# Deformable Voxel Grids for Shape Comparisons

arXiv: https://arxiv.org/abs/2211.11609 · HTML: https://mlsanity.com/paper/2211.11609/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 21 Nov 2022.

## Builds on (most cited first, 9 of 9)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Composite Shape Modeling via Latent Space Factorization](https://mlsanity.com/paper/1901.02968/) (2019)
- [DeformNet: Free-Form Deformation Network for 3D Shape Reconstruction from a Single Image](https://mlsanity.com/paper/1708.04672/) (2017)
- [ALIGNet: Partial-Shape Agnostic Alignment via Unsupervised Learning](https://mlsanity.com/paper/1804.08497/) (2018)

## Abstract (arXiv)

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.