Quantifying patterns in visual or tactile textures provides important information about the process or phenomena that generated these patterns. In manufacturing, these patterns can be intentionally introduced as a design feature, or they can be a byproduct of a specific process. Since surface texture has significant impact on the mechanical properties and the longevity of the workpiece, it is important to develop tools for quantifying surface patterns and, when applicable, comparing them to their nominal counterparts. While existing tools may be able to indicate the existence of a pattern, they typically do not provide more information about the pattern structure, or how much it deviates from a nominal pattern. Further, prior works do not provide automatic or algorithmic approaches for quantifying other pattern characteristics such as depths' consistency, and variations in the pattern motifs at different level sets. This paper leverages persistent homology from Topological Data Analysis (TDA) to derive noise-robust scores for quantifying motifs' depth and roundness in a pattern. Specifically, sublevel persistence is used to derive scores that quantify the consistency of indentation depths at any level set in Piezo Vibration Striking Treatment (PVST) surfaces. Moreover, we combine sublevel persistence with the distance transform to quantify the consistency of the indentation radii, and to compare them with the nominal ones. Although the tool in our PVST experiments had a semi-spherical profile, we present a generalization of our approach to tools/motifs of arbitrary shapes thus making our method applicable to other pattern-generating manufacturing processes.

翻译：量化视觉或触觉纹理中的图案，为生成这些图案的过程或现象提供了重要信息。在制造业中，这些图案可能是有意引入的设计特征，也可能是特定工艺的副产品。由于表面纹理对工件的机械性能和寿命具有显著影响，因此开发用于量化表面图案的工具，并在适用时将其与标称图案进行比较，显得尤为重要。现有工具虽能指示图案的存在，但通常无法提供关于图案结构或与标称图案偏差程度的更多信息。此外，以往研究未提供用于量化图案其他特征（如深度一致性及不同层次下图案模体的变化）的自动化或算法化方法。本文利用拓扑数据分析中的持续同调，推导出噪声鲁棒的分数，用于量化图案中模体的深度和圆度。具体而言，采用子水平集持续同调推导出得分，以量化压电振动冲击处理表面上任意水平集的压痕深度一致性。此外，我们将子水平集持续同调与距离变换相结合，以量化压痕半径的一致性，并将其与标称半径进行比较。尽管本实验中的压电振动冲击处理工具呈半球形轮廓，但我们提出了适用于任意形状工具/模体的泛化方法，从而使该方法可推广至其他生成图案的制造工艺。