Global Solvers for 3D Vision: Foundations, Frontiers, and a Call to the Robotics Community

Zhenjun Zhao, Javier Civera

Keywords: global optimization, certifiable algorithms, 3D vision, robotics, branch-and-bound, convex relaxation, graduated non-convexity

TL;DR: Global solvers for 3D vision are theoretically mature but underutilized—we map the landscape, identify open challenges, and invite the robotics community to close the gap.

Abstract: Global solvers for 3D vision, encompassing branch-and-bound, convex relaxation, and graduated non-convexity methods, provide something rare in modern robotics: certifiably optimal solutions to geometric estimation problems. Despite more than 60 years of theoretical development and demonstrated success across tasks ranging from the Wahba problem to bundle adjustment, these methods remain underutilized relative to their importance. This paper briefly presents the landscape of global solvers, identifies three fundamental open challenges, namely scalability, integration with deep learning, and standardized evaluation, and argues that the robotics optimization community is uniquely positioned to address them. As foundation models reshape 3D vision and safety-critical deployment demands grow, the need for certifiable geometric perception has never been more urgent. We invite the community to engage with this area. A continuously-updated literature summary and companion code tutorials are available at https://github.com/ericzzj1989/Awesome-Global-Solvers-for-3D-Vision.

Submission Number: 1