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

Deformable Voxel Grids for Shape Comparisons