Square Root Bundle Adjustment for Large-Scale Reconstruction

TL;DR

This paper introduces a square root bundle adjustment method that enhances numerical stability and speed for large-scale 3D reconstruction, especially suitable for single-precision computations.

Contribution

It presents a novel nullspace marginalization approach using QR decomposition, offering an algebraically equivalent but more stable and faster alternative to the Schur complement method.

Findings

Achieves comparable accuracy to double-precision Schur methods in single precision.

Runs significantly faster on large-scale problems.

Requires more memory on dense datasets.

Abstract

We propose a new formulation for the bundle adjustment problem which relies on nullspace marginalization of landmark variables by QR decomposition. Our approach, which we call square root bundle adjustment, is algebraically equivalent to the commonly used Schur complement trick, improves the numeric stability of computations, and allows for solving large-scale bundle adjustment problems with single-precision floating-point numbers. We show in real-world experiments with the BAL datasets that even in single precision the proposed solver achieves on average equally accurate solutions compared to Schur complement solvers using double precision. It runs significantly faster, but can require larger amounts of memory on dense problems. The proposed formulation relies on simple linear algebra operations and opens the way for efficient implementations of bundle adjustment on hardware platforms optimized for single-precision linear algebra processing.