Precise and robust whole brain, ventricle, and hippocampal atrophy measurements are important as they serve as biomarkers for Alzheimer’s disease. They are used as secondary outcomes in drug trials, and they correlate with the cognitive scores. When two successive scans are non-linearly aligned by registration, the volume change in a region of interest (ROI) is typically computed by Jacobian integration (JI), volumetric meshing (VM), or surface based methods like surface triangulation (ST) or surface flux (SF). JI and VM offer the possibility of a voxel-by-voxel atrophy measure for visualization or localization of atrophy and subsequent summing to an ROI measure of atrophy. ST and SF only offer whole ROI atrophy measures. JI and SF suffer from a lack of precision originating from respectively approximating a space and a time integral by a finite sum. VM suffers from a high computational burden and the ST from the lack of localization. In this paper we present the cube propagation (CP) algorithm having numerical precision as VM, offering the localization as JI and VM, but computational simplicity as the ST and SF. We demonstrate superior numerical precision to the the commonly used JI.