Epipolar geometry in practice: 3D runtime odometry with a web-camera

This paper intends to present and analyze all the necessary steps one needs to
take in order to build a simple application for structure from motion in
practice using only the epipolar constraint. In other words, toillustratein
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 re-introduced in
order to avoid misconceptions regarding the nature of the rotation matrix and
translation between two camera positions during consequent computations.
Strictly based on the formulation of the essential matrix in this paper, the most
important of its properties are given with proofs, merely to provide necessary
intuition into the series of derivations that ultimately lead to the recovery of the
orientation and baseline vector (up-to-scale). Finally, an application that
performs 3D position tracking of a simple web-camera is implemented (and
source code made available) in order to demonstrate the practical value of the
essential matrix with only a few of assumptions loosely in place (still
background and relatively reliable point tracking).