Advances in Global Solvers for 3D Vision

TL;DR

This survey reviews global solvers in 3D vision, categorizing three main paradigms, analyzing their theoretical and practical aspects, and outlining future research directions for certifiable and scalable geometric estimation.

Contribution

It provides the first comprehensive taxonomy and analysis of global solvers in geometric vision, unifying theoretical foundations and practical implementations.

Findings

Analyzes three core paradigms: BnB, CR, GNC.

Examines solver performance across ten vision tasks.

Identifies key trade-offs and future research directions.

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.