ParallaxBA: bundle adjustment using parallax angle feature parametrization

Abstract

The main contribution of this paper is a novel feature parametrization based on parallax angles for bundle adjustment (BA) in structure and motion estimation from monocular images. It is demonstrated that under certain conditions, describing feature locations using their Euclidean XYZ coordinates or using inverse depth in BA leads to ill-conditioned normal equations as well as objective functions that have very small gradients with respect to some of the parameters describing feature locations. The proposed parallax angle feature parametrization in BA (ParallaxBA), avoids both of the above problems leading to better convergence properties and more accurate motion and structure estimates. Simulation and experimental datasets are used to demonstrate the impact of different feature parametrizations on BA, and the improved convergence, efficiency and accuracy of the proposed ParallaxBA algorithm when compared with some existing BA packages such as SBA, sSBA and g2o. The C/C++ source code of ParallaxBA is available on OpenSLAM (https://openslam.org/).

Application and Performance Analysis of a New Bundle Adjustment Model

“…In fact, ParallaxBA was proposed first in the field of computer vision instead of aerial photogrammetry (Zhao et al, 2015). This new BA model is merely a free-net BA model that cannot achieve geo-location for the triangulated tie points, so it fails in supporting some applications for location and mapping in photogrammetry (Yan et al, 2017).…”

“…As for the hard numerical matching between the radius vector of the elevation and the lateral parameters caused by Euclidean coordinates, a new BA model based on parallax angle feature parametrization, ParallaxBA, has recently been proposed (Zhao et al, 2015). This model can work without the consideration of the dimensional irrelevance between the elevation and the lateral parameters, and reduce the relative error of the radius vector.…”

“…This model can work without the consideration of the dimensional irrelevance between the elevation and the lateral parameters, and reduce the relative error of the radius vector. In many cases, normal BA based Euclidean XYZ feature Parametrization will lead to a result containing an ill-conditioned equation and an objective function with very small gradients under certain conditions, while the ParallaxBA can address these bottlenecks (Zhao et al, 2015). In this paper, the applications (especially in aerial photogrammetry) and the performance of the new BA model are discussed, and the convergence performance of the model is particularly analysed, since the divergence and the slow convergence speed is a problem studied for long in the aerial photogrammetry.…”

“…, which is the observation variable to be optimized −1 = weight of the feature point When given the initial values of all the variables 0 , the solution of the optimization can be finally transformed to the solution of the following formula (Zhao et al, 2015):…”

“…In this paper, these two solutions are also applied to verify the convergence performance of the new BA model. Since the applications and the performance of the BA model are focused and payed more attention here, the details and some other parts of the method are not introduced, and more can be referred from Zhao and Yan's work (Yan et al, 2017;Zhao et al, 2015).…”