We present a morphological analysis of atom probe data of nanoscale microstructural features, using methods developed by the astrophysics community to describe the shape of superclusters of galaxies. We describe second-phase regions using Minkowski functionals, representing the regions’ volume, surface area, mean curvature and Euler characteristic. The alloy data in this work show microstructures that can be described as sponge-like, filament-like, plate-like, and sphere-like at different concentration levels, and we find quantitative measurements of these features. To reduce user decision-making in constructing isosurfaces and to enhance the accuracy of the analysis a maximum likelihood based denoising filter was developed. We show that this filter performs significantly better than a simple Gaussian smoothing filter. We also interpolate the data using natural cubic splines, to refine voxel sizes and to refine the surface. We demonstrate that it is possible to find a mathematically well-defined, quantitative description of microstructure from atomistic datasets, to sub-voxel resolution, without user-tuneable parameters.