Proportional Error Back-Propagation (PEB): Real-Time Automatic Loop Closure Correction for Maintaining Global Consistency in 3D Reconstruction with Minimal Computational Cost

This paper introduces a robust, real-time loop closure correction technique for achieving global consistency in 3D reconstruction, whose underlying notion is to back-propagate the cumulative transformation error appearing while merging the pairs of consecutive frames in a sequence of shots taken by an RGB-D or depth camera. The proposed algorithm assumes that the starting frame and the last frame of the sequence roughly overlap. In order to verify the robustness and reliability of the proposed method, namely, Proportional Error Back- Propagation (PEB), it has been applied to numerous case-studies, which encompass a wide range of experimental conditions, including different scanning trajectories with reversely directed motions within them, and the results are presented. The main contribution of the proposed algorithm is its considerably low computational cost which has the possibility of usage in real-time 3D reconstruction applications. Also, neither manual input nor interference is required from the user, which renders the whole process automatic.