Bundle Adjustment with Implicit Structure Modeling Using a Direct Linear Transform

Abstract

Bundle adjustment (BA) is considered to be the “golden standard” optimisation technique for multiple-view reconstruction over decades of research. The technique simultaneously tunes camera parameters and scene structure to fit a nonlinear function, in a way that the discrepancy between the observed scene points and their reprojections are minimised in a least-squares manner. Computational feasibility and numerical conditioning are two major concerns of todays BA implementations, and choosing a proper parametrization of structure in 3D space could dramatically improve numerical stability, convergence speed, and cost of evaluating Jacobian matrices. In this paper we study several alternative representations of 3D structure and propose an implicit modeling approach based on a Direct Linear Transform (DLT) estimation. The performances of a variety of parametrization techniques are evaluated using simulated visual odometry scenarios. Experimental results show that the computational cost and convergence speed is further improved to achieve similar accuracy without explicit adjustment over the structure parameters.