# Context without Commitment: Robust Dense Correspondence under Non-Rigid Deformation

arXiv: https://arxiv.org/abs/2609.37071 · HTML: https://mlsanity.com/paper/2609.37071/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 25 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 19 of 19)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Point-BERT: Pre-training 3D Point Cloud Transformers with Masked Point Modeling](https://mlsanity.com/paper/2111.14819/) (2021)
- [Masked Autoencoders for Point Cloud Self-supervised Learning](https://mlsanity.com/paper/2203.06604/) (2022)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [CoFiNet: Reliable Coarse-to-fine Correspondences for Robust Point Cloud Registration](https://mlsanity.com/paper/2110.14076/) (2021)
- [PointDSC: Robust Point Cloud Registration using Deep Spatial Consistency](https://mlsanity.com/paper/2103.05465/) (2021)
- [FLOT: Scene Flow on Point Clouds Guided by Optimal Transport](https://mlsanity.com/paper/2007.11142/) (2020)
- [PointGPT: Auto-regressively Generative Pre-training from Point Clouds](https://mlsanity.com/paper/2305.11487/) (2023)
- [REGTR: End-to-end Point Cloud Correspondences with Transformers](https://mlsanity.com/paper/2203.14517/) (2022)
- [Lepard: Learning partial point cloud matching in rigid and deformable scenes](https://mlsanity.com/paper/2111.12591/) (2021)
- [GeoTransformer: Fast and Robust Point Cloud Registration with Geometric Transformer](https://mlsanity.com/paper/2308.03768/) (2023)
- [Non-rigid Point Cloud Registration with Neural Deformation Pyramid](https://mlsanity.com/paper/2205.12796/) (2022)
- [Robust-DefReg: A Robust Deformable Point Cloud Registration Method based on Graph Convolutional Neural Networks](https://mlsanity.com/paper/2306.04701/) (2023)
- [DefTransNet: A Transformer-based Method for Non-Rigid Point Cloud Registration in the Simulation of Soft Tissue Deformation](https://mlsanity.com/paper/2502.06336/) (2025)
- [DINE: Distance Is Not Enough -- Learning Global Deformation Priors for Robust Soft-Tissue Point Cloud Registration](https://mlsanity.com/paper/2607.14946/) (2026)

## Abstract (arXiv)

Non-rigid point-cloud registration aims to find the corresponding target point for each point on a deforming source surface. Point-level matching keeps the full target cloud available, but correspondence becomes ambiguous when different regions have similar local geometry. Regional or coarse-to-fine methods provide broader spatial context, but an incorrect regional match can exclude the correct correspondence before dense matching. We propose CoCo-Reg, which uses regional patches to enrich dense point features without allowing patch predictions to restrict the final point-level search. CoCo-Reg constructs farthest-point-sampled patches, exchanges geometric information within and between source and target, supervises patch similarity using identity-corrected point overlap, and projects the resulting regional information back to dense point features. The final registration stage still scores the full target cloud before global point-level candidate selection. On 726 held-out ModelNet10 objects across nine deformation levels, two established learning-based baselines obtain mean correspondence errors of 0.1993 and 0.1921, whereas CoCo-Reg obtains 0.0547. Relative to its point-level baseline, this is a 72.6% reduction. CoCo-Reg achieves lower correspondence error on 92.3% of paired test objects and reduces the mean fraction of points with error above 0.1 from 47.3% to 17.3%. Chamfer distance and HD95 decrease in the same direction, and CoCo-Reg remains lower across all tested deformation levels. These results support using regional context for dense non-rigid correspondence without imposing a hard patch-level restriction on the final search. Because evaluation uses one checkpoint per method, the reported gains characterize the complete systems rather than the isolated causal contribution of an individual component. Code will be made publicly available.