Research on Self Calibration Without Minimization

In this paper we present a new metric camera self-calibration algorithm that does not require the global minimization of an error function and can produce all legal solutions to the three-camera self-calibration problem in a single pass. By contrast, virtually all previous self-calibration algorithms rely on nonlinear global optimization unless special assumptions are made about the camera or its motion. The key drawback to global-optimizationbased methods is that, for nontrivial error functions, they can run indefinitely. Therefore, because our new algorithm produces all solutions quickly and in a fixed amount of time, it is arguably the fastest self-calibration algorithm in existence. In addition, our algorithm makes it possible to determine experimentally the number of solutions to the three-camera self-calibration problem; an upper-bound of 21 was given by Schaffilitzky [17], but our experiments show this number is more typically 1 or 2. Finally, because our algorithm runs very quickly and requires only the theoretical minimum of three camera views, it can be used in conjunction with RANSAC for great robustness to noise when more than three views are available. This work was partially sponsored by the National Science Foundation under Grant No. IIS-9988426 and by the Defense Advanced Research Projects Agency (DARPA) and Rome Laboratory, Air Force Materiel Command, USAF, under agreement number F3060297-1-0138.