Rotation Averaging with the Chordal Distance: Global Minimizers and Strong Duality.

Area of Science:

• Computer Vision
• Optimization
• Robotics

Background:

• Rotation averaging is crucial for 3D reconstruction and SLAM.
• Existing methods struggle with non-convexity and achieving globally optimal solutions.
• Challenges include handling noise and large-scale datasets.

Purpose of the Study:

• To apply Lagrangian duality for solving rotation averaging problems.
• To achieve certifiably global solutions for non-convex rotation averaging.
• To develop an efficient and scalable algorithm for practical applications.

Main Methods:

• Utilizing Lagrangian duality to relax non-convex rotation constraints.
• Employing spectral graph theory to analytically prove the absence of a duality gap.
• Developing a novel, efficient, and parallelizable algorithm.

Main Results:

• Demonstrated that Lagrangian duality provides a tight relaxation for rotation averaging in many cases.
• Achieved certifiably global solutions in polynomial time.
• The proposed algorithm outperforms existing solvers on synthetic and real-world data, handling large instances.

Conclusions:

• Lagrangian duality offers a powerful approach to solve challenging non-convex rotation averaging problems.
• The developed method is efficient, scalable, and provides guarantees on solution optimality.
• This work advances the state-of-the-art in rotation averaging for computer vision applications.