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Structure-From-Motion Using Lines: Representation, Triangulation and Bundle Adjustment

Adrien Bartoli 1 Peter Sturm 2
2 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : 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 4 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.
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Contributor : Adrien Bartoli <>
Submitted on : Monday, September 11, 2006 - 3:48:19 PM
Last modification on : Thursday, March 5, 2020 - 4:53:35 PM
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  • HAL Id : hal-00092589, version 1


Adrien Bartoli, Peter Sturm. Structure-From-Motion Using Lines: Representation, Triangulation and Bundle Adjustment. Computer Vision and Image Understanding, Elsevier, 2005, 100, pp.416-441. ⟨hal-00092589⟩



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