Advances in Global Solvers for 3D Vision

2026-02-16

AI Summary

This work addresses the challenge of certifiable global optimality in non-convex geometric optimization for 3D vision by systematically reviewing and unifying three global solver paradigms—Branch-and-Bound (BnB), Convex Relaxation (CR), and Graduated Non-Convexity (GNC)—across ten core tasks, including the Wahba problem and bundle adjustment. It establishes the first comprehensive taxonomy and unified framework for global optimization in 3D vision, elucidating the fundamental trade-offs among optimality, robustness, and scalability. The study further outlines a promising direction that integrates data-driven priors with certifiable optimization. By providing a trustworthy perception roadmap for safety-critical applications, this work also contributes an open-source, continuously updated survey and code tutorial to foster reproducibility and community advancement.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Global solvers have emerged as a powerful paradigm for 3D vision, offering certifiable solutions to nonconvex geometric optimization problems traditionally addressed by local or heuristic methods. This survey presents the first systematic review of global solvers in geometric vision, unifying the field through a comprehensive taxonomy of three core paradigms: Branch-and-Bound (BnB), Convex Relaxation (CR), and Graduated Non-Convexity (GNC). We present their theoretical foundations, algorithmic designs, and practical enhancements for robustness and scalability, examining how each addresses the fundamental nonconvexity of geometric estimation problems. Our analysis spans ten core vision tasks, from Wahba problem to bundle adjustment, revealing the optimality-robustness-scalability trade-offs that govern solver selection. We identify critical future directions: scaling algorithms while maintaining guarantees, integrating data-driven priors with certifiable optimization, establishing standardized benchmarks, and addressing societal implications for safety-critical deployment. By consolidating theoretical foundations, practical advances, and broader impacts, this survey provides a unified perspective and roadmap toward certifiable, trustworthy perception for real-world applications. A continuously-updated literature summary and companion code tutorials are available at https://github.com/ericzzj1989/Awesome-Global-Solvers-for-3D-Vision.

Problem

• global solvers
• 3D vision
• geometric optimization
• nonconvexity
• certifiable solutions

Innovation

• Global Solvers
• Certifiable Optimization
• Geometric Vision
• Nonconvex Optimization
• Robust 3D Perception