# DC-Reg: Globally Optimal Point Cloud Registration via Tight Bounding with Difference of Convex Programming

arXiv: https://arxiv.org/abs/2603.25442 · HTML: https://mlsanity.com/paper/2603.25442/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 43 references that are in the map.
- First posted on arXiv 26 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [3D Registration with Maximal Cliques](https://mlsanity.com/paper/2305.10854/) (2023)
- [Guaranteed Outlier Removal for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/1711.10209/) (2017)
- [A Quaternion-based Certifiably Optimal Solution to the Wahba Problem with Outliers](https://mlsanity.com/paper/1905.12536/) (2019)
- [CLIPPER: A Graph-Theoretic Framework for Robust Data Association](https://mlsanity.com/paper/2011.10202/) (2020)
- [Block Coordinate Descent on Smooth Manifolds: Convergence Theory and Twenty-One Examples](https://mlsanity.com/paper/2305.14744/) (2023)
- [Deep Graph-based Spatial Consistency for Robust Non-rigid Point Cloud Registration](https://mlsanity.com/paper/2303.09950/) (2023)
- [Global Linear and Local Superlinear Convergence of IRLS for Non-Smooth Robust Regression](https://mlsanity.com/paper/2208.11846/) (2022)
- [A Concave Optimization Algorithm for Matching Partially Overlapping Point Sets](https://mlsanity.com/paper/1701.00951/) (2017)
- [Hybrid Trilinear and Bilinear Programming for Aligning Partially Overlapping Point Sets](https://mlsanity.com/paper/2101.07458/) (2021)

## Built on by (most cited first, 2 of 2)

- [A Differentiable Optimization Framework for Registering Sequential Bounding Boxes with Point Cloud Stream](https://mlsanity.com/paper/2609.34103/) (2026)
- [Rubix: Global Correspondence-Free Point Set Alignment through Assignment Geometry](https://mlsanity.com/paper/2610.10408/) (2026)

## Abstract (arXiv)

Achieving globally optimal point cloud registration under partial overlaps and large misalignments remains a fundamental challenge. While simultaneous transformation (boldsymbolθ) and correspondence (P) estimation has the advantage of being robust to nonrigid deformation, its non-convex coupled objective often leads to local minima for heuristic methods and prohibitive convergence times for existing global solvers due to loose lower bounds. To address this, we propose DC-Reg, a robust globally optimal framework that significantly tightens the Branch-and-Bound (BnB) search. Our core innovation is the derivation of a holistic concave underestimator for the coupled transformation-assignment objective, grounded in the Difference of Convex (DC) programming paradigm. Unlike prior works that rely on term-wise relaxations (e.g., McCormick envelopes) which neglect variable interplay, our holistic DC decomposition captures the joint structural interaction between boldsymbolθ and P. This formulation enables the computation of remarkably tight lower bounds via efficient Linear Assignment Problems (LAP) evaluated at the vertices of the search boxes. We validate our framework on 2D similarity and 3D rigid registration, utilizing rotation-invariant features for the latter to achieve high efficiency without sacrificing optimality. Experimental results on synthetic data and the 3DMatch benchmark demonstrate that DC-Reg achieves significantly faster convergence and superior robustness to extreme noise and outliers compared to state-of-the-art global techniques.