Abstract
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 inherent 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.
Highlights
Line based Structure from Motion methods based on lines create an abstraction based on straight line segments from a set of images
The 3D line abstraction methods based on straight line segments that are most frequently found in the literature are designed to work altogether with detailed point-based reconstructions [1], employing the camera extrinsic parameters obtained from these point rotation and translation invariants
In order to prove the validity of a 3D abstraction method, it has to be benchmarked against a Ground Truth dataset for Structure From Motion (SfM), which includes both intrinsic and extrinsic parameters for the cameras
Summary
Most of the methods for environment abstraction from multiple views are just relying on points and ignoring other basic shapes like lines. The 3D line abstraction methods based on straight line segments that are most frequently found in the literature are designed to work altogether with detailed point-based reconstructions [1], employing the camera extrinsic parameters obtained from these point rotation and translation invariants. This permits higher accuracy in the 3D reconstructions than using solely straight lines. Groups of segments will indicate the location of the most probable vanishing points from a camera plane [4] These geometric properties are not offered by points, lines can be a good complement when performing a spatial reconstruction [5, 6]. A recent work employed 3D lines to reconstruct surfaces [10]
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