  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.
