# Isomorphic mesh generation from point clouds with multilayer perceptrons

arXiv: https://arxiv.org/abs/2210.14157 · HTML: https://mlsanity.com/paper/2210.14157/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 79 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Builds on (most cited first, 30 of 44)

- [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)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [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)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Neural RGB-D Surface Reconstruction](https://mlsanity.com/paper/2104.04532/) (2021)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [OccuSeg: Occupancy-aware 3D Instance Segmentation](https://mlsanity.com/paper/2003.06537/) (2020)
- [SPLATNet: Sparse Lattice Networks for Point Cloud Processing](https://mlsanity.com/paper/1802.08275/) (2018)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [GSPN: Generative Shape Proposal Network for 3D Instance Segmentation in Point Cloud](https://mlsanity.com/paper/1812.03320/) (2018)
- [SDM-NET: Deep Generative Network for Structured Deformable Mesh](https://mlsanity.com/paper/1908.04520/) (2019)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [Learning Signed Distance Field for Multi-view Surface Reconstruction](https://mlsanity.com/paper/2108.09964/) (2021)
- [VV-Net: Voxel VAE Net with Group Convolutions for Point Cloud Segmentation](https://mlsanity.com/paper/1811.04337/) (2018)
- [Curriculum DeepSDF](https://mlsanity.com/paper/2003.08593/) (2020)
- [PointSIFT: A SIFT-like Network Module for 3D Point Cloud Semantic Segmentation](https://mlsanity.com/paper/1807.00652/) (2018)
- [Generative PointNet: Deep Energy-Based Learning on Unordered Point Sets for 3D Generation, Reconstruction and Classification](https://mlsanity.com/paper/2004.01301/) (2020)
- [Voxel2Mesh: 3D Mesh Model Generation from Volumetric Data](https://mlsanity.com/paper/1912.03681/) (2019)
- [Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks](https://mlsanity.com/paper/2006.13782/) (2020)

## Built on by (most cited first, 1 of 1)

- [Point Cloud to Mesh Reconstruction: Methods, Trade-offs, and Implementation Guide](https://mlsanity.com/paper/2412.10977/) (2024)

## Abstract (arXiv)

We propose a new neural network, called isomorphic mesh generator (iMG), which generates isomorphic meshes from point clouds containing noise and missing parts. Isomorphic meshes of arbitrary objects have a unified mesh structure even though the objects belong to different classes. This unified representation enables surface models to be handled by DNNs. Moreover, the unified mesh structure of isomorphic meshes enables the same process to be applied to all isomorphic meshes; although in the case of general mesh models, we need to consider the processes depending on their mesh structures. Therefore, the use of isomorphic meshes leads to efficient memory usage and calculation time compared with general mesh models. As iMG is a data-free method, preparing any point clouds as training data in advance is unnecessary, except a point cloud of the target object used as the input data of iMG. Additionally, iMG outputs an isomorphic mesh obtained by mapping a reference mesh to a given input point cloud. To estimate the mapping function stably, we introduce a step-by-step mapping strategy. This strategy achieves a flexible deformation while maintaining the structure of the reference mesh. From simulation and experiments using a mobile phone, we confirmed that iMG can generate isomorphic meshes of given objects reliably even when the input point cloud includes noise and missing parts.