# GEOMetrics: Exploiting Geometric Structure for Graph-Encoded Objects

arXiv: https://arxiv.org/abs/1901.11461 · HTML: https://mlsanity.com/paper/1901.11461/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2019.

## Built on by (most cited first, 27 of 27)

- [Neural Wavelet-domain Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2209.08725/) (2022)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [Holistic 3D Scene Understanding from a Single Image with Implicit Representation](https://mlsanity.com/paper/2103.06422/) (2021)
- [Shelf-Supervised Mesh Prediction in the Wild](https://mlsanity.com/paper/2102.06195/) (2021)
- [SAIL-VOS 3D: A Synthetic Dataset and Baselines for Object Detection and 3D Mesh Reconstruction from Video Data](https://mlsanity.com/paper/2105.08612/) (2021)
- [Active 3D Shape Reconstruction from Vision and Touch](https://mlsanity.com/paper/2107.09584/) (2021)
- [Neural Template: Topology-aware Reconstruction and Disentangled Generation of 3D Meshes](https://mlsanity.com/paper/2206.04942/) (2022)
- [Vox2Cortex: Fast Explicit Reconstruction of Cortical Surfaces from 3D MRI Scans with Geometric Deep Neural Networks](https://mlsanity.com/paper/2203.09446/) (2022)
- [Neural Wavelet-domain Diffusion for 3D Shape Generation, Inversion, and Manipulation](https://mlsanity.com/paper/2302.00190/) (2023)
- [SurfGen: Adversarial 3D Shape Synthesis with Explicit Surface Discriminators](https://mlsanity.com/paper/2201.00112/) (2022)
- [Pixel2Mesh++: 3D Mesh Generation and Refinement from Multi-View Images](https://mlsanity.com/paper/2204.09866/) (2022)
- [Learning 3D Object Shape and Layout without 3D Supervision](https://mlsanity.com/paper/2206.07028/) (2022)
- [TouchSDF: A DeepSDF Approach for 3D Shape Reconstruction using Vision-Based Tactile Sensing](https://mlsanity.com/paper/2311.12602/) (2023)
- [Neural deformation fields for template-based reconstruction of cortical surfaces from MRI](https://mlsanity.com/paper/2401.12938/) (2024)
- [Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstruction](https://mlsanity.com/paper/2305.17555/) (2023)
- [CorticalFlow: A Diffeomorphic Mesh Deformation Module for Cortical Surface Reconstruction](https://mlsanity.com/paper/2206.02374/) (2022)
- [Neural Volumetric Mesh Generator](https://mlsanity.com/paper/2210.03158/) (2022)
- [Flow-based GAN for 3D Point Cloud Generation from a Single Image](https://mlsanity.com/paper/2210.04072/) (2022)
- [Graph Neural Networks in Computer Vision -- Architectures, Datasets and Common Approaches](https://mlsanity.com/paper/2212.10207/) (2022)
- [Absolute 3D Pose Estimation and Length Measurement of Severely Deformed Fish from Monocular Videos in Longline Fishing](https://mlsanity.com/paper/2102.04639/) (2021)
- [Deep Active Latent Surfaces for Medical Geometries](https://mlsanity.com/paper/2206.10241/) (2022)
- [Mastering Spatial Graph Prediction of Road Networks](https://mlsanity.com/paper/2210.00828/) (2022)
- [Learnable Triangulation for Deep Learning-based 3D Reconstruction of Objects of Arbitrary Topology from Single RGB Images](https://mlsanity.com/paper/2109.11844/) (2021)
- [Pruning-based Topology Refinement of 3D Mesh using a 2D Alpha Mask](https://mlsanity.com/paper/2210.09148/) (2022)
- [End-to-end Deformable Attention Graph Neural Network for Single-view Liver Mesh Reconstruction](https://mlsanity.com/paper/2303.07432/) (2023)
- [Deep-Motion-Net: GNN-based volumetric organ shape reconstruction from single-view 2D projections](https://mlsanity.com/paper/2407.06692/) (2024)
- [MeshCone: Second-Order Cone Programming for Geometrically-Constrained Mesh Enhancement](https://mlsanity.com/paper/2412.08484/) (2024)

## Abstract (arXiv)

Mesh models are a promising approach for encoding the structure of 3D objects. Current mesh reconstruction systems predict uniformly distributed vertex locations of a predetermined graph through a series of graph convolutions, leading to compromises with respect to performance or resolution. In this paper, we argue that the graph representation of geometric objects allows for additional structure, which should be leveraged for enhanced reconstruction. Thus, we propose a system which properly benefits from the advantages of the geometric structure of graph encoded objects by introducing (1) a graph convolutional update preserving vertex information; (2) an adaptive splitting heuristic allowing detail to emerge; and (3) a training objective operating both on the local surfaces defined by vertices as well as the global structure defined by the mesh. Our proposed method is evaluated on the task of 3D object reconstruction from images with the ShapeNet dataset, where we demonstrate state of the art performance, both visually and numerically, while having far smaller space requirements by generating adaptive meshes