We introduce Deformable Voxel Grids (DVGs), an adaptation of Active Volumes for semi-automatic shape preprocessing. Intuitively, they deform the embedding space to a given shape in order to facilitate further shape processing and analysis, by means of shape-DVG registration.
A DVG is parameterized like a Topological Active Volume. It is a lattice V on the unit cube, evolving with an energy designed to smoothly embrace shape S. To compute the term of this energy which keeps the shape inside the grid, we approximate V with a dense ball covering, because each cell is hexahedral.

Once optimized, DVGs allow to express the shape in a local coordinates system, corresponding to a "cubification" of the shape. This accomplishes a shape normalization which, in turn, provides a proxy for various applications: dataset exploration, similarity search, deformations, approximation with quadrilaterals, and basic correspondences. We explain the intuition leading to these applications and sho, some results (in the abstract and in the supplementary material)