Bound and Conquer: Improving Triangulation by Enforcing Consistency
This work addresses accuracy issues in 3D reconstruction for computer vision applications, presenting a theoretical analysis with incremental improvements over existing methods.
The paper tackles the problem of improving triangulation accuracy in multi-camera systems by analyzing error decay with respect to the number of cameras, showing that consistent algorithms achieve optimal quadratic error decay, which is faster than other methods.
We study the accuracy of triangulation in multi-camera systems with respect to the number of cameras. We show that, under certain conditions, the optimal achievable reconstruction error decays quadratically as more cameras are added to the system. Furthermore, we analyse the error decay-rate of major state-of-the-art algorithms with respect to the number of cameras. To this end, we introduce the notion of consistency for triangulation, and show that consistent reconstruction algorithms achieve the optimal quadratic decay, which is asymptotically faster than some other methods. Finally, we present simulations results supporting our findings. Our simulations have been implemented in MATLAB and the resulting code is available in the supplementary material.