Power Variable Projection for Initialization-Free Large-Scale Bundle Adjustment

TL;DR

This paper introduces Power Variable Projection (PoVar), a scalable, initialization-free approach for large-scale bundle adjustment that leverages power series and Riemannian optimization, achieving state-of-the-art speed and accuracy.

Contribution

It extends variable projection with power series and Riemannian optimization to enable large-scale, initialization-free bundle adjustment.

Findings

Achieves state-of-the-art speed and accuracy on BAL dataset.

First method to address large-scale, initialization-free bundle adjustment.

Demonstrates scalability and effectiveness of PoVar approach.

Abstract

Most Bundle Adjustment (BA) solvers like the Levenberg-Marquardt algorithm require a good initialization. Instead, initialization-free BA remains a largely uncharted territory. The under-explored Variable Projection algorithm (VarPro) exhibits a wide convergence basin even without initialization. Coupled with object space error formulation, recent works have shown its ability to solve small-scale initialization-free bundle adjustment problem. To make such initialization-free BA approaches scalable, we introduce Power Variable Projection (PoVar), extending a recent inverse expansion method based on power series. Importantly, we link the power series expansion to Riemannian manifold optimization. This projective framework is crucial to solve large-scale bundle adjustment problems without initialization. Using the real-world BAL dataset, we experimentally demonstrate that our solver achieves state-of-the-art results in terms of speed and accuracy. To our knowledge, this work is the first to address the scalability of BA without initialization opening new venues for initialization-free structure-from-motion.