  Humans tend to build environments with structure, which consists of mainly
planar surfaces. From the intersection of planar surfaces arise straight lines.
Lines have more degrees-of-freedom than points. Thus, line-based
Structure-from-Motion (SfM) provides more information about the environment. In
this paper, we present solutions for SfM using lines, namely, incremental SfM.
These approaches consist of designing state observers for a camera's dynamical
visual system looking at a 3D line. We start by presenting a model that uses
spherical coordinates for representing the line's moment vector. We show that
this parameterization has singularities, and therefore we introduce a more
suitable model that considers the line's moment and shortest viewing ray.
Concerning the observers, we present two different methodologies. The first
uses a memory-less state-of-the-art framework for dynamic visual systems. Since
the previous states of the robotic agent are accessible -- while performing the
3D mapping of the environment -- the second approach aims at exploiting the use
of memory to improve the estimation accuracy and convergence speed. The two
models and the two observers are evaluated in simulation and real data, where
mobile and manipulator robots are used.
