Obtaining regional volume changes from a deformation field is more precise when using simplex counting (SC) compared with Jacobian integration (JI) due to the numerics involved in the latter. Although SC has been proposed before, numerical properties underpinning the method and a thorough evaluation of the method against JI is missing in the literature. The contributions of this paper are: (a) we propose surface propagation (SP)—a simplification to SC that significantly reduces its computational complexity; (b) we will derive the orders of approximation of SP which can also be extended to SC. In the experiments, we will begin by empirically showing that SP is indeed nearly identical to SC, and that both methods are more stable than JI in presence of moderate to large deformation noise. Since SC and SP are identical, we consider SP as a representative of both the methods for a practical evaluation against JI. In a real application on Alzheimer’s disease neuroimaging initiative data, we show the following: (a) SP produces whole brain and medial temporal lobe atrophy numbers that are significantly better than JI at separating between normal controls and Alzheimer’s disease patients; (b) SP produces disease group atrophy differences comparable to or better than those obtained using FreeSurfer, demonstrating the validity of the obtained clinical results. Finally, in a reproducibility study, we show that the voxel-wise application of SP yields significantly lower variance when compared to JI.