Is There Room for Improving Estimation Accuracy of the Structure and Motion Problem?

This paper discusses bounds for the accuracy of estimating camera poses and 3D scene structure from multiple images. In several applications in which accuracy is regarded as important, nonlinear optimization minimizing the so-called re-projection error is usually used, which corresponds to the maximum likelihood estimation under the assumption of some noise model. According to the recent results of Statistics, in such a case where the parameters to be estimated grows with the increase in the number of observations (the number of images or feature points in our case), simultaneously estimating all the parameters is not optimal and there is room for improving the estimation accuracy. In this paper we examine the possibility of improving the estimation accuracy in the structure and motion problem by adopting this theory. We conclude that the accuracy could not generally be improved in well-conditioned situations where the camera poses and the point distribution in space are uniform and not biased, and it can be improved in several ill-conditioned situations.