发表机构
New Jersey Institute of Technology（新泽西理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究计算3D图像持久同调时噪声影响，通过分析多孔介质合成3D图像在噪声下的持久同调，比较多种拓扑测度，评估其对噪声和去噪过程的稳健性。
AI 中文摘要
在计算子/超水平集持久同调（PH）时，噪声的影响可能会引入数百万个（短暂存在的）拓扑生成元，这对大型3D图像的PH计算以及任何涉及生成元数量的PH分析都构成了障碍。因此，在计算PH之前通常需要对数据进行去噪。我们分析了存在空间不相关噪声时多孔介质合成3D图像的PH，并对各种拓扑测度（如瓶颈距离、瓦瑟斯坦距离、持久性统计和持久性图像）进行了比较分析，以评估它们对噪声和去噪过程（即添加空间不相关高斯噪声，以及通过高斯卷积或机器学习方法去噪）的稳健性。
英文摘要
When computing sub/super-level-set persistent homology (PH), the effect of noise may introduce millions of (short-lived) topological generators, presenting an obstacle to both the computation of PH of large 3D images, and any analysis of PH that incorporates the number of generators. As such, it is often necessary to denoise the data before computing its PH. We analyze the PH of synthetic 3D images of porous media in the presence of spatially uncorrelated noise, and perform a comparative analysis of various topological measures (e.g. bottleneck distance, Wasserstein distance, persistence statistics and persistence images) to assess their robustness to both noise and the denoising process (i.e. adding spatially uncorrelated Gaussian noise, and denoising by either a Gaussian convolution or a machine learning approach).
Comments25 pages
