Thermal spray coatings are microscale coatings used to improve the surface properties of surfaces they are applied to. Statistical quantification can improve understanding of a thermal coating's microstructure; however, doing so in an automatic and autonomous manner from image data is non-trivial. A new methodology is developed to characterize thermal spray coatings from serial sectioning images (or other analogous image data) using manifold surfaces in higher dimensions, as well as associated operators on such data.