Build 3D abstractions with wireframes

This chapter serves as an introduction to 3D representations of scenes or
Structure From Motion (SfM) from straight line segments. Lines are frequently
found in captures of man-made environments, and in nature are mixed with
more organic shapes. The inclusion of straight lines in 3D representations
provide structural information about the captured shapes and their limits,
such as the intersection of planar structures. Line based SfM methods are not
frequent in the literature due to the difficulty of detecting them reliably, their
morphological changes under changes of perspective and the challenges inher-
ent to finding correspondences of segments in images between the different
views. Additionally, compared to points, lines add the dimensionalities carried
by the line directions and lengths, which prevents the epipolar constraint
to be valid along a straight line segment between two different views. This
chapter introduces the geometrical relations which have to be exploited for SfM
sketch or abstraction based on line segments, the optimization methods for its
optimization, and how to compare the experimental results with Ground-Truth
measurements.