  We present Deformable Voxel Grids (DVGs) for 3D shapes comparison and
processing. It consists of a voxel grid which is deformed to approximate the
silhouette of a shape, via energy-minimization. By interpreting the DVG as a
local coordinates system, it provides a better embedding space than a regular
voxel grid, since it is adapted to the geometry of the shape. It also allows to
deform the shape by moving the control points of the DVG, in a similar manner
to the Free Form Deformation, but with easier interpretability of the control
points positions. After proposing a computation scheme of the energies
compatible with meshes and pointclouds, we demonstrate the use of DVGs in a
variety of applications: correspondences via cubification, style transfer,
shape retrieval and PCA deformations. The first two require no learning and can
be readily run on any shapes in a matter of minutes on modest hardware. As for
the last two, they require to first optimize DVGs on a collection of shapes,
which amounts to a pre-processing step. Then, determining PCA coordinates is
straightforward and brings a few parameters to deform a shape.
