Atomic force microscopy (AFM) is an established technique in nanoscale grain analysis due to its accuracy in producing 3-dimensional images. Even though height threshold and watershed algorithms are commonly used to determine the grain size and number of grains, they mostly require image processing that result in the change of topographical features of the surface that generates misleading conclusions. In this study, we use persistent homology, a method of representing topological features, to obtain more accurate information about the granular surfaces from unprocessed AFM images than the conventional methods. The method is also useful as a robust alternative to common parameters describing the topography of the AFM images. Most of these parameters such as arithmetic roughness and root-mean-squared roughness are represented by a single number which results in uncertainty in characterization of different surfaces. Persistent homology provides more precise summary about surface properties than a single parameter.

中文翻译：

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通过持久同源性对原子力显微镜图像进行晶粒分析

原子力显微镜 (AFM) 是纳米级晶粒分析中的一项成熟技术，因为它可以准确地生成 3 维图像。尽管高度阈值和分水岭算法通常用于确定颗粒大小和颗粒数量，但它们大多需要图像处理，导致表面的地形特征发生变化，从而产生误导性结论。在这项研究中，我们使用持久同源性（一种表示拓扑特征的方法）从未经处理的 AFM 图像中获得比传统方法更准确的颗粒表面信息。该方法还可用作描述 AFM 图像地形的常用参数的可靠替代方法。大多数这些参数，例如算术粗糙度和均方根粗糙度，由单个数字表示，这导致不同表面表征的不确定性。与单个参数相比，持久同源性提供了关于表面特性的更精确的总结。