研究噪声对3D图像拓扑分析的影响，验证不同度量的鲁棒性。
Denoising 3D images: robustness of persistent homology measures
- 用多种拓扑度量对比噪声与去噪对3D图像分析的影响
- 发现持久同调度量在加噪后仍能保持稳定性能
- 适合做三维图像拓扑分析或去噪效果评估的研究者
在计算子/超水平集持久同调（PH）时，噪声会引入数百万个短暂存在的拓扑生成元，阻碍大规模3D图像的PH计算及基于生成元数量的分析。因此，计算PH前通常需去噪。本文分析了含空间不相关噪声的多孔介质合成3D图像的PH特性，比较了多种拓扑度量（如bottleneck距离、Wasserstein距离、持久性统计量和持久性图像）对噪声及去噪过程（包括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）的鲁棒性。
原文摘要 · Abstract (English)
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).
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