Towards smoother surfaces by applying subdivision to voxel data

In computed tomography, the approximation quality of a scan of a physical object is typically limited by the acquisition modalities, especially the hardware including X-ray detectors. To improve upon this, we experiment with a three-dimensional subdivision scheme to increase the resolution of the reconstructed voxel data. Subdivision schemes are often used to refine two-dimensional manifolds (mostly meshes) leading to smoother surfaces. In this work, we apply a refinement scheme to three-dimensional data first, and only then, start the surface extraction process. Thus, the main subject of this work lies not on subdivision surfaces, but rather on subdivision volumes. In the volumetric case, each subdivision iteration consumes eight times more storage space than the previous one. Hence, we restrict ourselves to a single subdivision iteration. We evaluate the quality of the produced subdivision volumes using synthetic and industrial data. Furthermore, we consider manufacturing errors in the original and in the subdivision volumes, extract their surfaces, and compare the resulting meshes in critical regions. Observations show that our specific choice of a subdivision scheme produces smoothly interpolated data while also preserving edges.