Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Wei Lian, Fei Ma, Hang Pan, Zhesen Cui, Wangmeng Zuo

Abstract

Achieving globally optimal point cloud registration under partial overlaps and large misalignments remains a fundamental challenge. While simultaneous transformation ($\boldsymbolθ$) and correspondence ($\mathbf{P}$) 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 $\mathbf{P}$. 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.

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

Abstract

Achieving globally optimal point cloud registration under partial overlaps and large misalignments remains a fundamental challenge. While simultaneous transformation () and correspondence () 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 and . 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.

Paper Structure

This paper contains 17 sections, 12 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology: The DC-Reg Framework
  4. General Bounding Operation
  5. Branch-and-Bound Algorithm
  6. Applications
  7. Case I: 2D Similarity Registration
  8. Case II: Efficient 3D Registration via RIFs
  9. Implementation Details
  10. Experiments and Results
  11. 2D Registration Experiments
  12. 2D Synthetic Data Analysis
  13. 2D Real-World Image Registration
  14. 3D Registration
  15. Evaluation on 3D Synthetic Data
  16. ...and 2 more sections

Figures (6)

  • Figure 1: obain concave underestimator $m_{ij}$ of $E_{ij}$ via DC decomposition and linearization of the convex term.
  • Figure 2: Pointwise minimum of concave functions is a concave function.
  • Figure 3: a) to (c): source point sets and examples of target point sets in the deformation and noise tests, respectively. (d) to (i): Examples of source and target point sets in the mixed outliers and inliers test ((d), (e)), separate outliers and inliers test ((f), (g)), and occlusion+outlier test ((h), (i)), respectively. In all cases, source points are indicated by red circles, while scene points are represented by blue crosses.
  • Figure 6: (a) Source images with source point sets superimposed. (b) For each category: target images with target point sets superimposed, registration results by DC-Reg, RPM-HTB LIAN2023126482, RPM-PA lian2021polyhedral and RPM-CAV RPM_model_occlude_PR using similarity transformation. The $n_p$ value for each method is chosen as $0.9$ the minimum of the cardinalities of two point sets.
  • Figure 7: (a) to (c): Source point sets and examples of target point sets in the deformation and noise tests, respectively. (d) to (i): Examples of source and target point sets in the mixed outliers and inliers test ((d), (e)), separate outliers and inliers test ((f), (g)), and occlusion+outlier test ((h), (i)), respectively. In all cases, source points are indicated by red circles, while target points are represented by blue crosses.
  • ...and 1 more figures