As computed tomography and related technologies have become mainstream tools across a broad range of scientific applications, each new generation of instrumentation produces larger volumes of more-complex 3D data. Lagging behind are step-wise improvements in computational methods to rapidly analyze these new large, complex datasets. Here we describe novel computational methods to capture and quantify volumetric information, and to efficiently characterize and compare shape volumes. It is based on innovative theoretical and computational reformulation of volumetric computing. It consists of two theoretical constructs and their numerical implementation: the spherical wave decomposition (SWD), that provides fast, accurate automated characterization of shapes embedded within complex 3D datasets; and symplectomorphic registration with phase space regularization by entropy spectrum pathways (SYMREG), that is a non-linear volumetric registration method that allows homologous structures to be correctly warped to each other or a common template for comparison. Together, these constitute the Shape Analysis for Phenomics from Imaging Data (SAPID) method. We demonstrate its ability to automatically provide rapid quantitative segmentation and characterization of single unique datasets, and both inter-and intra-specific comparative analyses. We go beyond pairwise comparisons and analyze collections of samples from 3D data repositories, highlighting the magnified potential our method has when applied to data collections. We discuss the potential of SAPID in the broader context of generating normative morphologies required for meaningfully quantifying and comparing variations in complex 3D anatomical structures and systems.