  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.
