Consistent and Optimal Triangulation: Analysis and Algorithms
In this paper, we investigate point localisation using multi-camera systems consisting of cameras with a finite number of pixels, under the assumption of known camera poses and error-free feature matching. We prove that, for any 2D multi-camera system and triangulation algorithm, the average localisation performance cannot asymptotically decay faster than quadratically as cameras are added to the system. Moreover, we show that consistent reconstruction algorithms achieve this error decay rate for uniformly spaced linear and circular camera arrays. We fully define what we mean by a consistent reconstruction algorithm and show that minimising the reprojection error measured with the l-infinity norm is consistent. In addition, we propose a new algorithm: SHARP, which is consistent and achieves the best possible localisation performance for any camera setup.
Record created on 2015-11-19, modified on 2016-08-09