# Joint Deep Multi-Graph Matching and 3D Geometry Learning from Inhomogeneous 2D Image Collections

arXiv: https://arxiv.org/abs/2103.17229 · HTML: https://mlsanity.com/paper/2103.17229/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 68 references that are in the map.
- First posted on arXiv 31 Mar 2021.

## Builds on (most cited first, 20 of 20)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Keep it SMPL: Automatic Estimation of 3D Human Pose and Shape from a Single Image](https://mlsanity.com/paper/1607.08128/) (2016)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [Unsupervised Learning of Probably Symmetric Deformable 3D Objects from Images in the Wild](https://mlsanity.com/paper/1911.11130/) (2019)
- [MoFA: Model-based Deep Convolutional Face Autoencoder for Unsupervised Monocular Reconstruction](https://mlsanity.com/paper/1703.10580/) (2017)
- [i3DMM: Deep Implicit 3D Morphable Model of Human Heads](https://mlsanity.com/paper/2011.14143/) (2020)
- [Learning Combinatorial Embedding Networks for Deep Graph Matching](https://mlsanity.com/paper/1904.00597/) (2019)
- [Deep Graph Matching Consensus](https://mlsanity.com/paper/2001.09621/) (2020)
- [Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching](https://mlsanity.com/paper/1911.11308/) (2019)
- [Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers](https://mlsanity.com/paper/2003.11657/) (2020)
- [FML: Face Model Learning from Videos](https://mlsanity.com/paper/1812.07603/) (2018)
- [Multi-Image Matching via Fast Alternating Minimization](https://mlsanity.com/paper/1505.04845/) (2015)
- [A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching](https://mlsanity.com/paper/1612.05476/) (2016)
- [Probabilistic Permutation Synchronization using the Riemannian Structure of the Birkhoff Polytope](https://mlsanity.com/paper/1904.05814/) (2019)
- [Higher-order Projected Power Iterations for Scalable Multi-Matching](https://mlsanity.com/paper/1811.10541/) (2018)
- [DS*: Tighter Lifting-Free Convex Relaxations for Quadratic Matching Problems](https://mlsanity.com/paper/1711.10733/) (2017)
- [Synchronisation of Partial Multi-Matchings via Non-negative Factorisations](https://mlsanity.com/paper/1803.06320/) (2018)
- [Multi-Image Semantic Matching by Mining Consistent Features](https://mlsanity.com/paper/1711.07641/) (2017)

## Built on by (most cited first, 3 of 3)

- [FIRe: Fast Inverse Rendering using Directional and Signed Distance Functions](https://mlsanity.com/paper/2203.16284/) (2022)
- [Universe Points Representation Learning for Partial Multi-Graph Matching](https://mlsanity.com/paper/2212.00780/) (2022)
- [Unsupervised Deep Graph Matching Based on Cycle Consistency](https://mlsanity.com/paper/2307.08930/) (2023)

## Abstract (arXiv)

Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based on deep graph matching formulations. While these approaches mainly focus on learning node and edge attributes, they completely ignore the 3D geometry of the underlying 3D objects depicted in the 2D images. We fill this gap by proposing a trainable framework that takes advantage of graph neural networks for learning a deformable 3D geometry model from inhomogeneous image collections, i.e.,~a set of images that depict different instances of objects from the same category. Experimentally, we demonstrate that our method outperforms recent learning-based approaches for graph matching considering both accuracy and cycle-consistency error, while we in addition obtain the underlying 3D geometry of the objects depicted in the 2D images.