# HyperCube: Implicit Field Representations of Voxelized 3D Models

arXiv: https://arxiv.org/abs/2110.05770 · HTML: https://mlsanity.com/paper/2110.05770/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 43 references that are in the map.
- First posted on arXiv 12 Oct 2021.

## Builds on (most cited first, 28 of 28)

- [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)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Learning Gradient Fields for Shape Generation](https://mlsanity.com/paper/2008.06520/) (2020)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)
- [Learning a Predictable and Generative Vector Representation for Objects](https://mlsanity.com/paper/1603.08637/) (2016)
- [Learning Efficient Point Cloud Generation for Dense 3D Object Reconstruction](https://mlsanity.com/paper/1706.07036/) (2017)
- [Hierarchical Surface Prediction for 3D Object Reconstruction](https://mlsanity.com/paper/1704.00710/) (2017)
- [Generative Models as Distributions of Functions](https://mlsanity.com/paper/2102.04776/) (2021)
- [OctNetFusion: Learning Depth Fusion from Data](https://mlsanity.com/paper/1704.01047/) (2017)
- [SurfNet: Generating 3D shape surfaces using deep residual networks](https://mlsanity.com/paper/1703.04079/) (2017)
- [SCORES: Shape Composition with Recursive Substructure Priors](https://mlsanity.com/paper/1809.05398/) (2018)
- [Hypernetwork approach to generating point clouds](https://mlsanity.com/paper/2003.00802/) (2020)
- [HyperPocket: Generative Point Cloud Completion](https://mlsanity.com/paper/2102.05973/) (2021)
- [HyperFlow: Representing 3D Objects as Surfaces](https://mlsanity.com/paper/2006.08710/) (2020)
- [Fast and Stable Interval Bounds Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1906.00628/) (2019)
- [Modeling 3D Surface Manifolds with a Locally Conditioned Atlas](https://mlsanity.com/paper/2102.05984/) (2021)

## Built on by (most cited first, 4 of 4)

- [HyperDet3D: Learning a Scene-conditioned 3D Object Detector](https://mlsanity.com/paper/2204.05599/) (2022)
- [Spelunking the Deep: Guaranteed Queries on General Neural Implicit Surfaces via Range Analysis](https://mlsanity.com/paper/2202.02444/) (2022)
- [Points2NeRF: Generating Neural Radiance Fields from 3D point cloud](https://mlsanity.com/paper/2206.01290/) (2022)
- [Continual Learning with Guarantees via Weight Interval Constraints](https://mlsanity.com/paper/2206.07996/) (2022)

## Abstract (arXiv)

Recently introduced implicit field representations offer an effective way of generating 3D object shapes. They leverage implicit decoder trained to take a 3D point coordinate concatenated with a shape encoding and to output a value which indicates whether the point is outside the shape or not. Although this approach enables efficient rendering of visually plausible objects, it has two significant limitations. First, it is based on a single neural network dedicated for all objects from a training set which results in a cumbersome training procedure and its application in real life. More importantly, the implicit decoder takes only points sampled within voxels (and not the entire voxels) which yields problems at the classification boundaries and results in empty spaces within the rendered mesh. To solve the above limitations, we introduce a new HyperCube architecture based on interval arithmetic network, that enables direct processing of 3D voxels, trained using a hypernetwork paradigm to enforce model convergence. Instead of processing individual 3D samples from within a voxel, our approach allows to input the entire voxel (3D cube) represented with its convex hull coordinates, while the target network constructed by a hypernet assigns it to an inside or outside category. As a result our HyperCube model outperforms the competing approaches both in terms of training and inference efficiency, as well as the final mesh quality.