Deformable Voxel Grids for Shape Comparisons
This addresses shape analysis for 3D modeling and computer vision, but it is incremental as it builds on existing voxel grid and Free Form Deformation methods.
The paper tackles the problem of 3D shape comparison and processing by introducing Deformable Voxel Grids (DVGs), which deform to approximate shape silhouettes via energy-minimization, enabling applications like correspondences, style transfer, shape retrieval, and PCA deformations with some tasks running in minutes on modest hardware.
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.