Relative Camera Pose Recovery and Scene Reconstruction with the Essential Matrix in a Nutshell

This paper intends to present and analyze all the necessary steps one needs to take in order to build a simple application for relative pose structure from motion using only the epipolar constraint. In other words, to illustrate in practice (i.e,, cook-book style) about how the most fundamental of concepts in epipolar geometry can be combined into a complete and disambiguated series of steps for camera motion estimation and 3D reconstruction in a relatively simple computer program. In particular, the essential matrix is defined with respect to the algebraic interpretation of the rotation matrix, in order to eliminate ambiguities with respect to how relative orientation is extracted from the epipolar constraint. Based on the latter formulation, we list the prominent properties of the essential matrix with proofs to provide necessary intuition into the series of derivations that ultimately lead to the recovery of the orientation and baseline vector.