  Given 2D point correspondences between an image pair, inferring the camera
motion is a fundamental issue in the computer vision community. The existing
works generally set out from the epipolar constraint and estimate the essential
matrix, which is not optimal in the maximum likelihood (ML) sense. In this
paper, we dive into the original measurement model with respect to the rotation
matrix and normalized translation vector and formulate the ML problem. We then
propose a two-step algorithm to solve it: In the first step, we estimate the
variance of measurement noises and devise a consistent estimator based on bias
elimination; In the second step, we execute a one-step Gauss-Newton iteration
on manifold to refine the consistent estimate. We prove that the proposed
estimate owns the same asymptotic statistical properties as the ML estimate:
The first is consistency, i.e., the estimate converges to the ground truth as
the point number increases; The second is asymptotic efficiency, i.e., the mean
squared error of the estimate converges to the theoretical lower bound --
Cramer-Rao bound. In addition, we show that our algorithm has linear time
complexity. These appealing characteristics endow our estimator with a great
advantage in the case of dense point correspondences. Experiments on both
synthetic data and real images demonstrate that when the point number reaches
the order of hundreds, our estimator outperforms the state-of-the-art ones in
terms of estimation accuracy and CPU time.
