On the second order statistics of essential matrix elements

Abstract

In this paper, we investigate the second order statistics of essential matrix elements. Using the Taylor expansion for a rotation matrix up to second order terms and considering relatively high uncertainties for the rotation angles and translation parameters, a covariance matrix is obtained which includes the second order statistics of essential matrix elements. The covariance matrix is utilized along with the coplanarity equations and acts as a regularization term. Using the regularization term brings considerable improvements in the recovery of camera motion which will be proven based on simulation and different real image sequences.