Build 3D Abstractions with Wireframes

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.