Dimensionality Reduction for Information Geometric Characterization of Surface Topographies

Stochastic textures with features spanning many length scales arise in a range of contexts in physical and natural sciences, from nanostructures like synthetic bone to ocean wave height distributions and cosmic phenomena like inter-galactic cluster void distributions. Here we used a data set of 35 surface topographies, each of 2400×2400 pixels with spatial resolution between 4 and 7 μm per pixel, and fitted trivariate Gaussian distributions to represent their spatial structures. For these we computed pairwise information metric distances using the Fisher-Rao metric. Then dimensionality reduction was used to reveal the groupings among subsets of samples in an easily comprehended graphic in 3-space. The samples here came from the papermaking industry but such a reduction of large frequently noisy spatial data sets is useful in a range of materials and contexts at all scales.