Optical Coherence Tomography Angiography (OCTA) is a novel, non-invasive imaging modality of retinal capillaries at micron resolution. While OCTA generates 3D image volumes, current analytic methods rely on 2D en face projection images for quantitative analysis. This obscures the 3D vascular geometry and prevents accurate characterization of retinal vessel networks. In this paper, we have developed an automated analysis framework that preserves the 3D geometry of OCTA data. This framework uses curvelet-based denoising, optimally oriented flux (OOF) vessel enhancement and projection artifact removal, as well as the generation of 3D vessel length from the Hamilton-Jacobi skeleton. We implement this method on a dataset of 338 OCTA scans from human subjects with diabetic retinopathy (DR) which is known to cause decrease in capillary density and compare them to healthy controls. Our results indicate that 3D vessel-skeleton-length (3D-VSL) captures differences in both superficial and deep capillary density that are not apparent in 2D vessel skeleton analyses. In statistical analysis, we show that the 3D small-vessel-skeleton-length (3D-SVSL), which is computed after the removal of the large vessels and associated projection artifacts, provides a novel metric to detect group differences between healthy controls and progressive stages of DR.This work was supported in part by NIH grants UH3NS100614, R21EY027879, U01EY025864, K08EY027006, P41EB015922, P30EY029220, Research to Prevent Blindness, and UL1TR001855 and UL1TR000130 from the National Center for Advancing Translational Science (NCATS) of the U.S. National Institutes of Health.