We propose a DVC technique that is based on higher-order finite-element discretization of the displacement field and a global optimization procedure. We use curvature penalization to suppress non-physical fluctuations of the displacement field and resulting erroneous strain concentrations. The performance of the proposed method is compared to the commercial code Avizo using trabecular bone images and found to perform slightly better in most cases.

In addition, we stress that the performance of a DVC method needs to be evaluated using double scans (zero strain), virtual deformation (imposed deformation) and real deformation. Double scans give insight into the presence of noise and artifacts whereas virtual deformation benchmarks allows evaluation of the performance without noise and artifacts. Investigation of the performance for actual deformed heterogeneous materials is needed for evaluation with noise, artifacts and non-zero strains.

We show that both decreasing the resolution of the displacement field (increasing subvolume size) as well as (increasing) curvature penalization (regularization) have a similar effect on the performance of evaluated DVC methods:​ Decreasing the detrimental effect of noise, artifacts and interpolation errors, but also decreasing the sensitivity of a DVC method to displacement peaks, discontinuities and strain concentrations. The needed amount of regularization is a trade-off between accuracy and precision of the estimated strain fields and their resolution.

The obtainable accuracy and precision of the estimated displacement fields are influenced by interpolation errors in the DVC procedure and the relative amount of detail, noise and artifacts in the images. Errors in the displacement field are typically magnified during the strain calculation. Based on the tests and subvolume sizes (16–50 voxels) in this study, the expected order of magnitude of the accuracy and precision is 0.1 micro-voxels and 1 milli-voxels for the displacements and 0.1 and 1 milli-strains of the strain fields.