Structure-from-motion using lines: Representation, triangulation, and bundle adjustment

By Adrien Bartoli, Peter F. Sturm. Computer Vision and Image Understanding, 2005

355 citations recorded by the source corpus.

We address the problem of camera motion and 3D structure reconstruction from line correspondences across multiple views, from initialization to final bundle adjustment. One of the main difficulties when dealing with line features is their algebraic representation. First, we consider the triangulation problem. Based on Plucker coordinates to represent the 3D lines, we propose a maximum likelihood algorithm, relying on linearizing the Plucker constraint and on a Plucker correction procedure, computing the closest Plucker coordinates to a given 6-vector. Second, we consider the bundle adjustment problem, which is essentially a nonlinear optimization process on camera motion and 3D line parameters. Previous overparameterizations of 3D lines induce gauge freedoms and/or internal consistency constraints. We propose the orthonormal representation, which allows handy nonlinear optimization of 3D lines using the minimum four parameters with an unconstrained optimization engine. We compare our algorithms to existing ones on simulated and real data. Results show that our triangulation algorithm outperforms standard linear and bias-corrected quasi-linear algorithms, and that bundle adjustment using our orthonormal representation yields results similar to the standard maximum likelihood trifocal tensor algorithm, while being usable for any number of views.

Subfields: Aerospace Engineering, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/43124bf88252aea86bc98a830c1f24062d6c6bb1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

In Computer Vision and Pattern Recognition

Citations in the corpus

Real-Time Monocular SLAM with Straight Lines (2006, background): “Lines also provide a great deal of information about the structure of the scene, and off-line structure from motion using lines is well-known (e.g. [18] [2]).”
PL-SVO: Semi-direct Monocular Visual Odometry by combining points and line segments (2016, background): “Dealing with line segments in images it is not as straightforward as points, since they are diﬃcult to represent [9] and also require high computational burden for the detection and matching tasks thus only a few solutions have been proposed [10] [11], barely reaching real-time speciﬁcations.”
Improving the Agility of Keyframe-Based SLAM (2008, background): “Related is Taylor and Kriegman’s work [13] which proposed minimizing a cost function measuring the least squares distance between observed edge segments and the projection of reconstructed lines, and Bartoli and Sturm [14] discuss optimal line parametrisations for the the minimisation procedure.”
PL-SLAM: A Stereo SLAM System Through the Combination of Points and Line Segments (2017, background): “These benefits, though, come at the expense of a higher computational burden in both detecting and matching line segments in images [14], and also in dealing effectively with segmentspecific problems such as partial occlusions, line disconnection, etc.”
A Survey on Structure from Motion (2017, methodology): “Experimental results are also provided in [7] to evaluate the performance of their overall approach.”