Understanding the displacement of granular beds under compaction is important for a range of industrial, geological and civil engineering applications. Such materials exhibit inhomogeneous internal displacements including strain localization, which mean that a method for the in situ evaluation of internal 3D displacement fields at high spatial resolutions would be a major development. This paper presents results from the compaction of a cylindrical bed of sugar, with diameter 7.0 mm and height 8.2 mm, using x-ray microtomography to evaluate the internal structure and digital volume correlation to calculate 3D displacement information from these data. In contrast to previous studies, which generally track a small number of marker particles, the research here uses the natural structure of the sugar to provide a random pattern for 3D image correlation, allowing full-field information to be captured. The results show good agreement when compared with a well-established 2D image correlation technique; moreover, they indicate structural features associated with deformation of granular materials that would not necessarily be observed in a 2D slice.