级的基于VTK的C++实现，用于复制目的。
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英文标题：
《Topologically Controlled Lossy Compression》
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作者：
Maxime Soler and Melanie Plainchault and Bruno Conche and Julien
Tierny
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最新提交年份：
2018
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分类信息：
一级分类：Electrical Engineering and Systems Science 电气工程与系统科学
二级分类：Image and Video Processing 图像和视频处理
分类描述：Theory, algorithms, and architectures for the formation, capture, processing, communication, analysis, and display of images, video, and multidimensional signals in a wide variety of applications. Topics of interest include: mathematical, statistical, and perceptual image and video modeling and representation; linear and nonlinear filtering, de-blurring, enhancement, restoration, and reconstruction from degraded, low-resolution or tomographic data; lossless and lossy compression and coding; segmentation, alignment, and recognition; image rendering, visualization, and printing; computational imaging, including ultrasound, tomographic and magnetic resonance imaging; and image and video analysis, synthesis, storage, search and retrieval.
用于图像、视频和多维信号的形成、捕获、处理、通信、分析和显示的理论、算法和体系结构。感兴趣的主题包括：数学，统计，和感知图像和视频建模和表示；线性和非线性滤波、去模糊、增强、恢复和重建退化、低分辨率或层析数据；无损和有损压缩编码；分割、对齐和识别；图像渲染、可视化和打印；计算成像，包括超声、断层和磁共振成像；以及图像和视频的分析、合成、存储、搜索和检索。
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一级分类：Computer Science 计算机科学
二级分类：Computational Geometry 计算几何
分类描述：Roughly includes material in ACM Subject Classes I.3.5 and F.2.2.
大致包括ACM课程I.3.5和F.2.2中的材料。
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一级分类：Computer Science 计算机科学
二级分类：Computer Vision and Pattern Recognition 计算机视觉与模式识别
分类描述：Covers image processing, computer vision, pattern recognition, and scene understanding. Roughly includes material in ACM Subject Classes I.2.10, I.4, and I.5.
涵盖图像处理、计算机视觉、模式识别和场景理解。大致包括ACM课程I.2.10、I.4和I.5中的材料。
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一级分类：Computer Science 计算机科学
二级分类：Graphics 图形学
分类描述：Covers all aspects of computer graphics. Roughly includes material in all of ACM Subject Class I.3, except that I.3.5 is is likely to have Computational Geometry as the primary subject area.
涵盖了计算机图形学的各个方面。大致包括所有ACM课程I.3的材料，除了I.3.5可能有计算几何作为主要的学科领域。
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/1802.02731
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