标题： 量化图像中Wasserstein度量的噪声敏感性 显示英文标题

标题： Quantifying the noise sensitivity of the Wasserstein metric for images

摘要： Wasserstein度量正越来越多地被用作将图像视为网格上的离散测度时的相似性评分，但其在噪声下的行为仍知之甚少。 在本工作中，我们考虑了有符号Wasserstein距离对像素级加性噪声的敏感性，并推导了非渐近上界。 在其他结果中，我们证明了有符号2-Wasserstein距离的误差与噪声标准差的平方根成比例，而欧几里得范数则成线性比例。 我们进行了支持理论结果的实验，并指出了一个奇特现象，即增加噪声水平可能会降低Wasserstein距离。 对冷冻电子显微镜图像的一个案例研究表明，即使欧几里得度量无法做到这一点，Wasserstein度量也可以保留几何结构。 显示英文摘要

摘要： Wasserstein metrics are increasingly being used as similarity scores for images treated as discrete measures on a grid, yet their behavior under noise remains poorly understood. In this work, we consider the sensitivity of the signed Wasserstein distance with respect to pixel-wise additive noise and derive non-asymptotic upper bounds. Among other results, we prove that the error in the signed 2-Wasserstein distance scales with the square root of the noise standard deviation, whereas the Euclidean norm scales linearly. We present experiments that support our theoretical findings and point to a peculiar phenomenon where increasing the level of noise can decrease the Wasserstein distance. A case study on cryo-electron microscopy images demonstrates that the Wasserstein metric can preserve the geometric structure even when the Euclidean metric fails to do so.