# Dual Geometric Graph Network (DG2N) -- Iterative network for deformable shape alignment

arXiv: https://arxiv.org/abs/2011.14723 · HTML: https://mlsanity.com/paper/2011.14723/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2020.

## Built on by (most cited first, 30 of 35)

- [Diffusion 3D Features (Diff3F): Decorating Untextured Shapes with Distilled Semantic Features](https://mlsanity.com/paper/2311.17024/) (2023)
- [Unsupervised Point Cloud Representation Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2202.13589/) (2022)
- [SCOOP: Self-Supervised Correspondence and Optimization-Based Scene Flow](https://mlsanity.com/paper/2211.14020/) (2022)
- [Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2303.10971/) (2023)
- [SE-ORNet: Self-Ensembling Orientation-aware Network for Unsupervised Point Cloud Shape Correspondence](https://mlsanity.com/paper/2304.05395/) (2023)
- [Point2SSM: Learning Morphological Variations of Anatomies from Point Cloud](https://mlsanity.com/paper/2305.14486/) (2023)
- [Denoising Functional Maps: Diffusion Models for Shape Correspondence](https://mlsanity.com/paper/2503.01845/) (2025)
- [Hierarchical Neural Semantic Representation for 3D Semantic Correspondence](https://mlsanity.com/paper/2509.17431/) (2025)
- [Implicit field supervision for robust non-rigid shape matching](https://mlsanity.com/paper/2203.07694/) (2022)
- [Non-Rigid Shape Registration via Deep Functional Maps Prior](https://mlsanity.com/paper/2311.04494/) (2023)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [DV-Matcher: Deformation-based Non-Rigid Point Cloud Matching Guided by Pre-trained Visual Features](https://mlsanity.com/paper/2408.08568/) (2024)
- [Unsupervised Template-assisted Point Cloud Shape Correspondence Network](https://mlsanity.com/paper/2403.16412/) (2024)
- [SAS: Segment Any 3D Scene with Integrated 2D Priors](https://mlsanity.com/paper/2503.08512/) (2025)
- [Point2SSM++: Self-Supervised Learning of Anatomical Shape Models from Point Clouds](https://mlsanity.com/paper/2405.09707/) (2024)
- [Surface-Aware Distilled 3D Semantic Features](https://mlsanity.com/paper/2503.18254/) (2025)
- [Weakly Supervised Bayesian Shape Modeling from Unsegmented Medical Images](https://mlsanity.com/paper/2405.09697/) (2024)
- [Deformation-Guided Unsupervised Non-Rigid Shape Matching](https://mlsanity.com/paper/2311.15668/) (2023)
- [Learning SO(3)-Invariant Semantic Correspondence via Local Shape Transform](https://mlsanity.com/paper/2404.11156/) (2024)
- [Symmetry Understanding of 3D Shapes via Chirality Disentanglement](https://mlsanity.com/paper/2508.05505/) (2025)
- [Deep Confidence Guided Distance for 3D Partial Shape Registration](https://mlsanity.com/paper/2201.11379/) (2022)
- [Learning Canonical Embeddings for Unsupervised Shape Correspondence with Locally Linear Transformations](https://mlsanity.com/paper/2209.02152/) (2022)
- [Equivariant Local Reference Frames for Unsupervised Non-rigid Point Cloud Shape Correspondence](https://mlsanity.com/paper/2404.00959/) (2024)
- [Mesh2SSM++: A Probabilistic Framework for Unsupervised Learning of Statistical Shape Model of Anatomies from Surface Meshes](https://mlsanity.com/paper/2502.07145/) (2025)
- [NF3DM: Combining Neural Fields and Deformation Models for 3D Non-Rigid Motion Reconstruction](https://mlsanity.com/paper/2412.08511/) (2024)
- [SAMBLE: Shape-Specific Point Cloud Sampling for an Optimal Trade-Off Between Local Detail and Global Uniformity](https://mlsanity.com/paper/2504.19581/) (2025)
- [Hyper-Network Neural Functional Maps for Unsupervised Robust 3D Shape Matching](https://mlsanity.com/paper/2606.30131/) (2026)
- [Temporally-Consistent Surface Reconstruction using Metrically-Consistent Atlases](https://mlsanity.com/paper/2111.06838/) (2021)
- [NFR: Neural Feature-Guided Non-Rigid Shape Registration](https://mlsanity.com/paper/2505.22445/) (2025)
- [Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided Approach](https://mlsanity.com/paper/2509.06862/) (2025)

## Abstract (arXiv)

We provide a novel new approach for aligning geometric models using a dual graph structure where local features are mapping probabilities. Alignment of non-rigid structures is one of the most challenging computer vision tasks due to the high number of unknowns needed to model the correspondence. We have seen a leap forward using DNN models in template alignment and functional maps, but those methods fail for inter-class alignment where nonisometric deformations exist. Here we propose to rethink this task and use unrolling concepts on a dual graph structure - one for a forward map and one for a backward map, where the features are pulled back matching probabilities from the target into the source. We report state of the art results on stretchable domains alignment in a rapid and stable solution for meshes and cloud of points.