A Self-calibration Bundle Adjustment Algorithm Based on Block Matrix Cholesky Decomposition Technology

Abstract

In this study, the problem of bundle adjustment was revisited, and a novel algorithm based on block matrix Cholesky decomposition was proposed to solve the thorny problem of self-calibration bundle adjustment. The innovation points are reflected in the following aspects: ① The proposed algorithm is not dependent on the Schur complement, and the calculation process is simple and clear; ② The complexities of time and space tend to O(n) in the context of world point number is far greater than that of images and cameras, so the calculation magnitude and memory consumption can be reduced significantly; ③ The proposed algorithm can carry out self-calibration bundle adjustment in single-camera, multi-camera, and variable-camera modes; ④ Some measures are employed to improve the optimization effects. Experimental tests showed that the proposed algorithm has the ability to achieve state-of-the-art performance in accuracy and robustness, and it has a strong adaptability as well, because the optimized results are accurate and robust even if the initial values have large deviations from the truth. This study could provide theoretical guidance and technical support for the image-based positioning and 3D reconstruction in the fields of photogrammetry, computer vision and robotics.

Keywords

• |bundle adjustment|self-calibration|block matrix|cholesky decomposition