# A2B: Anchor to Barycentric Coordinate for Robust Correspondence

arXiv: https://arxiv.org/abs/2306.02760 · HTML: https://mlsanity.com/paper/2306.02760/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 72 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [MegaDepth: Learning Single-View Depth Prediction from Internet Photos](https://mlsanity.com/paper/1804.00607/) (2018)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [DISK: Learning local features with policy gradient](https://mlsanity.com/paper/2006.13566/) (2020)
- [HPatches: A benchmark and evaluation of handcrafted and learned local descriptors](https://mlsanity.com/paper/1704.05939/) (2017)
- [YFCC100M: The New Data in Multimedia Research](https://mlsanity.com/paper/1503.01817/) (2015)
- [Kornia: an Open Source Differentiable Computer Vision Library for PyTorch](https://mlsanity.com/paper/1910.02190/) (2019)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [Working hard to know your neighbor's margins: Local descriptor learning loss](https://mlsanity.com/paper/1705.10872/) (2017)
- [Rethinking and Improving Relative Position Encoding for Vision Transformer](https://mlsanity.com/paper/2107.14222/) (2021)
- [COTR: Correspondence Transformer for Matching Across Images](https://mlsanity.com/paper/2103.14167/) (2021)
- [Learning to Find Good Correspondences](https://mlsanity.com/paper/1711.05971/) (2017)
- [Neighbourhood Consensus Networks](https://mlsanity.com/paper/1810.10510/) (2018)
- [Learning Two-View Correspondences and Geometry Using Order-Aware Network](https://mlsanity.com/paper/1908.04964/) (2019)
- [Patch2Pix: Epipolar-Guided Pixel-Level Correspondences](https://mlsanity.com/paper/2012.01909/) (2020)
- [MAGSAC: marginalizing sample consensus](https://mlsanity.com/paper/1803.07469/) (2018)
- [Learning to Match Features with Seeded Graph Matching Network](https://mlsanity.com/paper/2108.08771/) (2021)
- [ContextDesc: Local Descriptor Augmentation with Cross-Modality Context](https://mlsanity.com/paper/1904.04084/) (2019)
- [ClusterGNN: Cluster-based Coarse-to-Fine Graph Neural Network for Efficient Feature Matching](https://mlsanity.com/paper/2204.11700/) (2022)
- [Repeatability Is Not Enough: Learning Affine Regions via Discriminability](https://mlsanity.com/paper/1711.06704/) (2017)

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

- [Constraining Depth Map Geometry for Multi-View Stereo: A Dual-Depth Approach with Saddle-shaped Depth Cells](https://mlsanity.com/paper/2307.09160/) (2023)
- [Fast Full-frame Video Stabilization with Iterative Optimization](https://mlsanity.com/paper/2307.12774/) (2023)
- [Grid-Reg: Detector-Free Gridized Feature Learning and Matching for Large-Scale SAR-Optical Image Registration](https://mlsanity.com/paper/2507.04233/) (2025)

## Abstract (arXiv)

There is a long-standing problem of repeated patterns in correspondence problems, where mismatches frequently occur because of inherent ambiguity. The unique position information associated with repeated patterns makes coordinate representations a useful supplement to appearance representations for improving feature correspondences. However, the issue of appropriate coordinate representation has remained unresolved. In this study, we demonstrate that geometric-invariant coordinate representations, such as barycentric coordinates, can significantly reduce mismatches between features. The first step is to establish a theoretical foundation for geometrically invariant coordinates. We present a seed matching and filtering network (SMFNet) that combines feature matching and consistency filtering with a coarse-to-fine matching strategy in order to acquire reliable sparse correspondences. We then introduce DEGREE, a novel anchor-to-barycentric (A2B) coordinate encoding approach, which generates multiple affine-invariant correspondence coordinates from paired images. DEGREE can be used as a plug-in with standard descriptors, feature matchers, and consistency filters to improve the matching quality. Extensive experiments in synthesized indoor and outdoor datasets demonstrate that DEGREE alleviates the problem of repeated patterns and helps achieve state-of-the-art performance. Furthermore, DEGREE also reports competitive performance in the third Image Matching Challenge at CVPR 2021. This approach offers a new perspective to alleviate the problem of repeated patterns and emphasizes the importance of choosing coordinate representations for feature correspondences.