Grain analysis of atomic force microscopy images via persistent homology

Topological Data Analysis of Nanoscale Roughness in Brass Samples

Rough surfaces possess complex topographies, which cannot be characterized by a single parameter. The selection of appropriate roughness parameters depends on a particular application. Large datasets representing surface topography possess orderliness, which can be expressed in terms of topological features in high-dimensional dataspaces reflecting properties such as anisotropy and the number of lay directions. The features are scale-dependent because both sampling length and resolution affect them. We study nanoscale surface roughness using 3 × 3, 4 × 4, and 5 × 5 pixel patches obtained from atomic force microscopy (AFM) images of brass (Cu Zn alloy) samples roughened by a sonochemical treatment. We calculate roughness parameters, correlation length, extremum point distribution, persistence diagrams, and barcodes. These parameters of interest are discussed and compared.