Deformable Voxel Grids for Shape Comparisons

TL;DR

This paper introduces Deformable Voxel Grids (DVGs), a novel shape representation that adapts to geometry for improved comparison, deformation, and processing of 3D shapes without extensive learning.

Contribution

The paper proposes DVGs as a new shape embedding that deforms to fit silhouettes, enabling intuitive shape manipulation and efficient shape analysis tasks.

Findings

DVGs outperform regular voxel grids in shape embedding quality.

Shape correspondences and style transfer can be achieved without learning.

PCA on DVGs allows simple shape deformations with few parameters.

Abstract

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.