Parallax Bundle Adjustment on Manifold with Convexified Initialization

TL;DR

This paper introduces an improved parallax bundle adjustment method on manifolds with a convexified initialization, enhancing convergence, accuracy, and robustness in diverse outdoor environments and motion modes.

Contribution

It extends parallax BA to the manifold domain with a new observation-ray based objective, and proposes a convex pose-graph initialization that guarantees near-optimal solutions.

Findings

PMBA achieves better convergence and accuracy.

The convex pose-graph provides a reliable initial guess.

The method performs well across diverse environments and motions.

Abstract

Bundle adjustment (BA) with parallax angle based feature parameterization has been shown to have superior performance over BA using inverse depth or XYZ feature forms. In this paper, we propose an improved version of the parallax BA algorithm (PMBA) by extending it to the manifold domain along with observation-ray based objective function. With this modification, the problem formulation faithfully mimics the projective nature in a camera's image formation, BA is able to achieve better convergence, accuracy and robustness. This is particularly useful in handling diverse outdoor environments and collinear motion modes. Capitalizing on these properties, we further propose a pose-graph simplification to PMBA, with significant dimensionality reduction. This pose-graph model is convex in nature, easy to solve and its solution can serve as a good initial guess to the original BA problem which is intrinsically non-convex. We provide theoretical proof that our global initialization strategy can guarantee a near-optimal solution. Using a series of experiments involving diverse environmental conditions and motions, we demonstrate PMBA's superior convergence performance in comparison to other BA methods. We also show that, without incremental initialization or via third-party information, our global initialization process helps to bootstrap the full BA successfully in various scenarios, sequential or out-of-order, including some datasets from the "Bundle Adjustment in the Large" database.