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Polished brass alloy plate samples were treated by ultrasound in an alkaline buffer at different concentrations and sonication amplitudes. Sample topography was studied by atomic force microscopy and processed by algorithms of topological data analysis. Persistence diagrams, barcodes, autocorrelation functions, and spatial distribution of heights (min–max regions) were constructed. The isotropy/anisotropy of the surface, the level of roughness, and grain size distribution were analyzed for all samples. The brass alloy samples with various grain sizes can be useful as structured coatings with controlled bactericidal effects due to the presence of copper.