# HyperFlow: Representing 3D Objects as Surfaces

arXiv: https://arxiv.org/abs/2006.08710 · HTML: https://mlsanity.com/paper/2006.08710/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 7 of 7)

- [Go with the Flows: Mixtures of Normalizing Flows for Point Cloud Generation and Reconstruction](https://mlsanity.com/paper/2106.03135/) (2021)
- [HyperPocket: Generative Point Cloud Completion](https://mlsanity.com/paper/2102.05973/) (2021)
- [InsertNeRF: Instilling Generalizability into NeRF with HyperNet Modules](https://mlsanity.com/paper/2308.13897/) (2023)
- [HyperCube: Implicit Field Representations of Voxelized 3D Models](https://mlsanity.com/paper/2110.05770/) (2021)
- [Modeling 3D Surface Manifolds with a Locally Conditioned Atlas](https://mlsanity.com/paper/2102.05984/) (2021)
- [3D objects and scenes classification, recognition, segmentation, and reconstruction using 3D point cloud data: A review](https://mlsanity.com/paper/2306.05978/) (2023)
- [HyperColor: A HyperNetwork Approach for Synthesizing Auto-colored 3D Models for Game Scenes Population](https://mlsanity.com/paper/2108.01411/) (2021)

## Abstract (arXiv)

In this work, we present HyperFlow - a novel generative model that leverages hypernetworks to create continuous 3D object representations in a form of lightweight surfaces (meshes), directly out of point clouds. Efficient object representations are essential for many computer vision applications, including robotic manipulation and autonomous driving. However, creating those representations is often cumbersome, because it requires processing unordered sets of point clouds. Therefore, it is either computationally expensive, due to additional optimization constraints such as permutation invariance, or leads to quantization losses introduced by binning point clouds into discrete voxels. Inspired by mesh-based representations of objects used in computer graphics, we postulate a fundamentally different approach and represent 3D objects as a family of surfaces. To that end, we devise a generative model that uses a hypernetwork to return the weights of a Continuous Normalizing Flows (CNF) target network. The goal of this target network is to map points from a probability distribution into a 3D mesh. To avoid numerical instability of the CNF on compact support distributions, we propose a new Spherical Log-Normal function which models density of 3D points around object surfaces mimicking noise introduced by 3D capturing devices. As a result, we obtain continuous mesh-based object representations that yield better qualitative results than competing approaches, while reducing training time by over an order of magnitude.