3D surface topography provides critical information about surface textures and has begun to be used in additive manufacturing applications such as in-situ 3D monitoring and sample porosity comparisons, etc. In this research, we establish a thorough framework to quantify the similarity of 3D surface topography measurements and determine whether they are from the same surface or not based on the frequency domain representations after 2D Fourier transformation. Two measurements portraying the same surface are defined as a matched pair while the others are unmatched. This framework quantifies the similarity effectively, provides a new perspective for surface topography similarity evaluation, and serves as a benchmark work in 3D surface topography feature extraction in the frequency domain. Our work has a great potential to benefit not only the quality assurance of AM but also many other communities where surface topography data is useful.

3D 表面形貌提供有关表面纹理的关键信息，并已开始用于增材制造应用，例如原位3D 监测和样品孔隙率比较等。在这项研究中，我们建立了一个完整的框架来量化 3D 表面形貌测量的相似性，并根据 2D 傅里叶变换后的频域表示确定它们是否来自同一表面。描绘同一表面的两个测量被定义为匹配对，而其他测量则不匹配。该框架有效地量化了相似度，为地表地形相似度评估提供了新的视角，并作为频域3D地表地形特征提取的基准工作。我们的工作不仅有利于 AM 的质量保证，而且有利于许多其他表面地形数据有用的社区。